# Evaluation of UWB Beamformers in a Wireless Channeland Potential Microwave Implementations

код для вставкиСкачатьEvaluation of UWB Beamformers in a Wireless Channel and Potential Microwave Implementations by Liang Liang A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Electrical And Computer Engineering University of Toronto c 2011 by Liang Liang Copyright Library and Archives Canada Bibliothèque et Archives Canada Published Heritage Branch Direction du Patrimoine de l'édition 395 Wellington Street Ottawa ON K1A 0N4 Canada 395, rue Wellington Ottawa ON K1A 0N4 Canada Your file Votre référence ISBN: 978-0-494-76090-1 Our file Notre référence ISBN: NOTICE: 978-0-494-76090-1 AVIS: The author has granted a nonexclusive license allowing Library and Archives Canada to reproduce, publish, archive, preserve, conserve, communicate to the public by telecommunication or on the Internet, loan, distrbute and sell theses worldwide, for commercial or noncommercial purposes, in microform, paper, electronic and/or any other formats. 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Conformément à la loi canadienne sur la protection de la vie privée, quelques formulaires secondaires ont été enlevés de cette thèse. While these forms may be included in the document page count, their removal does not represent any loss of content from the thesis. Bien que ces formulaires aient inclus dans la pagination, il n'y aura aucun contenu manquant. Abstract Evaluation of UWB Beamformers in a Wireless Channel and Potential Microwave Implementations Liang Liang Master of Applied Science Graduate Department of Electrical And Computer Engineering University of Toronto 2011 Ultra-wideband (UWB) wireless communication is a topic of intense research. It has the potential for superior performance over comparable narrowband wireless systems. UWB wireless systems transmit pulses that have energy concentrated mainly from 3.1 GHz to 10.6 GHz. These pulses are transmitted at very low energy levels so as not to interfere with many existing wireless systems that operate in the same band. UWB communication systems can beneﬁt signiﬁcantly from beamforming networks where the received signal strength depends on angle of arrival. This thesis focuses on the characterization of a digital beamformer in a real wireless channel. The beamformer is evaluated using various methods to judge its performance impact on a real UWB communication system. An analog UWB beamformer in hardware is derived by taking advantage of a simple microwave circuit realization. The analog UWB beamformer is studied and its feasibility is evaluated. ii To my mommy and daddy iii Acknowledgements I would like to express my deepest gratitude towards my supervisor, Sean Victor Hum, for his invaluable guidance and support throughout my MASc study. He has been patient and devoted to my work. It has been a great honour to be able to work with him and I am looking forward to continue my study with him for PhD research. This thesis would not have been possible without his help. I would like to thank my friends and colleagues in Professor Hum’s research group, Jonathan, Krishna, Derek, Asanee and Natalie. Thank you so much for the intriguing technical discussions and always there to aid when I needed it. I would like to thank our lab manager Tse for your helpful advice on many types of equipment and the occasional chit-chats. To my fellow graduate students, Alex, Michael, Neeraj, I have learnt a lot from you throughout my time here and have always been there to lend a helping hand. To my friends in the communications group, Chunpo, Hui, Lei, words simply can not describe the times that it has been, so I can only say how much I appreciate it. It was truly unforgettable. I am deeply grateful for the unconditional love and support that my parents have given me. None of this would have been possible without them. I am forever grateful. Liang Liang University of Toronto, 2010 iv Contents 1 Introduction 1 1.1 Ultra-Wideband Wireless Communication . . . . . . . . . . . . . . . . . 1 1.2 Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Traditional Narrowband Beamforming . . . . . . . . . . . . . . . 4 1.2.2 Wideband Beamforming . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Motivation and Thesis Goals . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Background 2.1 10 Realization of Beamfomers . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Hardware Beamformers . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 Algorithmic Beamformers . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Space-Time Processing and Review of an Ideal TTD beamformer . . . . 16 2.3 Derivation of the IIR Beamformer . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 22 Beamformer Characteristics . . . . . . . . . . . . . . . . . . . . . 3 UWB Beamformer Characterization 27 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 UWB Channel Sounding Techniques . . . . . . . . . . . . . . . . . . . . 28 3.2.1 Time Domain Sounding Technique . . . . . . . . . . . . . . . . . 28 3.2.2 Frequency Domain Sounding Technique . . . . . . . . . . . . . . . 29 v 3.3 UWB Antenna Array Description . . . . . . . . . . . . . . . . . . . . . . 30 3.4 Far-Field Pattern Characterization . . . . . . . . . . . . . . . . . . . . . 32 3.4.1 Setup and Measurement of Far-Field Pattern . . . . . . . . . . . . 33 3.4.2 Evaluation of Far-Field Pattern . . . . . . . . . . . . . . . . . . . 35 3.4.3 Far-Field Pattern Results . . . . . . . . . . . . . . . . . . . . . . 36 Interference Rejection Characterization . . . . . . . . . . . . . . . . . . . 37 3.5.1 Setup and Measurement of the Interference Rejection Experiment 38 3.5.2 Interference Rejection Evaluation . . . . . . . . . . . . . . . . . . 40 3.5.3 Interference Rejection Experiment Results . . . . . . . . . . . . . 42 Monte Carlo BER Simulations . . . . . . . . . . . . . . . . . . . . . . . . 44 3.6.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.6.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.7 Beamformer Characterization Conclusions . . . . . . . . . . . . . . . . . 50 3.8 Sources of Errors in the Experiments . . . . . . . . . . . . . . . . . . . . 51 3.5 3.6 4 Potential Hardware Realization of a UWB Beamformer 57 4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Continuous-time Transfer Function . . . . . . . . . . . . . . . . . . . . . 58 4.2.1 Beam Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 63 Evaluation of Transfer Function Given Using S-parameters . . . . . . . . 66 4.3.1 70 4.3 4.4 Unit Cell Simulations . . . . . . . . . . . . . . . . . . . . . . . . . Microwave Circuit Realization of the UWB Beamformer . . . . . . . . . 73 4.4.1 Design of the In-Phase Wilkinson Power Divider . . . . . . . . . . 75 4.4.2 Design of the Out-of-Phase Wilkinson Power Divider . . . . . . . 76 4.4.3 Simulated Beam Characteristics of the Hardware Beamformer . . 82 4.4.4 Fabrication and Measurement of Wilkinson Power Dividers . . . . 87 4.4.5 Fabrication and Measurement of Out-Of-Phase Wilkinson Power Dividers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi 90 4.4.6 Calculated Beam Pattern Using Real Microwave Devices . . . . . 93 4.4.7 Feasibility Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 94 5 Conclusions 99 5.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A Fabrication and Measurements of BAVAs 103 A.1 Fabrication of BAVAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 A.2 Measurement of BAVAs . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 B CPW Wilkinson Power Divider Dimensions 112 Bibliography 113 vii List of Acronyms ADC Analog-to-digital converter ADS Advanced Design System AOA Angle of arrival AF Array factor AWGN Additive white Gaussian noise BAVA Balanced Antipodal Vivaldi Antenna BER Bit-error-rate BFM Beamformer BPSK Binary phase shift keying CPW Coplanar waveguide DSP Digital signal processing DUT Device under test EIRP Equivalent isotropically radiated power FDTD Finite-diﬀerence time-domain FIR Finite impulse response HFSS High Frequency Structure Simulator (Ansoft) IIR Inﬁnite impulse response ISI Inter-symbol-interference LNA Low-noise ampliﬁer MEMS Micro-electro-mechanical system viii RX Receiver SIR Signal-to-interference ratio SNR Signal-to-noise ratio TTD True-time-delay TX Transmitter UWB Ultra-wideband VNA Vector network analyzer ix List of Symbols ω1 Spatial frequency ω2 Temporal frequency s1 Spatial frequency in s-domain s2 Temporal frequency in s-domain n1 Spatial domain index n2 Time domain index z1 Discrete spatial frequency in z-domain z2 Discrete temporal frequency in z-domain ψbf m Angle in which a beamformer is set to ψbf m Angle in which the main lobe of the beamformer is pointed to ψsource Angle in which the desired signal is coming from Δx Spatial sampling period or array element spacing Ts Temporal sampling period fs Temporal sampling frequency Eb,signal Energy per bit of the desired signal Eb,int Energy per bit of the interference N Receiving arra size R Transmitted symbol rate L Downsample factor sij S-parameter of the ij th entry x List of Tables 1.1 Beamformer classiﬁcation. . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.1 Exponential curve parameters describing the fabricated BAVA. . . . . . . 32 3.2 Dimensions of optimized BAVA. . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Table of suppression levels (peak values in dB) from Figure 3.10. Values in parentheses are the theoretical suppression levels assuming free space channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Fabricated CPW Wilkinson power divider dimensions in mm. xi 44 . . . . . . 112 List of Figures 1.1 FCC spectral mask for indoor commercial UWB systems [1]. . . . . . . . 1.2 A narrowband beamformer with a phase shifter connected to each antenna element in the array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 2 5 A planar wave impinging on an array of equally spaced N antenna elements with inter-element spacing d. [Figure courtesy of Sean Victor Hum]. . . . 6 2.1 Received 2-D impulse signal from a linear array in the (t, x/c) domain. . 17 2.2 2-D spectrum of the received signal of an array of UWB receivers for ψ = 10◦ and N = 30 antenna elements. . . . . . . . . . . . . . . . . . . . 17 2.3 A TTD UWB beamformer. . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 2-D beam pattern of a TTD beamformer in Figure 2.3 for N = 30 ideal isotropic elements. The angle that the beamformer is set to ψbf m = 10◦ . Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Magnitude of 2-D transfer function (2.1). Colour scale in dB. . . . . . . . 20 2.6 First-order 2-D frequency-planar beam plane wave ﬁlter whose passband vector is normal to [L1 , L2 ]. . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Signal ﬂow graph implementing transfer function (2.5) and diﬀerence equation (2.9). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 20 23 2-D transfer function of (2.5). R = 0.01, Δx = 12 mm, ψbf m = 10◦ . Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii 24 2.9 2-D transfer function of the IIR beamformer spatially truncated to 30 elements with spacing 12 mm for isotropic antenna elements. ψbf m = 10◦ . Color scale shown is in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.10 2-D transfer function of the IIR beamformer plotted with respect to angle from broadside. ψbf m = 10◦ . Ideal isotropic antenna elements are used. . 25 2.11 Example of an array with a spatial downsample factor of L = 2. A unit cell is deﬁned in the dashed box in Figure 2.7. . . . . . . . . . . . . . . . 26 2.12 Spatially downsampled spectrum of a signal whose spectrum is shown in Figure 2.2. Downsample factor L = 2. Colour scale in dB. . . . . . . . . 26 3.1 BAVA dimension deﬁnitions [2]. . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Fabricated BAVA array. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Measured and simulated |s11 | of the BAVAs. . . . . . . . . . . . . . . . . 33 3.4 Measured (solid) and simulated (dashed) BAVA array element coupling values in a linear array with 12 mm spacing. . . . . . . . . . . . . . . . . 3.5 34 Far-ﬁeld pattern measurement setup. Note that a synthetic array is formed by displacing the array a distance Δx, the element spacing, in the direction shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 35 Far-ﬁeld gain pattern of IIR beamformer for ψbf m = 20◦ , from ideal calculations (solid red), measurements with coupling (solid black), and without antenna coupling (dashed black). . . . . . . . . . . . . . . . . . . . . . . 37 3.7 UWB channel impulse response measurement setup. . . . . . . . . . . . . 39 3.8 Top view of the measured oﬃce environment. . . . . . . . . . . . . . . . 40 3.9 Interference rejection experiment setup. Signals can arrive directly from four possible angles from broadside of the array ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }. 40 xiii 3.10 Time-domain output of the beamformer plotted for various beamformer set AOAs. Red is the normalized received signal amplitude with no beamformers present all have the same peak. Black is the received signal with the beamformer enabled and they are temporally oﬀset for clarity. . . . . 43 3.11 Simulated UWB communication system. . . . . . . . . . . . . . . . . . . 45 3.12 BER of the simulated UWB communication system. N = 120, Δx = 12 mm, ψbf m = ψsource = 10◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.13 BER of the simulated UWB communication system. N = 20, Δx = 72 mm, ψbf m = ψsource = 10◦ , with antenna coupling eﬀect. See. Figure 3.14 for legend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.14 BER of the simulated UWB communication system. N = 8, Δx = 180 mm, ψbf m = ψsource = 10◦ , no antenna coupling eﬀect. BER performance is degraded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.15 BER of the simulated UWB communication system. N = 20, Δx = 72 mm, ψbf m = ψsource = 27◦ , with antenna coupling eﬀect. The impact of the beam squninting resulted no performance gain from the beamformer. See Figure 3.14 for legend. . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.16 BER of the simulated UWB communication system. N = 20, Δx = 72 mm, ψsource = 27◦ , ψbf m = 22◦ with antenna coupling eﬀect. See Figure 3.14 for legend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.17 Actual AOA ψbf m , the angle of the main lobe, as a function of AOA of the beamformer ψbf m for N = 30, Δx = 12 mm. . . . . . . . . . . . . . . 56 4.1 Unit cell from the signal ﬂow graph in Figure 2.7. . . . . . . . . . . . . . 58 4.2 An RC network terminated by transmission lines. . . . . . . . . . . . . . 60 4.3 2-D transfer function given by equation (4.12) for ψbf m = 10◦ . Colour 4.4 scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 New unit cell of the new beamformer. . . . . . . . . . . . . . . . . . . . . 62 xiv 4.5 Far-ﬁeld pattern of the new transfer function in Figure 4.3 . . . . . . . . 4.6 Far-ﬁeld pattern of the digital IIR beamformer tuned ψbf m = 10◦ corresponding to Figure 2.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 63 64 2-D transfer function given by equation (4.12) for ψbf m = 40◦ . Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.8 Far-ﬁeld pattern of the new transfer function in Figure 4.7 . . . . . . . . 65 4.9 Location of the peak angle as a function of frequency for Figure 4.8 . . . 65 4.10 2-D transfer function for ψbf m = 40◦ spatially truncated to N = 30 elements. Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.11 Far-ﬁeld gain pattern of the new beamformer whose transfer function is shown in Figure 4.10 for ψbf m = 40◦ . . . . . . . . . . . . . . . . . . . . . 67 4.12 Generic unit cell port deﬁnition. Ports 4 and 5 of one cell are connected to ports 2 and 3 of the next cell. Ports 2 and 3 of the ﬁrst cell and ports 4 and 5 of the last cell are terminated in matched loads. . . . . . . . . . 67 4.13 Advanced Design System (ADS) unit cell simulation setup. . . . . . . . . 71 4.14 A signal delay matching scheme for the realization the IIR beamformer in hardware. Cell I has a delay dcell which is compensated by a delay line with delay dcell at port 1 of the next cell. . . . . . . . . . . . . . . . . . . 72 4.15 Layout of the Wilkinson realized in CPW form. . . . . . . . . . . . . . . 77 4.16 Simulated s-parameters of the Wilkinson power divider realized in CPW form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.17 Simulated group delay of s21 and s31 of the CPW Wilkinson power divider. 78 4.18 Simulated phase balance of the CPW Wilkinson power divider. . . . . . . 78 4.19 Layout of the wideband phase inversion circuit. Radius of the stub is 16.5 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.20 Simulated s-parameters of the phase inversion circuit. . . . . . . . . . . . 80 4.21 Simulated group delay of the phase inversion circuit. . . . . . . . . . . . 80 xv 4.22 Simulated phase inversion characteristics of the phase inverter. . . . . . . 81 4.23 Layout of the out-of-phase Wilkinson power divider with the deﬁned port numbering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.24 Simulated s-parameters of the out-of-phase Wilkinson power divider. . . 83 4.25 Simulated group delay of the out-of-phase Wilkinson power divider. . . . 83 4.26 Simulated phase balance between the output ports of the out-of-phase Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.27 Magnitude of ideal transfer function T F2 (s2 ) and simulated one obtained from unit cell simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.28 Phase of ideal transfer function T F2 (s2 ) and simulated one obtained from unit cell simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.29 2-D far-ﬁeld pattern from 2.5 GHz to 3.5 GHz of the new beamformer with simulated s-parameters of the in-phase and out-of-phase Wilkinson power dividers. Colour scale in dB. . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.30 Beam pattern for various frequencies in Figure 4.29. . . . . . . . . . . . . 87 4.31 Fabricated Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . 88 4.32 Measured (solid) and simulated (dashed) s-parameters of the Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.33 Measured (solid) and simulated (dashed) group delay of the Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.34 Measured (solid) and simulated (dashed) phase balance of the Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.35 Fabricated out-of-phase Wilkinson power divider. . . . . . . . . . . . . . 91 4.36 Measured (solid) and simulated (dashed) s-parameters of the out-of-phase Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.37 Measured (solid) and simulated (dashed) group delay of the out-of-phase Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi 92 4.38 Measured (solid) and simulated (dashed) phase balance of the out-of-phase Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.39 2-D far-ﬁeld pattern of the beamformer using real in-phase and out-ofphase Wilkinson power dividers. Colour scale in dB. . . . . . . . . . . . . 94 4.40 Beam pattern for various frequencies of the beamformer with real in-phase and out-of-phase Wilkinson power dividers. . . . . . . . . . . . . . . . . . 95 4.41 Magnitude of ideal transfer function T F2 (s2 ) versus the one obtained from ADS unit cell simulation using real in-phase and out-of-phase Wilkinson power divider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.42 Phase of ideal transfer function 2 versus the one obtained from ADS unit cell simulation using real in-phase and out-of-phase Wilkinson power divider. 96 4.43 Cef f as a function of ψbf m . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 A.1 BAVA fabricated in two piece as shown. . . . . . . . . . . . . . . . . . . 104 A.2 |s11 | of all fabricated antennas and that of the simulated. . . . . . . . . . 106 A.3 Measured (solid) and simulated (dashed) 4-port s-parameters of the BAVA array with element spacing 12 mm. . . . . . . . . . . . . . . . . . . . . . 107 A.4 E-plane cut for antenna 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 108 A.5 H-plane cut for antenna 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 109 A.6 E-plane cut for all fabricated antennas. . . . . . . . . . . . . . . . . . . . 110 A.7 H-plane cut for all fabricated antennas. . . . . . . . . . . . . . . . . . . . 111 B.1 (a) Wilkinson power divider with (b) cross section views. . . . . . . . . . 112 xvii Your life is deﬁned by its opportunities... even the ones you miss. xviii Chapter 1 Introduction 1.1 Ultra-Wideband Wireless Communication Ultra-wideband signaling for wireless communications has received a lot of research attention in recent years. It is a fast emerging technology that has attractive features with a large number of applications, including wireless personal area networks, sensor networks, imaging systems, etc. The Federal Communications Commission (FCC) has authorized unlicensed use of spectrum for UWB systems between 3.1 GHz to 10.6 GHz with restricted equivalent isotropically radiated power (EIRP) below −41.3 dBm/MHz and other frequencies are restricted to an even lower power of −75 dBm/MHz [1]. Figure 1.1 shows the FCC spectral mask for indoor commercial UWB systems. Due to the restricted energy for transmission, UWB wireless systems have unique interference challenges as the electromagnetic spectrum in the UWB band is already used by other wireless systems. Moreover, multiple users could access the same physical channel and transmitting in the same UWB band creating further interference. Furthermore, the signal in the channel bounces oﬀ objects creating multipath which arrives at the receiver from all directions making it diﬃcult to decode the transmitted message. One way to mitigate the multipath eﬀects as well as interference from other wireless systems is to use 1 2 Chapter 1. Introduction −40 UWB EIRP Emission Level [dBm] −45 −50 −55 −60 −65 −70 −75 −80 1 2 3 4 Frequency [GHz] 5 6 7 8 9 10 Figure 1.1: FCC spectral mask for indoor commercial UWB systems [1]. beamformers where signals arriving from desired directions are enhanced while signals arriving from undesired directions are attenuated. Research has shown, in a 2-D simulated environment, that UWB beamformers can be used to signiﬁcantly improve system performance. Speciﬁcally, they have been shown to decrease the bit-error-rate (BER) and increase the channel capacity by orders of magnitude [3]. Beamformers oﬀer a promising solution to address the interference and multipath issues of a wireless channel. This thesis presents work on some quantitative measures of the behaviour of beamformers in a real wireless communication channel. 1.2 Beamforming A beamformer is a component in a communication system that provides angle-dependent spatial discrimination. It can operate in either a transmitting or receiving mode. There are two major components in a beamformer. The ﬁrst component is an array of antennas used for transmitting an outgoing series of signals or for sampling the received signals in time and space. The second major component is a beamforming network that is Chapter 1. Introduction 3 connected to the array of antenna elements. Angle-dependent spatial discrimination is achieved by the appropriate design of the beamforming network. For a beamformer in the receive mode, the beamforming network appropriately weights the received signals from all antennas in the array such that the signals arriving from a desired angle is enhanced while signals arriving from other angles are attenuated as much as possible. Similarly, for a beamformer in transmit mode, the signal at the desired angle is enhanced while the signals transmitted to other angles are attenuated. A beamformer is also a multi-dimensional spatial ﬁlter. When a 1-D linear array of antenna elements is used, this spatial ﬁlter is a 2-D ﬁlter whose transfer characteristic depends on both temporal frequency and spatial frequency. It has a corresponding 2-D transfer function in the spectral domain, as well as an impulse response in time and space. The 2-D transfer function has a corresponding beam pattern that determines the amount of spatial discrimination that is experienced by a signal as a function of angle. There are several main properties of a beamformer: • transmitting or receiving mode (or both) • narrowband or wideband • adaptive or ﬁxed • hardware or software • digital or analog Although a beamformer in general can be used in a transmitter or a receiver, this thesis focuses on receiving beamformers. The bandwidth of the beamformer is determined by the bandwidth of the antenna elements and the bandwidth of the beamforming network. The beamformer is considered to be adaptive when the beam pattern of the beamforming network is made to be tunable. The beamforming network can be realized in hardware or in software, both implementing a designed algorithm to process the signals. The 4 Chapter 1. Introduction Digital Analog Delay & Sum Algorithmic Table 1.1: Beamformer classiﬁcation. beamforming network in hardware can be made to process the signals in digital form by utilizing a digital signal processing (DSP) platform or in analog form by using the appropriate analog signal processing circuits. Since the focus of the thesis is on receiving, ultra-wideband, adaptive beamformers, the implementation can be classiﬁed into one of the following categories listed in Table 1.1. Digital beamformers typically employ ﬁnite impulse response (FIR) ﬁlters where a delay and sum architecture is used. The digital beamformers can implement a wideband beamforming mathematical algorithm realized either using software or on a hardware DSP platform. Analog beamformers typically employ a delay and sum approach and use a true-time-delay (TTD) architecture whereby signals received from an array are delayed appropriately prior being coherently summed. Such architecture is described in detail in later sections. The particular beamformer of interest in this thesis is an adaptive wideband receiving beamformer that is digital and algorithmic. This beamformer has a low computational complexity for digital implementations, and also lends itself to a simple microwave analog circuit topology that could be realized. Since few others have realized analog beamformers of this form, a potential analog version of the proposed digital beamformer is investigated in this thesis. 1.2.1 Traditional Narrowband Beamforming When multiple antennas are arranged in an array, its far-ﬁeld pattern can be calculated using classical array theory and it is the basis of a spatial ﬁlter. A typical narrowband beamforming network is shown in Figure 1.2, which is shown here in the receiving mode. Each antenna in the array is connected to a phase shifter whose value depends on the 5 Chapter 1. Introduction Figure 1.2: A narrowband beamformer with a phase shifter connected to each antenna element in the array. desired angle of the main lobe. At the desired angle, measured from the broadside direction of the array, the signals from each element in the antenna array add in-phase and they constructively interfere at the beamformer output. Signals received from this direction are the strongest. At other angles, the signals from the antenna elements do not add in-phase. The signal strength at these angles is much weaker compared to angles where the signals constructively interfere. The far-ﬁeld pattern of an uniform array of antenna elements is the product of two patterns – the antenna element pattern and the array factor (AF) pattern. The antenna element pattern is typically ﬁxed. The array factor pattern depends on many factors: frequency, array geometry and amplitude and phase of the weight elements in the beamformer. Consider Figure 1.3, which shows a linear array of antenna elements spaced with inter-element distance d. θ is deﬁned with respect to the axis of the array. The array factor pattern P (θ) is computed as P (θ) = a0 + a1 ejβd cos θ + a2 ejβ2d cos θ + ... + aN −1 ejβ(N −1)d cos θ N −1 = am ejβmd cos θ , (1.1) m=0 where β is the free space propagation constant, am is the amplitude weighting of each 6 Chapter 1. Introduction Figure 1.3: A planar wave impinging on an array of equally spaced N antenna elements with inter-element spacing d. [Figure courtesy of Sean Victor Hum]. antenna element and N is the total number of antennas. Since β = 2π λ = 2πf c is dependent on temporal frequency f (where c is the speed of light), the shape of the array factor pattern changes as a function of frequency. Moreover, it can be easily shown that the angle of the main lobe, θmax , for uniform amplitude weights where am = 1, must satisfy 2πf d cos θmax + Δφ = 0, c (1.2) where Δφ is the uniform phase diﬀerence between two adjacent phase shifters. It is clear from this equation that as f changes, Δφ needs to track linearly with frequency in order to have a constant θmax . Most microwave phase shifters do not have this property, and consequently the angle of the main lobe shifts. This implies that if a wideband signal was received using this beamformer, the main lobe of the receiver can not point to a set direction for all frequencies, which can result in signal loss. Diﬀerent amplitude weighting distributions would produce diﬀerent array factor patterns. Side-lobe levels can also be controlled by using diﬀerent amplitude distributions. An ideal wideband beamformer would have its far-ﬁeld pattern independent of frequency. Particularly, the shape and angle of the main lobe would remain unchanged as frequency is swept. However, in practice, a frequency-independent far-ﬁeld pattern can Chapter 1. Introduction 7 only be achieved within a limited bandwidth. Reconﬁgurable wideband beamforming is diﬃcult to achieve in general, and is discussed in the next section. 1.2.2 Wideband Beamforming Wideband beamforming refers the frequency-invariant property of the pattern associated with a beamformer. However, with a ﬁxed aperture size, it is diﬃcult to maintain a constant beam shape over the entire UWB frequency spectrum. Hence, in this thesis, a particular characteristic of the beam pattern, namely the direction of the main lobe, is considered to be a measure of a beamformer’s bandwidth. If the angle of the main lobe does not vary signiﬁcantly as frequency is swept, then the beamformer is considered to be wideband. There are two approaches to achieve wideband beamforming. The ﬁrst approach is to use a true-time-delay (TTD) architecture. This architecture works by using TTD elements connected to each antenna to compensate for the delay of the signal between two adjacent antenna elements. When all the signals are delay-matched, the signals from each antenna element are then summed coherently to produce a signal with a much larger strength. The beamformer can be made adaptive if the TTD elements themselves can be tuned. The second approach to achieve wideband beamforming is to appropriately design an algorithm to process the signal from each antenna. This signal processor is the beamforming network. The advantage of this approach is that a wide variety of far-ﬁeld patterns can be achieved as diﬀerent algorithms would achieve diﬀerent far-ﬁeld patterns. The designed algorithm would allow for trade oﬀ between performance characteristics such as beam width, bandwidth, complexity, etc. In practice, the algorithms are typically realized on a DSP platform after the signals have been digitalized by analog-to-digital converters (ADCs). In Chapter 2, the details of these two approaches are discussed. Chapter 1. Introduction 1.3 8 Motivation and Thesis Goals UWB beamformers oﬀer promising potential in providing interference and noise rejection in a real radio channel. Beamformers can also provide a level of protection against multipath eﬀects while dynamically adapting to changes in the channel environment. The beamformer of particular interest in this thesis is an algorithmic inﬁnite impulse response (IIR) beamformer, which is described in detail in Chapter 2. Previous work has shown that this beamformer was capable of providing signiﬁcant improvements to the performance of a communication system [3]. However, the performance of the beamformer was characterized in a 2-D simulated environment which is not suﬃcient to capture the abundance of multipath reﬂections and scattering in a real three-dimensional channel. In addition, ideal transmitters and receiver arrays were used which does not capture the eﬀects of real UWB antennas and element coupling in the receiving array. Finally, UWB beamformers have been not been characterized in real radio channels. It is, in part, the goal of this thesis to characterize beamformers in a real radio channel to assess their effectiveness in combating the multipath eﬀects and interference from other UWB wireless users in the same channel. Wideband beamformers that are also reconﬁgurable are diﬃcult to realize in hardware. Although they exist in literature, as shown in the literature survey in Chapter 2, they all typically deployed in the true-time-delay (TTD) architecture which is typically realized in hardware in an integrated circuit form. Hardware tunable wideband beamformers have not been widely explored as the wide bandwidth and tunability properties over such wide frequency range pose a very challenging research problem. In addition to the characterization of beamformers in a real radio channel, it is the goal of this thesis to propose the design of a potential hardware realization of an analog wideband tunable beamformer. This potential hardware realization of the beamformer does not employ a true-time-delay architecture and diﬀers in architecture compared to others presented in literature. The analog microwave beamformer would have the features of the digital Chapter 1. Introduction 9 beamformer with no analog-to-digital converters and the systolic array of DSP hardware associated with the digital beamformer. 1.4 Thesis Outline The chapters in this thesis are outlined as follows. Chapter 2 provides an overview of how the beamformers are realized followed by a detailed derivation of the beamformer to be characterized. Chapter 3 begins by describing how the wireless UWB channel was characterized, followed by assessment of the performance parameters of the beamformer using a variety of methods, namely, far-ﬁeld pattern measurement, interference rejection experiment and Monte Carlo bit-error-rate (BER) simulations. Chapter 4 focuses on a potential hardware realization of this particular beamformer. A feasibility study is included followed by simulations and measurements of the potential beamformer in hardware. Chapter 5 concludes this thesis by drawing conclusions about the beamformer and describes future work that can be done in this area. Chapter 2 Background In this chapter, some background information related to the diﬀerent types of beamformers is presented. A beamformer can be categorized into two main types – ones that employ a TTD architecture and ones that employ a signal processing architecture to realize an algorithm as the means to achieve beamforming. The beamformer of interest in this thesis is of the algorithmic type, though later in the thesis a physical realization of this beamformer is presented. Its mathematical derivation is presented in this chapter. The properties of the beamformer resulting from its derivation are summarized. 2.1 Realization of Beamfomers Beamformers can be realized in hardware or in software. Hardware beamformers typically consist of a TTD architecture using tunable TTD elements. The algorithmic type of beamformers that do not employ a TTD architecture typically are realized on a DSP platform to leverage the ﬂexible implementations of various signal processing techniques. References to these beamformers are discussed in the following sections. 10 Chapter 2. Background 2.1.1 11 Hardware Beamformers UWB beamformers realized in hardware typically utilize a TTD architecture where tunable delay devices are employed. After signal delays are properly compensated by the tunable delay devices, a coherent summation is performed of all the signals from each antenna element such that the signals are added constructively, creating the desired signal with a larger amplitude. However, the design of accurate tunable delays devices with precision delay control is not trivial. The tunability of the delay devices is achieved mainly in two ways: changing the speed of signal propagation in the device or changing the physical length of the device. Tunable delay devices can be realized in many forms – hardware integrated circuits, RF microwave distributed circuits or simply lumped elements. This section summarizes a representative set of realized UWB beamformers employing a TTD architecture. TTD elements can be realized by using distributed micro-electro-mechanical system (MEMS) transmission lines in an integrated circuit form. [4] realizes TTD elements by placing MEMS-actuated bridges periodically over a section of a coplanar waveguide (CPW) transmission line. The MEMS bridges are placed across the center conductor and connected the two ground planes of the CPW transmission line. The MEMS bridges increase the capacitance per unit length of the transmission line as they are only a few microns in height. Tunability is achieved by applying a DC voltage to the center conductor causing the MEMS bridges to bend towards it, changing the eﬀective capacitance per unit length. Hence, the group velocity of the signal propagating on the transmission is changed and a tunable delay device is realized. Artiﬁcial transmission lines can also be synthesized using tunable inductances [5]. The variable inductance is achieved by placing a second coil in close proximity with the primary coil whose inductance is the per unit inductance of the artiﬁcial transmission line. The current in the second coil is controlled by loading it with varactor diodes whose capacitance can be changed by a control voltage. The current in the second coil changes Chapter 2. Background 12 the mutual inductance between the primary and secondary coils which in turn changes the self inductance of the primary coil. Since the inductance of the transmission line is changed, the group velocity of signal propagation is changed as well. The previous two references have shown that the group velocity of the signal can be modiﬁed on a transmission line to change the signal delay. [6] realizes a wideband beamformer by using electronically-controlled trombone lines where a signal experiences a path of diﬀerent lengths depending on which switches and ampliﬁers are turned on. The characteristic impedance of the transmission line remains the same as the inductance and capacitance per unit length do not change. The beamformer in this work conceptually used a TTD architecture, however, it employed clever derivative of this architecture by sharing signal delay paths to save chip area while relaxing the required maximum delay of the TTD elements. The wideband beamformers shown so far are in an integrated circuit form. The TTD elements can also be realized using optical devices. [7] develops a TTD ﬁber-optic UWB beamformer utilizing a tunable wavelength laser and dispersive ﬁber prism whose delay depends on the wavelength of the light in the ﬁber. A receiving array of eight broadband spiral antenna elements modulates an array of Mach-Zehnder modulators. The output light from an optical port has an intensity that is proportional to the amplitude of the modulating voltage waveform. The modulated light from the array of Mach-Zehnder modulators is fed into an array of dispersive ﬁbers whose optical signal delay depends on the wavelength of the tunable laser. The wavelength of the light is tuned such that the desired amount of delay is generated by the ﬁbers. Signals were combined optically and PIN photodiodes were used to convert the optical signals back to electrical signals for more processing. A TTD UWB beamformer implemented using optical components is then realized. Chapter 2. Background 2.1.2 13 Algorithmic Beamformers Many diﬀerent types of algorithms exist in the literature for implementing wideband beamforming, each having their own unique characteristics. These algorithms are typically implemented solely in software as they can be very complex. In this section, a survey of diﬀerent types of algorithmic beamformers and their architectures are summarized. [8] describes a procedure to design a beamforming algorithm to produce a beam pattern that is frequency invariant. This method is derived from an ideal continuous array of sensors, whose required frequency response can be calculated given a particular beam pattern. The continuous array of sensors is then discretized for practical implementations. This method produces a beam pattern that is virtually independent of frequency by utilizing frequency dilation properties of a linear array. [9] gives examples of how to design the algorithm. [10] develops a multi-rate and a single-rate method to realize the algorithm on a DSP platform. Although it is possible to realize the frequency invariant beam pattern using this design approach, its complexity for multidimensional arrays increases signiﬁcantly [9]. Wideband beamforming can also be achieved by a direct optimization of the coeﬃcients of the FIR ﬁlters connected to the receiving array of antennas elements [11]. In a conventional narrowband beamforming network in equation (1.1), the beam pattern P (θ) is a linear combination of the received signal governed by a set of complex weights am . However, instead of having a ﬁxed complex weighting, the weights can be made to be dependent on frequency such that the beam pattern is as close to the desired one as possible. For instance, let am,n be the complex weight at the mth antenna element at frequency n ffs , where n is the frequency index and fs is the sampling frequency. The set of am,n are the optimization variables subject to constraints given by the desired beam pattern. Such optimization problems can be done via available convex optimization methods [12]. However, for large sensor sizes, the number of variables for optimization is extremely large. Chapter 2. Background 14 Beamspace adaptive arrays are another method to achieve adaptive wideband beamformers [13, 14]. In this architecture, the sampled digital signals from each antenna element in the receiving array are fed to an array of beamformers, which are individually realized by a FIR fan ﬁlter consisting of delay and sum circuits with variable coeﬃcients. The design techniques for FIR fan ﬁlters for wideband beamforming are readily available and examples are given [14, 15]. Each beamformer in the array forms a beam in a particular direction with one beam designated as the primary beam and the rest are designated as so-called auxiliary beams. The auxiliary beams cover all possible directions where interference and noise could arrive. The overall system output is a linear combination of the outputs from all beamformers. The weights associated with the output from each beamformer are adaptively determined based on the direction and the strength of the interference in the environment with the goal of minimizing the received interference. The process to ﬁnd the optimal weights is iterative [13]. The discussion so far is limited to beamforming by using FIR ﬁlters which can be implemented in the form of a delay and sum architecture. FIR ﬁlters have only zeros in the transfer function while IIR ﬁlters can have both zeros and poles. It is well known that an IIR ﬁlter provides steeper rolloﬀ characteristics than an FIR ﬁlter of the same order. A beamformer whose transfer function is IIR would have a lower order for same rolloﬀ characteristics compared to a FIR beamformer. [16] describes a method to design a multidimensional IIR beamformer. This paper uses a network resonance design approach where a 3-D transfer function Ta (kx , ky , ω) has a resonance (the passband of the transfer function) on a plane in the (kx , ky , ω) domain, which is the 3-D Fourier transform of the (x, y, t) domain. A second transfer function Tb (kx , ky , ω) is designed in the same way. The overall 3-D transfer function T (kx , ky , ω) = Ta (kx , ky , ω)Tb (kx , ky , ω) has a passband that is a line deﬁned by the intersection of passbands (planes) of Ta and Tb . This forms a highly selective beam in 3-D that can be tuned to any angle by changing the line of intersection. To discretize such a transfer function in both space and time, a 3-D bilinear transform is Chapter 2. Background 15 applied to T so that the overall transfer function can be realized using discrete sensors in two dimensions of space and digitally processed in discrete time. More complex shapes can be designed using the network resonance concept. [17] considers a cone-shaped beam designed using this approach. [3] shows a wideband receiving beamformer using the network resonance concept approach discussed above. It is an IIR ﬁlter with poles in the spatio-temporal frequency domain. Network resonance can also be synthesized using FIR techniques as well. However, the IIR nature of this beamformer allows for a lower complexity compared to FIR beamformers for the same rolloﬀ characteristics. This beamformer is completely characterized by a few parameters and no complicated design procedure is necessary. The coeﬃcients are algebraically deﬁned and hence the beam is readily steerable to any angle. It will be shown in a later section that the beam angle can be set with only one parameter. Furthermore, it will be shown in later sections that this beamformer has a simple signal ﬂow graph whose circuit topology is simple to realize in both digital and analog form. This topology is the beamformer of interest in this thesis. This digital beamformer does not employ a TTD architecture nor does it have a complex design procedure associated with some of the beamformers in literature with FIR ﬁlters. It does not need expensive integrated circuit typically associated with hardware TTD beamformers. The hardware version of this beamformer, described in detailed in Chapter 4, has a very simple microwave circuit topology which can be readily implemented in planar form. Furthermore, previous work has shown that this particular beamformer is capable of improving system performance by many orders of magnitude [3]. However, the performance was evaluated in a simulated 2-D environment. In this thesis, the performance of this beamformer will be characterized in a real wireless UWB channel and conclusions will be drawn based on its impact on a real wireless communication system. This beamformer will be referred to as the “IIR beamformer” for the remainder of this thesis. Its properties Chapter 2. Background 16 are reviewed in the next section in order to gain an appreciation of the beamformer. 2.2 Space-Time Processing and Review of an Ideal TTD beamformer It is important to be familiar with the two-dimensional spectrum of a broadband signal received by an one-dimensional linear array of antenna elements as this multi-dimensional signal is to be processed by beamformers for the remainder of this thesis. The spectrum of the input is to be multiplied by the 2-D transfer functions of beamformers to obtain the desired signal. The characteristics of an ideal TTD beamformer are also reviewed as its architecture is often employed in hardware UWB beamformers, as seen in Section 2.1.1, and this beamformer type which will serve as a reference for performance comparison to the IIR beamformer later on this thesis. When an impinging impulse signal arriving from angle ψ, deﬁned with respect to broadside of the array, the 2-D signal in the (t, x/c) domain is shown in Figure 2.1, where x is the axis of the receiving linear array and c is the speed of light. Let α be the angle in which the straight line makes with the x = x/c axis as shown in Figure 2.1. The relationship between dt and dx is dt = dx sin(ψ) . It is easy to see that tan(α) = c dt dt dx = dx = sinc ψ (c) = sin ψ. Hence, α = tan−1 [sin ψ] deﬁnes the space-time angle dx dx of incoming wave with respect to the x -axis. The 2-D Fourier transform of the received signal in Figure 2.1 has a region of support inclined at the same angle as the space-time angle α. Figure 2.2 shows the 2-D spectrum of the received signal by having N = 30element in the receiving array for ψ = 10◦ . Figure 2.3 shows the architecture of an ideal TTD UWB beamformer in the receiving mode. Each antenna element in the array is connected to a TTD device, shown here as a piece of ideal transmission line which is also called a TTD phase shifter. The lengths of these transmission lines are determined by the position of the antenna that it is connected 17 Chapter 2. Background Figure 2.1: Received 2-D impulse signal from a linear array in the (t, x/c) domain. Figure 2.2: 2-D spectrum of the received signal of an array of UWB receivers for ψ = 10◦ and N = 30 antenna elements. to and the angle of the impinging UWB wave. The amount of delay for the mth delay element is governed by dm = mΔx/c sin(ψT T D ), where Δx is the element spacing, ψT T D is the desired beamforming angle with respect to broadside of the array and c is the speed of light in free space. When the delays are properly compensated in this fashion, a coherent sum is performed and all the signals add constructively at the output of the 18 Chapter 2. Background Figure 2.3: A TTD UWB beamformer. beamformer. Figure 2.4 shows the 2-D beam pattern of a 30-element TTD beamformer when the desired beam angle is set to 10◦ . Its wideband characteristics are clearly visible in this ﬁgure as its main lobe points to the same direction, ψT T D = 10◦ , for all frequencies. However, it is clear from the ﬁgure that the shape of the beam pattern does change with frequency as expected as the phase at each frequency diﬀers. Nevertheless, this beamformer is considered to be wideband due to its squint-free property of its main lobe. 2.3 Derivation of the IIR Beamformer The particular beamformer of interest in this thesis is described below. Its derivation comes from the network resonance approach [3] where a ﬁctitious 2-D analog circuit is resonant at a particular set of frequencies. The ﬁrst-order 2-D ﬁctitious circuit is shown 19 Chapter 2. Background in Figure 2.6 whose transfer function T (s1 , s2 ) is given by T (s1 , s2 ) = R Y (s1 , s2 ) , ≡ R + s 1 L1 + s 2 L 2 W (s1 , s2 ) (2.1) where W (s1 , s2 ) and Y (s1 , s2 ) are the 2-D Laplace transforms of the input and output respectively. The frequencies s2 = jω2 , s1 = jω1 represent the temporal frequency and spatial frequency, ko sin(ψ), respectively, where ko is the free space wavenumber and ψ is the angle of arrival of the incoming broadband wave with respect to the broadside direction of the array. The magnitude of transfer function (2.1) is shown in Figure 2.5. This transfer function achieves unity when the frequencies (ω1 , ω2 ) satisfy ω1 L1 + ω2 L2 = 0, (2.2) Figure 2.4: 2-D beam pattern of a TTD beamformer in Figure 2.3 for N = 30 ideal isotropic elements. The angle that the beamformer is set to ψbf m = 10◦ . Colour scale in dB. Chapter 2. Background 20 Figure 2.5: Magnitude of 2-D transfer function (2.1). Colour scale in dB. which is a straight line in the (ω1 , ω2 ) that makes an angle α with the ω2 axis, given by α = tan−1 (L2 /L1 ). This line is the passband of the 2-D ﬁlter over which the beamformer exhibits high spatial selectivity and broad bandwidth. Note that transfer function (2.1) describes a passive circuit and its transfer function is meaningful for only positive inductances L1 and L2 . Hence for positive L1 and L2 , it is clear from equation (2.2) that either ω1 or ω2 must be negative in order to satisfy this equation. This implies that the beamformer can only scan in one quadrant, i.e. from 0◦ to 90◦ , as measured from broadside. The other quadrant can be scanned by reversing the spatial order of the received signals. Figure 2.6: First-order 2-D frequency-planar beam plane wave ﬁlter whose passband vector is normal to [L1 , L2 ]. The 2-D continuous transfer function given by equation (2.1) can not be realized easily 21 Chapter 2. Background since a continuous array of sensors is needed (continuous s1 ). Here, both dimensions are discretized so that the signal is sampled digitally in time and spatially using discrete sensors. A standard 2-D bilinear transform [18] of equation (2.1) is found by setting, s1 s2 1 − z1−1 2 = Δx 1 + z1−1 1 − z2−1 2 , = cTs 1 + z2−1 (2.3) (2.4) where Δx and Ts is the spatial and temporal sampling period respectively and c is the speed of light. It is worth noting here that the discretization in the time (s2 ) domain is not necessary if the signal can be processed in the continuous-time domain. However, for now we consider the discrete-space and discrete-time version of the beamformer. The discrete 2-D transfer function is given by H(z1 , z2 ) = α (1 + z1−1 )(1 + z2−1 ) , 1 + b10 z1−1 + b01 z2−1 + b11 z1−1 z2−1 (2.5) where bij = α = R+ 2 (−1)i L1 Δx 2 R + Δx L1 R R+ 2 L Δx 1 + + + 2 (−1)j L2 cTs 2 L cTs 2 . 2 L cTs 2 (2.6) (2.7) Here, z1 and z2 represent spatial and temporal frequencies respectively in the z-domain, respectively. The bij coeﬃcients are functions of the original parameters of the continuous transfer function, R, Δx and Ts . The R parameter is used to set the 3 dB rolloﬀ frequencies in the ﬁrst-order circuit, analogous to the 3 dB frequency of a ﬁrst-order lowpass RC circuit. The smaller the value of R, the lower the frequency is, in this case, the sharper the main lobe of the beamformer becomes. These bij coeﬃcients mathematically set the angle to which the beamformer is tuned, ψbf m . The spatial sampling period, Δx, 22 Chapter 2. Background is the antenna spacing in a linear array of antenna elements. Since both the signals have been spatially and temporally discretized, one can use a DSP platform with a discrete array of sensors to realize this 2-D transfer function. Transfer function (2.5) can be re-arranged as W (z1 , z2 )(1 + z1−1 )(1 + z2−1 ) = Y (z1 , z2 )(1 + b10 z1−1 + b01 z2−1 + b11 z1−1 z2−1 ), (2.8) and it can be written as a diﬀerence equation given by y(n1 , n2 ) = 1 1 w(n1 − i, n2 − j) − i=0 j=0 1 1 bij y(n1 − i, n2 − j), i=0 j=0 i+j=0 (2.9) where n1 and n2 are the spatial and temporal indices, respectively, and w(n1 , n2 ) is the 2-D discrete-time discrete-space input to the beamformer. Figure 2.7 shows the signal ﬂow graph that realizes equation (2.9). Deﬁned in the dashed box is a unit cell which processes the signal from the current antenna, previous antenna and the outputs from the previous unit cell. Each antenna is connected to one unit cell. The progression of the signal from one unit cell to the next implements the spatial feedback loop that corresponds to the spatial feedback in equation (2.9). A temporal feedback loop clearly exists at the output of the unit cell. Hence this 2-D ﬁlter is of the IIR type in both space and time. 2.3.1 Beamformer Characteristics In this section, the receiving beam pattern of the IIR beamformer is studied. Figure 2.8 shows the ideal 2-D transfer function (2.5) in the Nyquist square |ω1 | < ωs1 /2 and |ω2 | < ωs2 /2. For low spatial and temporal frequencies, this discrete 2-D transfer function approximates the original continuous transfer function shown in Figure 2.5 very well. In this region, the passband approximates a straight line in the (ω1 , ω2 ) domain where Chapter 2. Background 23 Figure 2.7: Signal ﬂow graph implementing transfer function (2.5) and diﬀerence equation (2.9). the beam shape and pointing angle is not a strong function of temporal frequency. In practice, only a ﬁnite number of antenna elements and unit cells can be realized. Thus, the array is truncated by a spatial rectangular window. As a result, the ideal sharp peak in Figure 2.8 are spread to a broader width and energy is spilled into adjacent spatial frequencies, as shown in Figure 2.9. The spatial windowing eﬀect is clearly visible in this ﬁgure as sidelobes. Mapping the spatial frequencies in terms of angle from broadside gives a 2-D far-ﬁeld pattern shown in Figure 2.10. Here, the beam squinting is clearly visible as the direction of main lobe is a function of temporal frequency. One can downsample the inputs in the spatial domain to reduce the number of required antenna elements in the receiving array, alleviating potential hardware constraints and costs. However, aliasing occurs if the signal is spatially undersampled, Chapter 2. Background 24 Figure 2.8: 2-D transfer function of (2.5). R = 0.01, Δx = 12 mm, ψbf m = 10◦ . Colour scale in dB. Figure 2.9: 2-D transfer function of the IIR beamformer spatially truncated to 30 elements with spacing 12 mm for isotropic antenna elements. ψbf m = 10◦ . Color scale shown is in dB. deﬁned when the sampling period is greater than the Nyquist period. This leads to repetitions in the spectrum of the signal in the frequency domain. For a downsample factor of L, the received signal the w(n1 , n2 ) have a corresponding downsampled signal Chapter 2. Background 25 Figure 2.10: 2-D transfer function of the IIR beamformer plotted with respect to angle from broadside. ψbf m = 10◦ . Ideal isotropic antenna elements are used. ŵ(n1 , n2 ) = w(n1 L, n2 ) for n1 = kL, k ∈ Z and ŵ(n1 , n2 ) = 0 otherwise. Hence the unit cells at index n1 = kL are connected to antennas while the rest of the unit cells are fed with zero-inputs. Figure 2.11 shows an example to illustrate the mechanism in which the spatial downsampling occurs for downsampling factor of L = 2. The new 2-D input spectrum to the beamformer is same as the original spectrum except that duplicate copies of the original spectrum appears an extra L − 1 times in the Nyquist square, as shown in Figure 2.12 for L = 2. This downsampled input spectrum is then multiplied by the transfer function shown in Figure 2.9. Clearly, the spatially aliased components in Figure 2.12 lie in the stop band region of Figure 2.9. Thus, those aliased frequency components are not expected to make signiﬁcant contributions for reasonable downsampling factors, which is why spatial downsampling can be exploited by this type of beamformer. 26 Chapter 2. Background Figure 2.11: Example of an array with a spatial downsample factor of L = 2. A unit cell is deﬁned in the dashed box in Figure 2.7. Figure 2.12: Spatially downsampled spectrum of a signal whose spectrum is shown in Figure 2.2. Downsample factor L = 2. Colour scale in dB. Chapter 3 UWB Beamformer Characterization 3.1 Motivation Previous work has characterized the performance of the IIR beamformer described in Chapter 2 in a simulated environment [3]. An array of ideal ﬁeld samplers was used that neglected the eﬀects of a real array of UWB antennas, such as the frequency-dependent pattern of the antennas, mutual coupling between elements and impedance matching. These non-ideal eﬀects, which are not captured by the simulations in [3], can degrade the performance of the IIR beamformer in real life. Furthermore, the performance of the IIR beamformer was evaluated in a 2-D simulated environment. This 2-D model is not suﬃcient in capturing all the realistic eﬀects that exist in a radio channel as there are considerably more multipath eﬀects and scattering ﬁelds from objects in the third dimension. It is the goal of this chapter to characterize the digital IIR beamformer in a real wireless UWB channel. There are several challenges to overcome in order to characterize the performance of the beamformer. First, an array of real UWB antennas must be designed and fabricated. The antennas are to be arranged in a linear array so that realistic eﬀects of the antenna array are captured in the performance assessment of the 27 Chapter 3. UWB Beamformer Characterization 28 IIR beamformer. Next, the impulse response of a wireless channel over an ultra-wide bandwidth needs to be measured. By knowing the impulse response, the channel output can be determined given any excitation via convolution. The IIR beamformer is characterized using three diﬀerent methods. The ﬁrst method measures its far-ﬁeld pattern with realistic UWB antennas. The second method measures the interference rejection capability of the beamformer when multiple users are transmitting at the same time. The third method measures the improvement in bit-error-rate (BER) of a wireless communication system with and without the beamformer in place. The improvement in BER is also compared to that achieved by an ideal TTD beamformer as this architecture is often employed in hardware realizations of beamformers, as discussed in Chapter 2. 3.2 UWB Channel Sounding Techniques An oﬃce environment is one type of channel that is often used in many of UWB applications. Short-range applications such as Wireless Personal Networks, Wireless HDTV and Wireless USB could all have an oﬃce environment as its communication channel. Hence, an indoor oﬃce channel was chosen to be characterized for the experiments in this chapter. There are two main approaches to excite a wireless channel for it to be characterized – one is in the time domain while the other is in the frequency domain. There are a number of advantages to both approaches and they are summarized here. 3.2.1 Time Domain Sounding Technique The simplest approach to measure a channel’s impulse response is to send a short pulse in time whose bandwidth covers the entire frequency range of interest [19]. The received signal in time is a good approximation of wideband impulse response of the channel. A high speed oscilloscope can be used to capture the received signal whose spectrum Chapter 3. UWB Beamformer Characterization 29 is a close approximation to the channel’s frequency response over the excited signal bandwidth. The most attractive aspect of this direct measurement system is its lack of complexity. The frequency response of the channel can be displayed in real time on the oscilloscope via a simple Fourier transform. However, this direct approach is rarely used in practice because very high instantaneous pulse energy is needed to have a decent range. One method often used in practice is to use a modulated pseudo-random bit sequence to excite the channel. A well-known property of maximal length pseudo-random bit sequences is that the autocorrelation is a close approximation to a delta function. Hence, this property can be used to measure the impulse response of an UWB channel [20, 21, 22]. The impulse response of the channel can be obtained by taking the cross correlation of the input and output of the channel. This approach is attractive because the total transmitted energy can be increased by using a longer pseudo-random sequence and the post-processing gain allows for more dynamic range and a lower noise ﬂoor. However, more sophisticated equipments are needed to measure the channel’s impulse response. An arbitrary waveform generator is needed to produce the desired pseudo-random bit sequence. Modulators are needed to modulate the baseband signal up to (and potentially down from) the carrier frequency and a high-speed RF sampling oscilloscope is needed to capture the received signal for post-processing. 3.2.2 Frequency Domain Sounding Technique A vector network analyzer (VNA) can be used to directly measure the frequency response of a device under test (DUT). At each frequency point, the VNA evaluates the s-parameters of the DUT and s21 is taken to be the transfer function of the DUT. In an UWB channel measurement, the wireless channel with the transmitting and receiving antennas is the DUT. Many researchers have used this method to obtain the frequency response of a wireless channel to compute the channel’s statistics [23, 24, 25]. To obtain Chapter 3. UWB Beamformer Characterization 30 the measured s21 from the VNA of the DUT, the VNA is calibrated such that the measured s-parameters do not include the eﬀects of the test cables connected to the VNA. The advantage of this method is that it is simple to set up. Only one instrument is required to obtain the frequency response of the channel. However, long cables are needed between the transmitting and receiving antennas limiting the length of the channel that can be measured. The channel must also remain stationary over the sweep time of the instrument. Since a small oﬃce environment is to be characterized, the channel length of an oﬃce is not exceedingly long and cables with such lengths are readily available. Hence, this frequency domain method is chosen for the characterization of an indoor oﬃce channel. 3.3 UWB Antenna Array Description An array of UWB antennas was fabricated in order to measure the characteristics of the beamformer with real UWB antennas. The type of UWB antenna chosen was a balanced antipodal Vivaldi antenna (BAVA) which was originally designed for breast cancer detection [2]. Vivaldi antennas are non-resonant traveling type of antenna where the guided wave transitions smoothly to a free-space wave. It has an extremely wide impedance bandwidth, ranging from approximately 2.4 GHz to in excess of 10 GHz and it has low dispersion compared to other types of UWB antennas [26]. A detailed study of the eﬀects of the dimensions of the BAVA is presented in [2]. The authors of [2] designed the BAVA to be submerged in canola oil which exhibits a dielectric constant of 2.5. In this work, the dimensions of the BAVA were modiﬁed to operate in free space for use in wireless communication. The BAVA was simulated in a ﬁnite-diﬀerence time-domain (FDTD) simulator called SEMCAD. The dimensions of the BAVA were numerically optimized to minimize |s11 | of the antenna over the widest frequency range. The dimensional parameters are deﬁned in Chapter 3. UWB Beamformer Characterization 31 Figure 3.1. Each curve describing the exponential section of the BAVA can be described using an equation in the form Z = ±AeP (x−B) + C. Table 3.1 describes the set of equations deﬁning the curved boundaries of the BAVA. The optimized BAVA dimension parameters are shown in Table 3.2. A photograph of the fabricated array of BAVAs is shown in Figure 3.2. Figure 3.1: BAVA dimension deﬁnitions [2]. Figure 3.2: Fabricated BAVA array. Figure 3.3 shows the measured and simulated |s11 | of all the fabricated BAVAs when each of them are isolated. The measured |s11 | values are very close to simulated values for Chapter 3. UWB Beamformer Characterization Curve Et Ef Ea A W ts−W g 2(eP t∗Lt −1) Af W ts+W a 2(eP a∗La −1) 32 P B C Pt 0 Wg/2 - At Pf Lt+Lts Wts/2 - Af Pa Lt+Lts -Wts/2 - Aa Table 3.1: Exponential curve parameters describing the fabricated BAVA. Parameter Value [mm] Wts 2.24 Wg 10 Ws 2 Wa 56 W 76 Pa 0.05 Pt -0.15 Pf 0.4 Af 0.1 Lt 23 La 60 Lts 1 Table 3.2: Dimensions of optimized BAVA. all four fabricated BAVAs. The measured (solid curves) and simulated (dashed curves) coupling values when the BAVAs are arranged in a linear array with 12 mm spacing are shown in Figure 3.4. The coupling values between adjacent antennas are quite high, averaging at about −10 dB from 3 GHz to 10 GHz. The measured full 4-port s-parameters of the BAVA array and the measured far-ﬁeld pattern of each antenna are included in Appendix A along with the detailed fabrication steps. 3.4 Far-Field Pattern Characterization The ﬁrst method to characterize the beamformer is to measure its far-ﬁeld pattern with a real receiving antenna array. The aim is to verify that the far-ﬁeld pattern of the beamformer is not aﬀected signiﬁcantly by the real UWB antennas. Particularly, the 33 Chapter 3. UWB Beamformer Characterization 0 −5 −10 −15 |s11| [dB] −20 −25 −30 −35 −40 −45 −50 Antenna 1 Antenna 2 Antenna 3 Antenna 4 Simulated 2 4 6 8 Frequency [GHz] 10 12 Figure 3.3: Measured and simulated |s11 | of the BAVAs. mutual coupling between the antenna elements could distort the far-ﬁeld pattern of the beamformer. 3.4.1 Setup and Measurement of Far-Field Pattern Figure 3.5 shows the far-ﬁeld pattern measurement setup. A four-element linear array of BAVAs with 12 mm element spacing was placed in an anechoic chamber. 12 mm was chosen as the antenna spacing to avoid spatial aliasing of the received signal, as it satisﬁes the Nyquist sampling period of 15 mm assuming a maximum frequency of 10 GHz is used for communication. A VNA measured the complex transmission coeﬃcient s21 between the transmitter and the receiver. This coeﬃcient is a function of the angle of incidence and antenna position. A synthetic array of N -elements can be created by 34 Chapter 3. UWB Beamformer Characterization 0 −5 −10 S−Parameters [dB] −15 −20 −25 −30 −35 |s21| −40 |s31| |s41| −45 −50 |s32| 2 3 4 5 6 7 Frequency [GHz] 8 9 10 Figure 3.4: Measured (solid) and simulated (dashed) BAVA array element coupling values in a linear array with 12 mm spacing. moving the four fabricated antennas to the appropriate distances, eﬀectively creating an array size that is larger than the size of the physical array, hence saving fabrication time and cost. A synthetic array with reasonable size had to be chosen subject to a reasonably directive beam pattern of the beamformer and the physical constraints of moving the fabricated antenna elements in the anechoic chamber on a rotating platform. A 16-element synthetic array was found to be a good compromise and was implemented by moving the four antennas to the appropriate positions 15 times. Each time, the entire array is moved by the element spacing of Δx = 12 mm, as shown in Figure 3.5. One receiving antenna (#2) was connected to the VNA while the remaining three acted as dummy antennas connected to matched loads. Hence, the antenna coupling eﬀect due to dummy antennas #1, #3 and #4 was included in the measured complex gain. The antenna coupling eﬀect from more distant elements was not considered because 35 Chapter 3. UWB Beamformer Characterization it was expected that the immediately adjacent elements would dominate the coupling eﬀect while elements further away would not contribute signiﬁcantly. Furthermore, in spatially downsampled conﬁgurations shown in later sections, the element spacing is much greater than 12 mm and the eﬀects of non-adjacent elements are even less pronounced. 3.4.2 Evaluation of Far-Field Pattern For a given measured transmission coeﬃcient, the excitation to the IIR beamformer, for the mth antenna element at a particular angle from broadside ψ is Em (t, ω, ψ) = Am (ω, ψ) cos(ωt + γm (ω, ψ)) (3.1) for m = 1, 2, ..., 16. Am (ω, ψ) and γm (ω, ψ) are the measured magnitude and phase of the complex gain s21 at frequency ω and angle ψ. Two sets data for Am (ω, ψ) and γm (ω, φ) are measured corresponding to cases with and without dummy elements in place. When there are no dummy antenna elements present, then the measured complex gain is that of a purely synthetic 16-element array. Likewise, when the three remaining dummy elements Figure 3.5: Far-ﬁeld pattern measurement setup. Note that a synthetic array is formed by displacing the array a distance Δx, the element spacing, in the direction shown. Chapter 3. UWB Beamformer Characterization 36 are present, then the measured complex gain includes mutual coupling eﬀects. To compute the far-ﬁeld pattern of beamformer, the input Em (t) is the input to the diﬀerence equation (3.1), all of which is computed and processed in MATLAB. The output y(n1 , n2 ) is computed for each angle of incidence of the signal ψ ∈ (−90◦ , 90◦ ) in equation (3.1) and the amplitude of the output sinusoid is known. This amplitude variation as a function of angle is the far-ﬁeld pattern of the beamformer at a particular frequency. 3.4.3 Far-Field Pattern Results Figure 3.6 shows the measured far-ﬁeld gain pattern for three cases with the IIR beamformer tuned to ψbf m = 20◦ with N = 16-element array spaced at 12 mm. The solid red curve is the gain pattern of the IIR beamformer assuming ideal ﬁeld samplers with isotropic patterns and no mutual coupling. The dashed black curve is the gain pattern from a purely synthetic 16-element array. The solid black curve is the gain pattern that includes element coupling eﬀects. The gain of the uncoupled case with a purely synthetic array is higher than the gain of the coupled case. This behaviour is expected and is likely caused by the signiﬁcant mutual coupling between adjacent elements as well as a degradation in the active impedance match, both of which reduce the measured gain. The total measured pattern is expected to be the pattern of the beamformer multiplied by the antenna element pattern. The gain diﬀerence between the ideal (red) curve and the curve without antenna coupling (dashed black) is expected to be the BAVA gain as shown in Figure A.5 at 20◦ from broadside. The diﬀerence in gain of the red the curve and the dashed black curve approximately corresponds to measured gain at 20◦ from broadside in Figure A.5. The measured far-ﬁeld pattern (black curves) are for the worse case mutual coupling scenario as the antennas are at only 12 mm apart. Overall, the general shape of all the plots are still very close to each other across a wide range of frequencies. This show 37 Chapter 3. UWB Beamformer Characterization 4.4 GHz 20 20 10 10 Gain [dBi] Gain [dBi] 3.2 GHz 0 −10 −20 −10 −20 −50 0 ψ° 5.6 GHz 50 20 20 10 10 Gain [dBi] Gain [dBi] 0 0 −10 −20 −50 0 ψ° 6.8 GHz 50 −50 0 ψ° 50 0 −10 −20 −50 0 ψ° 50 Figure 3.6: Far-ﬁeld gain pattern of IIR beamformer for ψbf m = 20◦ , from ideal calculations (solid red), measurements with coupling (solid black), and without antenna coupling (dashed black). that even with worst case antenna spacing, the beam characteristics are not sensitive to mutual coupling between the antenna elements. Thanks to the gain provided by the BAVA elements, the gain of the beamformer with real antennas is more than that of the beamformer alone. The introduction of the real antenna elements as the receiving array does not signiﬁcantly degrade the pattern shape and the real antennas have added gain to the beamformer, proving that real antennas are well-suited for this digital beamformer. 3.5 Interference Rejection Characterization Of signiﬁcant interest is the beamformer’s interference rejection capability in a multi-user environment as multiple UWB users could be transmitting in the same channel causing Chapter 3. UWB Beamformer Characterization 38 interference with one another. This experiment characterizes the interference rejection capability of the beamformer in the time-domain where multiple users simultaneously transmit wideband signals causing interference. The interference rejection capability of the IIR beamformer in a real radio channel with rich multipath eﬀects is unknown. The far-ﬁeld pattern of the IIR beamformer has been shown to be very robust even with real UWB antennas with signiﬁcant antenna element coupling. The beam pattern characterization described in the previous experiment was in the frequency domain where far-ﬁeld pattern characteristics are examined at discrete points in frequency. Hence, the interference rejection capability is assessed in the time-domain in this experiment. 3.5.1 Setup and Measurement of the Interference Rejection Experiment The interference rejection experiment setup is shown in Figure 3.7. In this setup, a VNA was used to acquire the impulse response in the frequency domain of an oﬃce environment from 2 GHz to 10 GHz, which is shown in Figure 3.8 where RX is the centre of the receiving array. The transfer function was taken to be the measured s21 . An inverse Fourier transform was applied to obtain the channel’s bandpass impulse response. This method has the advantage of being simple to set up and capable of obtaining highly accurate measurements. During the data acquisition process, nothing in the vicinity of the channel was moving and the channel was assumed to be stationary. Measurements were checked for repeatability. The VNA was calibrated so that the measured frequency response only included the antennas and the wireless channel. Furthermore, the RMS delay spread of the measured channel impulse response was checked against that of the reported in the literature for a small oﬃce channel environment. The RMS delay spread in the measurements was approximately 10 ns which is consistent with the lower bound reported for indoor channels [19]. Similar to the far-ﬁeld pattern measurement setup, the same three dummy antenna elements were in place to capture element coupling eﬀects Chapter 3. UWB Beamformer Characterization 39 in the measurements. Figure 3.7: UWB channel impulse response measurement setup. The receiver array was placed on an arm of a scanner capable of moving within a span of 1.5 m spatial window to an accuracy of a few microns. 12 mm element spacing was used, satisfying the spatial Nyquist period of 15 mm for a maximum frequency of 10 GHz. Up to a 120-element (1.5 m) synthetic array could be realized on the positioner. A computer script was written to control the position of the antenna array and captured the measured s21 from the VNA at proper positions. The angle of arrival (AOA) is deﬁned with respect to the broadside direction of the receiver array. One transmitter is moved to four diﬀerent positions so that impinging signals from four diﬀerent AOAs could be produced ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }. The interference rejection simulation setup is shown in Figure 3.9. 40 Chapter 3. UWB Beamformer Characterization Figure 3.8: Top view of the measured oﬃce environment. Figure 3.9: Interference rejection experiment setup. Signals can arrive directly from four possible angles from broadside of the array ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }. 3.5.2 Interference Rejection Evaluation The received signal at the mth antenna element, rm (t), in the receiving array is derived from the measured impulse response from each transmitter. It is the superposition of the Chapter 3. UWB Beamformer Characterization 41 signals from each of the transmitter convolved with the corresponding impulse response. rm (t) is expressed as rm (t) = 3 hmi (t) ∗ si (t), (3.2) i=0 where hmi (t) is the measured impulse response from the ith transmitter to the mth antenna element and is the inverse Fourier transform of the measured s21 , si (t) is the signal transmitted by the ith transmitter and ∗ denotes linear convolution. A multi-user interference scenario is created when each transmitter emits a broadband pulse, si (t) = δ(t − iTd ) delayed by Td , such that the received signal rm (t) is the superposition of the delayed impulse responses from each transmitter, rm (t) = 3 hmi (t − iTd ). (3.3) i=0 A small amount of delay Td is introduced to temporally separate the received pulses from such that received pulse from a single transmitter can be clearly shown, but in practice the signals can overlap and still be resolved by the beamformer. It is expected that when there is no beamformer at the receiver, the received signal would consist of four peaks corresponding to the four transmitted pulses. The amplitudes of the four received peaks are solely determined by the channel response. Since the channel responses diﬀer, the received four peak amplitudes may diﬀer. Thus, in equation (3.3), hmi (t) is normalized to unity before the received signals are summed such that when there is no beamformer exist at the receiver, the four received peaks all have the same amplitude. This serves as a base for comparison to the case when the beamformer is enabled at the receiver. The amount of attenuation of the received signal is then solely caused by the beamformer, a direct measurement of the wideband interference rejection capability of the beamformer in the multipath radio channel. Chapter 3. UWB Beamformer Characterization 3.5.3 42 Interference Rejection Experiment Results A 120-element receiving array with 12 mm element spacing was used in this experiment. When the beamformer was set to the ﬁrst transmitter located at broadside of the receiving array ψbf m = ψsource = 0◦ in Figure 3.10(a), the received signal from that direction had the highest peak as expected. Similarly, for ψbf m = ψsource ∈ {10◦ , 20◦ , 27◦ }, the received signal amplitude had the highest peak when the beamformer was tuned to them, as shown in Figures 3.10(b), 3.10(c), 3.10(d) respectively. The suppression levels are summarized in Table 3.3. The suppression levels of the signals are measured relative to the highest peak of the received signal. Values in parentheses in this table are the theoretical suppression levels in an ideal channel. It is clear that the signals arriving from angles that were not where the beamformer is tuned to experienced a great deal of attenuation. The transmitters were spatially separated by only 10◦ (7◦ for the last transmitter) and provided on average of approximately 9.4 dB suppression for adjacent transmitters. The further it is from the tuned angle of the beamformer, the greater the attenuation is experienced by the signal. This behaviour is expected as the gain of the far-ﬁeld pattern of the beamformer quickly drops when deviated from the tuned angle. Note that the receiving array and the beamformer is in the azimuth plane, therefore no spatial discrimination is provided in the elevation plane other than the antenna pattern itself. Hence the signals bouncing oﬀ the ground or ceiling arriving at the receiver in the elevation plane are not spatially ﬁltered by the beamformer. However, the beamformer still provides signiﬁcant spatial discrimination overall. It is also worth noting that the measured suppression levels are not expected to be the same as the suppressions level from the measured far-ﬁeld pattern. The far-ﬁeld pattern is in the frequency domain and its gain varies across frequency. This wideband interference rejection levels includes the gain and pattern variations for all frequencies. Furthermore, this interference rejection experiment was performed in a multipath rich 43 Chapter 3. UWB Beamformer Characterization real radio channel where the signals can arrive from any angle, perturbing the received peak level. Hence, the measured interference rejection levels can only compared to the far-ﬁeld pattern on a ﬁrst-order basis. To capture the eﬀect of the beamformer more rigorously as a part of a communication system, Monte Carlo BER tests of an UWB communication system are performed in the next section, with and without the beamformer to gauge its performance. 1 1 X: 0.3997 Y: 1 0.8 Received Signal [au] Received Signal [au] X: 0.0792 Y: 1 0.6 X: 0.3989 Y: 0.3066 0.4 X: 0.7209 Y: 0.1223 0.2 0 0 0.5 0.6 0.4 X: 0.7209 Y: 0.332 X: 0.0794 Y: 0.3004 X: 1.043 Y: 0.2418 0.2 X: 1.043 Y: 0.0947 1 0.8 0 1.5 0 0.5 Time [μ s] 1 (a) IIR beamformer tuned to ψbf m = 0◦ (b) IIR beamformer tuned to ψbf m = 10◦ 1 1 X: 1.042 Y: 1 0.8 Received Signal [au] Received Signal [au] X: 0.7212 Y: 1 X: 1.043 Y: 0.646 0.6 0.4 X: 0.3997 Y: 0.265 0 X: 0.0839 Y: 0.7518 0.8 0.6 X: 0.7211 Y: 0.3016 0.4 X: 0.4031 Y: 0.2194 X: 0.0833 Y: 0.1562 0.2 0 1.5 Time [μ s] 0.2 0.5 1 Time [μ s] (c) IIR beamformer tuned to ψbf m = 20◦ 1.5 0 0 0.5 1 1.5 Time [μ s] (d) IIR beamformer tuned to ψbf m = 27◦ Figure 3.10: Time-domain output of the beamformer plotted for various beamformer set AOAs. Red is the normalized received signal amplitude with no beamformers present all have the same peak. Black is the received signal with the beamformer enabled and they are temporally oﬀset for clarity. Chapter 3. UWB Beamformer Characterization 44 Tx Location 1 2 3 4 ◦ 0 0 -10.3 (-30.4) -18.3 (-36.0) -20.5 (-38.3) ◦ 10 -10.5 (-20.4) 0 -9.6 (-13.5) -12.3 (-19.5) 20◦ -16.1 (-22.8) -11.5 (-20.3) 0 -3.8 (-5.0) ◦ 27 -2.5 (-23.6) -13.3 (-22.2) -10.4 (-13.9) 0 Table 3.3: Table of suppression levels (peak values in dB) from Figure 3.10. Values in parentheses are the theoretical suppression levels assuming free space channel. 3.6 Monte Carlo BER Simulations The goal of the Monte Carlo BER simulations is to assess the improvement in BER that can be provided by the beamformer in a multi-user scenario by using real measured channel responses. Previous work has shown that this beamformer lowered the BER of the received signal in an UWB wireless system by several orders of magnitude [3]. However, the performance of the beamformer was shown in a simulated two-dimensional environment with an isotropic transmitter and an ideal array of ﬁeld samplers as the receiving array. Realistic eﬀects of the UWB antenna as a transmitter and antenna element coupling in the receiving array were not captured. Furthermore, the simulated nature of the 2-D channel was not adequate to capture the eﬀects of abundant multipath and scattered ﬁelds in a real channel, especially when the simulation was in only two dimensions. In this experiment, one user transmitted the desired signal while the others acted as interferers, emulating interference signals generated by other UWB users in the same channel. The amount of interference rejection capability of this experiment is captured in the improvement of the BER of the received signal. When the beamformer is tuned to the desired transmitter, the BER is expected to be much lower compared to that when no beamforming is present. The eﬀects of the IIR beamformer on the BER curves are studied in detail in diﬀerent beamformer conﬁgurations. In addition, since many modern UWB beamformers implemented in hardware utilize the TTD architecture, it will be used as the reference to gauge the performance of the IIR beamformer. 45 Chapter 3. UWB Beamformer Characterization 3.6.1 Simulation Setup Figure 3.11 shows the simulated UWB communication system. The locations of the four transmitters are the same as the one described in the interference rejection experiment shown in Figure 3.9. The generated random bits are fed into a pulse shaper to convert the bits to pulse shapes that represent the bits. A raised cosine was used as the pulse shape, which is given by, 2Wo sinc(2Wo t) cos(2π(W − Wo t)) , 1 − 4(W − Wo )t2 (3.4) where W is the desired bandwidth, Wo = 1/2T represents the minimum Nyquist bandwidth for the rectangular spectrum and W − Wo is the excess bandwidth. T = 250 ps and W = 1.7Wo is used to produce a frequency content from approximately 2 GHz to 10 GHz. The signal from the pulse shaper is then sent through a channel whose impulse response is that of the measured ones from the interference rejection experiment. The impulse response from each transmitter to each antenna element in the receiving array is known. This received signal is then passed through a matched ﬁlter, the output of which is decoded assuming a perfect symbol timing recovery. Since a multi-user scenario environment is desired, one of the AOAs, ψsource ∈ {0◦ , 10◦ , 20◦ , 27◦ }, is selected to be the desired signal source while the transmitters located at the three remaining AOAs acted Figure 3.11: Simulated UWB communication system. Chapter 3. UWB Beamformer Characterization 46 as interference sources. The signal-to-interference ratio (SIR) in dB is deﬁned as SIRdB = 10 log10 Eb,signal Eb,int (3.5) where Eb,signal and Eb,int are the energy per bit of the desired signal and total energy per bit of all interferers respectively, measured at the receiver. Both quantities include the eﬀects of multipath captured in the measured channel response. A constant additive white Gaussian noise (AWGN) of power Eb /No = 10 dB is added to the received signal to model the superposition of independent noise sources, including but not limited to, analog-to-digital converters quantization noise, background noise from environment picked up by the UWB antennas, and the thermal noise in the receiver equipment. Diﬀerent array conﬁgurations of the beamformer were studied. The following parameters were varied to study their impact on the system performance: • Number of antenna elements, N • Antenna spacing, Δx • Angle of arrival of received signal, ψsource • Symbol rate, R • Eﬀect of mutual coupling A minimum number of antenna elements N is desired to reduce the cost of the receiver hardware. The beam squint of the main lobe of the beamformer for high ψbf m is expected to negatively impact the BER performance for such angles. ψsource ∈ {10◦ , 27◦ } was tested to assess the impact of the beam squinting and the performance results were compared to a TTD beamformer, which does not suﬀer from beam squinting. The close proximity of the antenna elements yields relatively high mutual coupling, which may also reduce the BER performance, hence cases with and without antenna coupling eﬀect were also compared. Chapter 3. UWB Beamformer Characterization 3.6.2 47 Simulation Results Eﬀect of Antenna Coupling, Symbol Rate and Bilinear Warping Two symbol transmission (bit) rates were simulated, R ∈ {1, 2} Gb/s, with binary phase shift keying (BPSK) as the modulation format. Figure 3.12 shows the receiver BER curves as a function of SIR for the array conﬁguration with N = 120 elements, Δx = 12 mm and ψbf m = ψsource = 10◦ . In Figure 3.12(a), the two circled curves shows the receiver BER for the two transmission rates when no beamformer was employed. The BER quickly drops and saturates on a ﬂoor as the SIR is increased. This behaviour is expected as at high SIRs, the power of the interfering signal is negligible compared to the signal power and the only source of decoding error is the added AWGN noise and the multipath eﬀects causing inter-symbol-interference (ISI), both of which are independent of SIR. When either IIR or TTD beamformers are used, the BER ﬂoor is pushed to a much lower level, showing that beamformers are very eﬀective in rejecting multipath interference. For the same BER, a much higher SIR is needed at the receiver when beamformers are not used, showing an improvement in SIR provided by the beamformer. Higher symbol rates yielded a higher BER as expected due to higher ISI. The performance of both of the two beamformers are reasonably close despite that the IIR beamformer suﬀers from the eﬀects of bilinear warping at high frequencies as shown in Figure 2.10. Figure 3.12(b) shows the BER curves when the antenna mutual coupling eﬀect is introduced. For the TTD beamformer, the coupling worsens the BER by approximately 3 dB for both symbol rates. For the IIR beamformer, the coupling eﬀects did not change the BER signiﬁcantly for both symbol rates. For symbol rate R = 2 Gb/s, the coupling eﬀect has caused the BER to be increased slightly at high SIR. The reason for this behaviour is thought to be the following. At low SIRs, the power from the interference signal dominates the contributions to decoding errors, while at high SIRs, the ISI dominates the decoding errors while ISI is higher when antenna coupling is present. Chapter 3. UWB Beamformer Characterization 48 The mutual coupling eﬀect is the worst in this conﬁguration as the element spacing is the smallest at 12 mm. Despite this, the IIR beamformer provided signiﬁcant improvements compared to no beamforming at the receiver. Its performance is comparable to that of the TTD beamformer despite that the IIR beamformer has warping eﬀects. Eﬀect of Spatial Downsampling The input can be downsampled in the spatial domain to reduced the number of required antenna elements. The mechanism to spatially downsample is described in Figure 2.11, where every L − 1 input is zeroed between every Lth cell. Figure 3.13 shows the BER performance of the two beamformers with the two symbol rates at downsampling factor L = 6, where the number of antenna elements has reduced to N = 120/6 = 20 and element spacing increased to Δx = 72 = 6 × 12 mm. In this downsampled case, both beamformers still oﬀer signiﬁcant improvement in BER relatively to the no beamforming case with only 20 elements. For symbol rate R = 1 Gb/s, the IIR beamformer provides about 2 orders of magnitude improvement in BER compared to no beamforming. For a symbol rate of R = 2 Gb/s, the IIR beamformer provides over an order of magnitude of improvement. The TTD beamformer performs moderately better for the lower symbol rate as the main lobe of the TTD beamformer does not point to a diﬀerent direction as a function of frequency. The higher the symbol rate, the higher the ISI in the received signal, makes the frequency invariant nature of the receiver more important to receive error-free symbols. With the antenna elements spaced at 72 mm, the eﬀect of the element coupling is much less than when elements were placed at only 12 mm. It was found that further decreasing the number of elements degrades the BER. Figure 3.14 shows the spatial downsampling factor of L = 15 with N = 8 antenna elements spaced at Δx = 180 = 15 × 12 mm. At this high downsampling factor, the original received spectrum is folded in the spatial domain 14 times. Figure 2.12 shows an example of the 2-D spectrum for downsample Chapter 3. UWB Beamformer Characterization 49 factor L = 2, where the signals is only folded 1 time. For L = 15, a great deal of the spatially aliased components of the original signal fall back to be within the passband (main lobe) of the beamformer, contributing signiﬁcantly to decoding errors. Eﬀect of Angle of Arrival The IIR beamformer suﬀers from beam squinting resulting from the 2-D bilinear transform of the transfer function. The actual angle that the main lobe of the IIR beamformer points, ψbf m , is diﬀerent from the angle in which the beamformer is set to, ψbf m . For each ψbf m , ψbf m depends on frequency. The higher that ψbf m is set to, the worse the beam squinting becomes. Figure 3.17 shows the actual angle of the main lobe, ψbf m as a function of the angle that the beamformer is set to, ψbf m . At ψbf m = 27◦ , ψbf m ranges from approximately 31◦ to 61◦ in the frequency range of 2.5 GHz to 8 GHz. This squint is expected to negatively impact the BER performance of the beamformer. To quantitatively capture this eﬀect, Figure 3.15 shows the BER for ψsource = ψbf m = 27◦ . The performance in BER in this case has degraded signiﬁcantly and the BER is higher compared to no beamforming at all, rendering the IIR beamformer useless. However, this eﬀect can be mitigated by pre-tuning the ψbf m of the beamformer to an angle such that, at the center frequency of 6 GHz, the beamformer is tuned to ψsource . ◦ Figure 3.17 shows that for ψbf m = 22◦ corresponds to ψbf m = 27 at 6 GHz. With this conﬁguration, Figure 3.16 shows the BER performance when beamformer is pretuned to 22◦ . The performance in BER is now improved signiﬁcantly and comparable to the performance achieved by the TTD beamformer. This shows that the pre-tuning is eﬀective in addressing the beam squinting. The pre-tune angles can be calculated or stored as a look-up-table in a real communication system. Chapter 3. UWB Beamformer Characterization 3.7 50 Beamformer Characterization Conclusions The IIR beamformer has been characterized with real antenna array using three diﬀerent methods. The ﬁrst method was the measurement of the beamformer’s far-ﬁeld pattern using real UWB antenna as the receiving array. It was shown that the measured gain of the beamformer with real antennas was higher than that of the beamformer alone as the antenna elements provided gain of its own. Despite being in the worest coupling scenario with element spacing of 12 mm, the measured far-ﬁeld pattern agreed closely with the ideal pattern. This showed that the real UWB antenna array is well-suited for the beamformer. The second method to characterize the beamformer was to assess its wideband interference rejection capability in a real radio channel. Multiple users were placed at diﬀerent angles of arrival where each user transmitted a wideband pulse. The IIR beamformer was placed at the receiver to observe the signal attenuation level based on angle of arrival. It was shown that the beamformer provided an excellent spatially selectivity despite the fact the beamformer was implemented in the azimuth plane while signals arriving from the elevation plane were not spatially discriminated by the beamformer. The interference rejection capability of the beamformer was shown to be excellent even in the multipath rich environment of a real radio channel. This also showed the beamformer’s eﬀectiveness in mitigating multipath eﬀects. The third method was to assess the performance of the beamformer is in terms of BER of a wireless communication system. BER simulations were conducted with multiple users transmitting in the same physical channel causing interference with one another. The impact of the beamformer on BER in a realistic UWB communication system was assessed for diﬀerent beamformer conﬁgurations, namely, symbol rate, element spacing, angle of arrival and antenna coupling. It was shown that even in the case with the highest antenna coupling values, the BER did not degrade signiﬁcantly. Quantitatively, the improvement in BER is consistent with that is seen in earlier reported work [3], Chapter 3. UWB Beamformer Characterization 51 despite the fact that the simulated conditions in a 2-D channel are very diﬀerent from that the measuredno channel. Diﬀerent symbol rates and pulse shapes were used and the beamformer still yielded a signiﬁcant improvement in BER in a real radio channel. The spatial downsampling mechanism was proven to be eﬀective, reducing the number of required antenna elements by a factor of 6 from 120 elements to 20 elements. For higher ψbf m , the BER was worse compared to angles that are closer to broadside due to bilinear transform in the beamformer’s transfer function. Strategically pre-tuning the beamformer was shown to mitigate the eﬀect of the beam squinting and lowered the BER to a level that was comparable to that of a TTD beamformer. The analysis of the IIR beamformer has shown its promising potential. In the next chapter, a potential hardware realization of this digital beamformer is discussed in detail. Real physical microwave circuits are fabricated to assess the feasibility of the hardware beamformer. 3.8 Sources of Errors in the Experiments The errors in the experiment mainly reside in the measured UWB frequency response of the channel in the anechoic chamber and in the oﬃce environment. In the anechoic chamber, the four BAVAs were placed on a rotating platform and its gain is measured as a function of frequency and position. Accurate angular and linear alignment of the BAVAs was required. A great deal of eﬀort was spent to align the antennas. However, there could still be some errors left leading to distortion in the measured far-ﬁeld patterns of the beamformer. During the frequency response acquisition of the oﬃce environment, the measured s21 from a VNA is taken to be the transfer function of the UWB channel. Any stochastic process in the channel would result in errors in the simulated BER. Hence, multiple acquisitions over the same channel were carried out and checked for repeatability and Chapter 3. UWB Beamformer Characterization 52 consistency. It is diﬃcult to comment exactly the type of errors that would result in the measurement from a particular VNA. However, the s-parameter measurement from a modern network analyzer is extremely accurate and is considered to be trustworthy. Moreover, the measured impulse response of the small oﬃce channel was compared to that of the response of other small oﬃce environment, the mean excess delay and the RMS delay spread were all in the expected range of a typical oﬃce environment. 53 Chapter 3. UWB Beamformer Characterization 0 10 −1 BER 10 −2 10 −3 10 −4 10 −20 −15 −10 −5 0 SIR [dB] 5 10 15 20 (a) No antenna coupling eﬀect. TTD Bfm Rate 1 Gb/s TTD Bfm Rate 2 Gb/s IIR Bfm Rate 1 Gb/s IIR Bfm Rate 2 Gb/s No Bfm Rate 1 Gb/s No Bfm Rate 2 Gb/s 0 10 −1 BER 10 −2 10 −3 10 −4 10 −20 −15 −10 −5 0 SIR [dB] 5 10 15 20 (b) With antenna coupling eﬀect. Figure 3.12: BER of the simulated UWB communication system. N = 120, Δx = 12 mm, ψbf m = ψsource = 10◦ . 54 Chapter 3. UWB Beamformer Characterization 0 10 −1 BER 10 −2 10 −3 10 −4 10 −20 −15 −10 −5 0 SIR [dB] 5 10 15 20 Figure 3.13: BER of the simulated UWB communication system. N = 20, Δx = 72 mm, ψbf m = ψsource = 10◦ , with antenna coupling eﬀect. See. Figure 3.14 for legend. 0 10 −1 BER 10 −2 10 TTD Bfm Rate 1 Gb/s TTD Bfm Rate 2 Gb/s IIR Bfm Rate 1 Gb/s IIR Bfm Rate 2 Gb/s No Bfm Rate 1 Gb/s No Bfm Rate 2 Gb/s −3 10 −4 10 −20 −15 −10 −5 0 SIR [dB] 5 10 15 20 Figure 3.14: BER of the simulated UWB communication system. N = 8, Δx = 180 mm, ψbf m = ψsource = 10◦ , no antenna coupling eﬀect. BER performance is degraded. 55 Chapter 3. UWB Beamformer Characterization 0 10 −1 BER 10 −2 10 −3 10 −4 10 −20 −15 −10 −5 0 SIR [dB] 5 10 15 20 Figure 3.15: BER of the simulated UWB communication system. N = 20, Δx = 72 mm, ψbf m = ψsource = 27◦ , with antenna coupling eﬀect. The impact of the beam squninting resulted no performance gain from the beamformer. See Figure 3.14 for legend. 0 10 −1 BER 10 −2 10 −3 10 −4 10 −20 −15 −10 −5 0 SIR [dB] 5 10 15 20 Figure 3.16: BER of the simulated UWB communication system. N = 20, Δx = 72 mm, ψsource = 27◦ , ψbf m = 22◦ with antenna coupling eﬀect. See Figure 3.14 for legend. Chapter 3. UWB Beamformer Characterization 56 Figure 3.17: Actual AOA ψbf m , the angle of the main lobe, as a function of AOA of the beamformer ψbf m for N = 30, Δx = 12 mm. Chapter 4 Potential Hardware Realization of a UWB Beamformer In Chapter 3, the performance of the IIR beamformer was evaluated using three different methods to assess its capabilities. It was shown that the beamformer is robust against mutual coupling and it can improve the BER of an UWB communication system by several orders of magnitude. In this chapter, a potential realization of a hardware UWB beamformer, which processes the received signal in the continuous-time domain, is studied. A detailed feasibility analysis is also conducted to assess the performance of such a beamformer using real physical components. 4.1 Motivation To realize the IIR beamformer algorithm using conventional DSP techniques, one would need an array of ADCs as shown in Figure 2.7. These ADCs need to sample the signals at radio frequencies in order to prevent aliasing. Since the upper frequency of the UWB band is at approximately 10 GHz, the sampling frequency must be at least 20 GHz to prevent aliasing. Flash ADCs are typically used for such a high sampling rate and they are very expensive and consume a lot of power [27]. Furthermore, a massive systolic 57 Chapter 4. Potential Hardware Realization of a UWB Beamformer 58 Figure 4.1: Unit cell from the signal ﬂow graph in Figure 2.7. array needs to be built [28] in order to realize this beamformer in digital form which, while more eﬃcient than other DSP implementations, still requires a tremendous number of calculations per second. The realization of the signal ﬂow graph is possible without the need for digitization and it could be implemented using RF microwave circuits in the continuous-time domain. The resulting beamformer would then have all the features of the digital IIR beamformer but with a lower cost and lower power requirements than present DSP technologies allow. 4.2 Continuous-time Transfer Function Figure 4.1 shows signal ﬂow graph of the unit cell with the deﬁned port numbers. There are only two unique transfer functions in the unit cell to be realized, T F1 (z2 ) and T F2 (z2 ). They correspond to the transfer functions from port 1 to 4 (T F1 (z2 )), port 2 to 4 (T F1 (z2 )) Chapter 4. Potential Hardware Realization of a UWB Beamformer 59 and port 3 to 4 (T F2 (z2 )). They can be derived as 1 + z2−1 1 + b01 z2−1 b10 + b11 z2−1 . T F2 (z2 ) = − 1 + b01 z2−1 T F1 (z2 ) = (4.1) (4.2) If an analog circuit can realize the above two transfer functions exactly, then one would arrive at the desired response exactly. In practice, an analog circuit can only approximate the transfer functions. The resistor R in circuit Figure 2.6 only controls the passband width of the transfer function. It is desired for it to be as small as possible in order to achieve the sharpest beam. Taking the limit as R → 0 in equation (2.6), b11 = −1 and (4.3) b01 = −b10 . (4.4) From now on, the value of the bij coeﬃcients are to be taken as such. Hence the angle the beamformer is set to, ψbf m , can be considered to be a function of b01 only. The goal is to ﬁnd a new transfer function that can be easily realized by simple RF microwave circuits. The following derivation of the new transfer function was found to be the simplest for realization. Consider bilinear transformed versions of equations (4.1) and (4.2). Substituting z2−1 = 1 − s2 T2s , 1 + s2 T2s (4.5) where Ts = 1/fs is the temporal sampling period, the two new transfer functions T F1 (s2 ) and T F2 (s2 ) are now in the continuous-time Laplace domain s2 , T F1 (s2 ) = 2 1 + b01 T F2 (s2 ) = −1 + s2 s2 1 Ts 1−b01 2 1+b01 2 Ts 1−b01 2 1+b01 +1 (4.6) +1 . (4.7) Chapter 4. Potential Hardware Realization of a UWB Beamformer 60 Figure 4.2: An RC network terminated by transmission lines. The two new transfer functions are in the form of a low-pass resistor-capacitor (RC) network which easily can be realized by RC network connected to a transmission line as shown in Figure 4.2. The transfer function of the circuit, taken to be its s21 , can be shown to be T Fshc (s2 ) ≡ s21 (s2 ) = where Ref f = R+Z0 2+R/Z0 2/(2 + R ) Z0 s2 CRef f + 1 , (4.8) , C is the shunt capacitance, R is the series resistance and Z0 is the characteristic impedance of two transmission lines feeding the circuit. A small Ref f R+Z0 Ts 1−b01 is desired such that C 2+R/Z is comparable to in equations (4.6) and (4.7). 2 1+b01 0 The variable gain term 1+b2 01 is the voltage gain of the signal and it is dependent on ψbf m . For ease of fabrication R is set to be zero allowing Ref f to be the smallest possible value of 25 Ω. Hence, for R = 0 and Z0 = 50 Ω, the transfer function is simply T Fshc (s2 ) = 1 , s2 (25)C + 1 (4.9) which is the form of the desired low-pass network in equations (4.6) and (4.7) with C= 1 Ts 1 − b01 . 25 2 1 + b01 (4.10) For each angle that the IIR beamformer is set to, ψbf m , there is a corresponding value for b01 given by equation (2.6), which has a corresponding value for C given by equation (4.10). Hence, ψbf m can changed by varying C. An electronically tunable capacitance, such as a varactor diode, can be used to tune C which in turn tunes ψbf m . With the new deﬁnitions of the two transfer functions (4.6) and (4.7), the new 2-D Chapter 4. Potential Hardware Realization of a UWB Beamformer 61 transfer function is derived as follows. The relationship between the output y(n1 , s2 ) and the input w(n1 , s2 ) can be written as y(n1 , s2 ) = (w(n1 , s2 ) + w(n1 , s))T F1 (s2 ) + y(n1 − 1, s2 )T F2 (s2 ), (4.11) where n1 is the spatial index and s2 is the continuous temporal frequency in the Laplace domain. It follows that the new 2-D transfer function is given by Y (z1 , s2 ) (1 + z1−1 ) = T F1 (s2 ) W (z1 , s2 ) 1 − z1−1 T F2 (s2 ) (4.12) where T F1 (s2 ) and T F2 (s2 ) are given in equations (4.6) and (4.7) respectively. Note that T F1 (s2 ) only modiﬁes the magnitude and the phase of the overall transfer function in the s2 domain. It does not have any eﬀect on where the passband of the transfer function is located. Hence, for simplicity, T F1 (s2 ) can be set to 1. The gain term 1+b2 01 in equation (4.6) and corresponding need for an ampliﬁer to realize it are now eliminated. Figure 4.3 shows the 2-D transfer function (4.12) for ψbf m = 10◦ . For the IIR digital beamformer in the same conﬁguration, shown in Figure 2.8, it is clear the new transfer function does not suﬀer from the eﬀects of the bilinear warping as its passband is almost a straight line, similar to the ideal analog transfer function shown in Figure 2.5. The potential microwave circuit design for the unit cell has a simple topology shown in Figure 4.4. In this new unit cell, the transfer functions from port 1 to 4, from port 2 to 4 and from port 1 to 5 is are all assumed to be all-pass functions. The transfer function from port 3 to 4 is that described by equation (4.7). Devices in dashed lines are the power dividers and combiners needed to add and divide signals. A wideband Wilkinson power divider could be used to realize such device. A shunt variable capacitor C is connected to the transmission line followed by a voltage ampliﬁer with gain value of 2 as required by equation (4.7). A wideband 180◦ phase shifter is also needed to realize the −1 multiplicative constant. This unit cell requires very little hardware and is simple to build. Chapter 4. Potential Hardware Realization of a UWB Beamformer 62 Figure 4.3: 2-D transfer function given by equation (4.12) for ψbf m = 10◦ . Colour scale in dB. Figure 4.4: New unit cell of the new beamformer. An array of such unit cells connected would have the desired beamforming capability. The beam characteristics of this circuit network are summarized in the following section. Chapter 4. Potential Hardware Realization of a UWB Beamformer 63 0 3 GHz 4 GHz 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz −10 −20 [dB] −30 −40 −50 −60 −70 −80 −60 −40 −20 0 20 Angle From Broadside ψ° 40 60 80 Figure 4.5: Far-ﬁeld pattern of the new transfer function in Figure 4.3 4.2.1 Beam Characteristics Figure 4.5 shows the far-ﬁeld pattern of the new beamformer tuned to ψbf m = 10◦ corresponding to the transfer function plotted in Figure 4.3, assuming the microwave networks used to realize the transfer function are ideal. There is virtually no beam squinting and the angle of the main lobe points to 10◦ for all frequencies within the UWB band. Figure 4.6 shows the far-ﬁeld pattern for the IIR beamformer also tuned to 10◦ . Comparing these two ﬁgures, it is clear that the new beamformer suﬀers much less beam squinting compared to the IIR beamformer. When the new beamformer is set to ψbf m = 40◦ , Figure 4.7 shows its transfer function with the corresponding far-ﬁeld pattern shown in Figure 4.8, where a slight beam squinting of the main lobe can be observed. Figure 4.9 shows the angle of the main lobe as a function of frequency for ψbf m = 40◦ . The main lobe squints slightly towards the broadside direction as frequency is increased. Chapter 4. Potential Hardware Realization of a UWB Beamformer 64 0 3 GHz 4 GHz 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz −10 −20 [dB] −30 −40 −50 −60 −70 −80 −60 −40 −20 0 20 Angle From Broadside ψ° 40 60 80 Figure 4.6: Far-ﬁeld pattern of the digital IIR beamformer tuned ψbf m = 10◦ corresponding to Figure 2.8. Figure 4.7: 2-D transfer function given by equation (4.12) for ψbf m = 40◦ . Colour scale in dB. Chapter 4. Potential Hardware Realization of a UWB Beamformer 65 0 3 GHz 4 GHz 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz −10 −20 [dB] −30 −40 −50 −60 −70 −80 −60 −40 −20 0 20 Angle From Broadside ψ° 40 60 80 Figure 4.8: Far-ﬁeld pattern of the new transfer function in Figure 4.7 40 39 Angle of peak [deg] 38 37 36 35 34 33 3 4 5 6 Frequency [GHz] 7 8 9 Figure 4.9: Location of the peak angle as a function of frequency for Figure 4.8 Chapter 4. Potential Hardware Realization of a UWB Beamformer 66 In practice, only a limited number of unit cells can be realized, spatially truncating the array. Figure 4.10 shows the transfer function for N = 30 elements spaced at Δx = 12 mm with ψbf m = 40◦ and capacitance C = 0.514 pF. The eﬀect of the spatial truncation is apparent in this ﬁgure, manifesting itself as side-lobes. Figure 4.11 shows the corresponding far-ﬁeld gain pattern of the beamformer in the same conﬁguration. The angle of the main lobe shifts towards the broadside direction as frequency is swept from 3 GHz to 9 GHz. The beamformer produces a variable antenna gain ranging from 15 dBi to 20 dBi across the UWB frequency band. Figure 4.10: 2-D transfer function for ψbf m = 40◦ spatially truncated to N = 30 elements. Colour scale in dB. 4.3 Evaluation of Transfer Function Given Using Sparameters Given an arbitrary set of 5-port s-parameters of an unit cell, it is desired to calculate its 2-D transfer function to calculate its beam pattern. The 5-port s-parameters of the unit Chapter 4. Potential Hardware Realization of a UWB Beamformer 67 20 3 GHz 4 GHz 5 GHz 6 GHz 7 GHz 8 GHz 9 GHz Gain [dBi] 10 0 −10 −20 −30 −80 −60 −40 −20 0 20 Angle From Broadside ψ° 40 60 80 Figure 4.11: Far-ﬁeld gain pattern of the new beamformer whose transfer function is shown in Figure 4.10 for ψbf m = 40◦ . Figure 4.12: Generic unit cell port deﬁnition. Ports 4 and 5 of one cell are connected to ports 2 and 3 of the next cell. Ports 2 and 3 of the ﬁrst cell and ports 4 and 5 of the last cell are terminated in matched loads. cell can obtained from any sources – ideal theoretical calculated s-parameters, simulated 5-port parameters from software or measured 5-port parameters. Figure 4.12 shows how + the cells are cascaded. Let vn,p denote the traveling voltage into the pth port of cell n. − Likewise, let vn,p denote the voltage traveling wave out of the pth port of cell n. For the Chapter 4. Potential Hardware Realization of a UWB Beamformer 68 ﬁrst cell, at a particular frequency, the system of equations governing the traveling waves at its nodes are written as + − vI,2 = v0,5 = 0 for the ﬁrst cell, n = 0 − + + + + + vI,2 = s21 vI,1 + s22 vI,2 + s23 vI,3 + s24 vI,4 + s25 vI,4 + − vI,3 = v0,4 = 0 for the ﬁrst cell, n = 0 − + + + + + vI,3 = s31 vI,1 + s32 vI,2 + s33 vI,3 + s34 vI,4 + s35 vI,5 + − vI,4 = vII 3 − + + + + + vI,4 = s41 vI,1 + s42 vI,2 + s43 vI,3 + s44 vI,4 + s45 vI,5 + − vI,5 = vII 2 − + + + + + vI,5 = s51 vI,1 + s52 vI,2 + s53 vI,3 + s54 vI,4 + s55 vI,5 . (4.13) where cell n = 0 index is used to denote a dummy zero-input cell at the input of the beamformer. Similarly, the equations governing the traveling voltages at the ports of cell II are + − = vI,5 vII,2 − + + + + + vII,2 = s21 vII,1 + s22 vII,2 + s23 vII,3 + s24 vII,4 + s25 vII,4 + − vII,3 = vI,4 − + + + + + vII,3 = s31 vII,1 + s32 vII,2 + s33 vII,3 + s34 vII,4 + s35 vII,5 + − vII,4 = vIII 3 set to 0 if last cell, n = N − + + + + + vII,4 = s41 vII,1 + s42 vII,2 + s43 vII,3 + s44 vII,4 + s45 vII,5 + − vII,5 = vIII 2 set to 0 if last cell, n = N − + + + + + vII,5 = s51 vII,1 + s52 vII,2 + s53 vII,3 + s54 vII,4 + s55 vII,5 . (4.14) The system of equations for each unit cell can be arranged as written above. These Chapter 4. Potential Hardware Realization of a UWB Beamformer 69 sets of equations can be arranged in a matrix form Av = B, where a matrix A contain the 5-port s-parameters values of the unit cell, v is a column vector of the traveling voltage waves in and out of the nodes of each unit cell and matrix B is a column vector containing the excitations to each unit cell. The following example shows the value of A, v and B assuming only two unit cells are connected. A MATLAB algorithm is written to generate the A, v and B vectors for the generic case when N unit cells are cascaded as shown in Figure 4.12. ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ A=⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ s22 s32 s42 s52 0 0 0 0 1 0 0 0 0 0 0 0 s23 s33 s43 s53 0 0 0 0 0 1 0 0 0 0 0 0 s24 s34 s44 s54 0 0 0 0 0 0 1 0 0 0 0 0 s25 s35 s45 s55 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 s22 s32 s42 s52 0 0 0 0 1 0 0 0 0 0 0 0 s23 s33 s43 s53 0 0 0 0 0 1 0 0 0 0 0 0 s24 s34 s44 s54 0 0 0 0 0 0 1 0 0 0 0 0 s25 s35 s45 s55 0 0 0 0 0 0 0 1 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ v=⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + vI,2 + vI,3 + vI,4 + vI,5 + vII,2 + vII,3 + vII,4 + vII,5 − vI,2 − vI,3 − vI,4 − vI,5 − vII,2 − vII,3 − vII,4 − vII,5 0 −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ (4.15) ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (4.16) Chapter 4. Potential Hardware Realization of a UWB Beamformer 70 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ B=⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ + −s21 vI,1 + −s31 vI,1 + −s41 vI,1 + −s51 vI,1 + −s21 vII,1 + −s31 vII,1 + −s41 vII,1 + −s51 vII,1 0 .. . ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (4.17) 0 + To obtain the 2-D frequency response of an array of unit cells, vI,1 (s2 ) = 1 for all frequencies, which corresponds to a spatial impulse. Matrix A and column vector B are known given the 5-port s-parameters of the unit cell and the excitation to the unit cells. v can be calculated via a matrix inversion of A given by v = A−1 B. (4.18) Hence, the traveling waves at all nodes in the circuit are known. The 2-D output is taken at port 4 for all unit cells, Y (n1 , s2 ) = vn+4 (s2 ) + vn−4 (s2 ) n ∈ {I, II, III, IV, ..., N } (4.19) where N is the total number of unit cells calculated. This calculation is repeated for each frequency of interest followed by a Fourier transform with respect to n1 in equation (4.19), resulting in the 2-D transfer function in Figure 4.10. 4.3.1 Unit Cell Simulations Previous sections have described the new beamformer with beam characteristics that are highly desirable. A potential realizable microwave circuit of one unit cell is shown in Figure 4.4. When the s-parameters of each component in the unit cell are known, the overall 5-port s-parameters of the cell can be calculated. Hence, the overall transfer func- Chapter 4. Potential Hardware Realization of a UWB Beamformer 71 tion and beam pattern can be calculated according to method described in the previous section. A simulation was set up in Agilent Advanced Design System (ADS) to compute the overall 5-port s-parameters of the unit cell when the s-parameters of each individual microwave components are known. Figure 4.13 shows the simulation setup in ADS. The required microwave components are connected in the fashion as shown. Figure 4.13: Advanced Design System (ADS) unit cell simulation setup. The s-parameters of each component in Figure 4.13 can be obtained either from ideal, simulated or measured data. Real RF microwave devices would have propagation delays which do not exist in the ideal circuit shown in Figure 4.4. Thus, when real microwave devices are employed, the delays of the signals must be matched before they are added. In the actual microwave circuit fabrication, this delay matching can be achieved by adjusting the lengths of transmission lines as necessary to match the delays of signals. Figure 4.14 shows the case when cell I has a delay of dcell seconds from the input ports 1, 2 and 3 to the output ports 4 and 5. This delay can be compensated by adding a delay (transmission line) at port 1 of the next cell as shown in this ﬁgure. By doing so, the input signals at ports 1, 2 and 3 of cell II would all arrive at the same time. A similar delay with value 2dcell can be added at port 1 for cell III to match the delay from cells I and II. Chapter 4. Potential Hardware Realization of a UWB Beamformer 72 Figure 4.14: A signal delay matching scheme for the realization the IIR beamformer in hardware. Cell I has a delay dcell which is compensated by a delay line with delay dcell at port 1 of the next cell. Four phase shifters with values φi for i ∈ {1, 2, 3, 4} are placed at proper locations in Figure 4.13 in order to compensate for the delay by the real microwave devices. For example, the ideal transfer function from port 1 to 5 is an all-pass function. However, with a real power divider, there would be delay incurred between the input and output. The purpose of φ1 phase shifter is to phase advance (or group advance the signal) the output of the divider so that the transfer function from port 1 to 5 is an all-pass function with no delay. In the actual realization of the unit cell, these delays are matched to the same amount but it is more convenient in simulation to delay match the signal to 0 seconds. Similarly for φ2 , it is phase advanced with a value of twice the delay of the power divider. These four phase shifters are implemented in ADS via an equation-based 2-port network with s21 = s12 = ejωd , where d is the required delay. This allows for the calculation of the realistic response of the system, without having to introduce the delay-compensation network discussed above for each unit cell. Instead, the delay-less cells can simply be cascaded. Port 3 in Figure 4.13 shows a balun with the phase of one output port is 180◦ out of phase with respect to the other output port. This achieves the phase inversion needed in Chapter 4. Potential Hardware Realization of a UWB Beamformer 73 equation (4.7). A voltage ampliﬁer with a gain value of A is needed at port 4 because each time the signal passes through a power divider, its voltage amplitude drops by a factor √ of 1/ 2. Hence an ampliﬁer is needed to scale the voltage back up to an appropriate √ value with A = ( 2)3 . However, the microwave implementation of the ampliﬁer was not considered in this study. Port 2 in Figure 4.13 is connected to a power divider with one output port terminated in a matched load. The purpose of this power divider is to amplitude and phase match the signal coming in from port 1 of the unit cell, as that signal has already passed through a power divider. Since the transfer functions of the power dividers are expected to be similar after fabrication, the signals can be expected to be reasonably amplitude and phase matched before they are added by another power divider. 4.4 Microwave Circuit Realization of the UWB Beamformer The initial focus of the microwave circuit realization of the beamformer was the development of the wideband microwave 3-port power dividers and baluns needed to realized the beamformer. The impact of the non-ideal characteristics of these devices on the beamformer is unknown. Hence, before real devices were employed, ideal devices were ﬁrst used in the unit cell circuit shown in Figure 4.13 to develop a sense of tolerance levels allowed in the non-ideal characteristics of real microwave devices. It was found that the dispersion of the microwave circuits needs to be kept at minimum along with the port reﬂection coeﬃcient and port isolation. These three parameters largely determine the performance of the beamformer and the quality of the corresponding beam pattern. With this in mind, the microwave components were designed with priority given to these three parameters. Wideband power dividers that operate over the entire 3 GHz to 10 GHz UWB fre- Chapter 4. Potential Hardware Realization of a UWB Beamformer 74 quency range are diﬃcult to design. It would likely require multiple stages to cover the entire frequency range. With the stringent requirements on the port reﬂection coeﬃcient and output port isolation, the design of the power divider over such wide band of frequencies is outside of scope of this thesis. However, a proof-of-concept beamformer in hardware can be designed to show the principle of operation of the beamformer at a lower centre frequency of 3 GHz and over a narrower bandwidth. Diﬀerent planar transmission line technologies were assessed for realizing the microwave combiners. It was determined that the quasi-TEM mode of a microstrip transmission line had too much dispersion, causing the beam pattern to distort signiﬁcantly. However, coplanar waveguide (CPW) transmission line have a much lower dispersion in comparison. Furthermore, its uniplanar structure allowed for easy fabrication and also facilitated the realization of a phase inversion circuit needed to realize the −1 term in equation (4.7), which is discussed shortly. Hence, CPW topology was chosen as the form to realize all microwave components. Wideband power dividers are needed for the addition operators in equation (4.7). All three ports of the power divider must have a low reﬂection coeﬃcient. Poor impedance matching would cause changes from the desired transfer function. Consider the all-pass transfer function from port 2 to 4 in Figure 4.13 as an example. If the power divider is perfectly impedance-matched at all three ports, then the transfer function from port 2 to 4 would simply be the product of each transfer function of the power dividers. If high port reﬂection coeﬃcients exist, then signals would bounce back and forth on the transmission line connecting the components, creating poles in the overall transfer function that disturbs the desired all-pass characteristic. Similarly, good port isolation between the output ports of the power divider is desired. Poor port isolation would disturb transfer function in the same manner. There are many wideband power dividers in literature that have excellent performance characteristics and they come in a variety of diﬀerent sizes and forms. Various methods Chapter 4. Potential Hardware Realization of a UWB Beamformer 75 have been developed to design power dividers with wideband features [29, 30, 31, 32], but none possess characteristics that are suitable for the needs of the beamformer. The design of a power divider is typically concerned with the port reﬂection coeﬃcient, power splitting ratio, port isolation and port phase balance and is not typically designed with dispersion as a priority, which is an important and stringent parameter required by unit cell of the beamformer. A Wilkinson power divider was chosen as the candidate for the power divider as it has many attractive properties. A good input reﬂection coeﬃcient can be obtained over a reasonably wide bandwidth. The power splitting ratio is constant over a wide bandwidth. Port isolation is expected to be excellent but over a narrower bandwidth. A good port reﬂection coeﬃcient is expected to alleviate the requirement on the port isolation. A multi-stage Wilkinson power divider can be designed but since each section is resonant, it introduces a ripple in the group delay that contributes to dispersion. A single stage Wilkinson power divider is chosen to show a proof-of-concept beamformer in hardware. An out-of-phase power divider is needed for the phase inversion required in equation (4.7). A phase inversion circuit is simple to realize by swapping signal and ground conductors in CPW, changing the signal polarity. Because both the ground plane and signal line are on the same plane, no complicated vias need to be drilled or plated. By connecting a phase inversion circuit to one of the output ports of the Wilkinson power divider, a balun can be created. The following section describes the simulated and measured data for the Wilkinson power divider and out-of-phase Wilkinson power divider. 4.4.1 Design of the In-Phase Wilkinson Power Divider Figure 4.15 shows the structure of the Wilkinson power divider with the deﬁned port numbering. The design of this Wilkinson power divider was based on [33]. This circuit consists of a CPW transmission line connected to a coupled CPW transmission line Chapter 4. Potential Hardware Realization of a UWB Beamformer 76 for the quarter-wavelength transformer section. A 100 Ω resistor is connected between the centre conductors of the output ports. The fabricated dimensions of the power divider were numerically optimized to be within fabrication limits. The gap sizes of the 50 Ω CPW and the coupled CPW section and its length were modiﬁed for minimum port reﬂection coeﬃcient and high output port isolation over the widest frequency range possible, centred at 3 GHz. The ﬁnal dimensions of the CPW Wilkinson power divider are included in Appendix B. Figure 4.16 shows the simulated s-parameters of the Wilkinson power divider as characterized by Ansoft High Frequency Structure Simulator (HFSS). Its |s21 | varies only from −3.5 dB at 1 GHz to −3.1 dB at the centre frequency to −3.9 dB at 5 GHz. |s11 |, |s22 | and |s33 | are excellent and are below −10 dB from 1 GHz to 4.5 GHz. The port isolation, s32 , has the narrowest bandwidth. Its magnitude is less than −10 dB from 1.75 GHz to 4.25 GHz. This is to be expected as the quarter-wavelength transformer is a narrow band structure and is relatively sensitive to frequency changes. Figures 4.17 and 4.18 shows the group delay and phase balance as a function of frequency. It is desired that there be minimum variation in the group delay over a wide range of frequency to minimize dispersion. Here, the group delay of both s21 and s31 only varies by about 5 ps for from 2 GHz to 4.5 GHz. This amount of dispersion was found to be tolerable as it was found previously that the tolerable dispersion was approximately 20 ps for the Wilkinson power divider. Phase balance, calculated to be ∠(s21 /s31 ), is ideally zero for all frequencies as the signals are phase-balanced. Shown in the ﬁgure, the phase variation is less than 1◦ . 4.4.2 Design of the Out-of-Phase Wilkinson Power Divider A phase inversion circuit is needed to realized the inversion in equation (4.7). The realization of microwave circuits in CPW form allows for convenient realization of a phase inversion circuit as all the conductors are on the same layer. The signal polarity Chapter 4. Potential Hardware Realization of a UWB Beamformer 77 Figure 4.15: Layout of the Wilkinson realized in CPW form. 0 −5 S−Parameters [dB] −10 −15 −20 −25 |s11| |s22| −30 |s33| |s21| −35 |s32| −40 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.16: Simulated s-parameters of the Wilkinson power divider realized in CPW form. can easily be inverted by swapping the signal and ground conductors. Figure 4.19 shows the 2-port wideband phase inversion structure [34] with deﬁned port numbering. CPW transmission lines are used at the two ports so that it can be connected with the rest of the Chapter 4. Potential Hardware Realization of a UWB Beamformer 78 X: 3 Y: 374.9 376 374 X: 3 Y: 373.7 Delay [ps] 372 370 368 366 364 Group Delay s21 Group Delay s31 362 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.17: Simulated group delay of s21 and s31 of the CPW Wilkinson power divider. 0.8 0.6 Phase Balance [Deg] 0.4 0.2 0 −0.2 −0.4 −0.6 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.18: Simulated phase balance of the CPW Wilkinson power divider. microwave components. There are two ‘X’-crossings for each of the slotline of the CPW to invert the signal polarity. A wideband quarter-wavelength radial stub is placed at the two ‘X’-crossings to create a wideband open circuit that electromagnetically separates the two ground planes to the left and right side of the radial stub. The radius of the stub is 16.5 mm. Air bridges used for the ‘X’-crossings are as shown in the inset of Figure 4.19. Chapter 4. Potential Hardware Realization of a UWB Beamformer 79 Figure 4.20 shows the simulated s-parameters of this phase inverter. The transmission coeﬃcient s21 is very constant as a function of frequency, with the magnitude ranging from −0.36 dB at 1 GHz to −1.8 dB at 5 GHz. s11 and s22 are excellent and they are below −10 dB for all frequencies from 1 GHz to 5 GHz. Note that resonance contributed by the wideband radial stubs is not centered at the design frequency of 3 GHz but instead has been lowered by lengthening the stubs to a frequency such that the dispersion of s21 is kept at a minimum at the desired frequency. The reason for doing so is because the system is dispersion sensitive and minimizing the group delay variation is more important than minimizing reﬂections. Note that the port reﬂection coeﬃcients are still very good at frequencies around 3 GHz. It is desired that the insertion phase of the phase inverter is exactly ±180◦ for all frequencies. Figure 4.22 shows the phase characteristics of the phase inverter as a function of frequency. A reference transmission line of the same length was used a phase reference as shown in Figure 4.19. The phase diﬀers from −180◦ by 10◦ from 2 GHz to 4 GHz, which is deemed as acceptable for achieving a wideband signal inversion. The diﬀerence of 10◦ is thought to be mostly contributed by the electrical length diﬀerence between the reference transmission line and the phase inverter. Figure 4.19: Layout of the wideband phase inversion circuit. Radius of the stub is 16.5 mm. Chapter 4. Potential Hardware Realization of a UWB Beamformer 80 0 X: 3 Y: −0.3577 X: 5 Y: −1.824 −5 S−Parameters [dB] −10 −15 −20 −25 −30 |s11| |s22| −35 |s21| −40 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.20: Simulated s-parameters of the phase inversion circuit. 315 310 305 Group Delay [ps] 300 295 290 285 280 275 270 265 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.21: Simulated group delay of the phase inversion circuit. This phase inverter is then attached to one of the output ports of the CPW Wilkinson power divider designed in the previous section [35]. The dimensions of the Wilkinson power divider and that of the phase inverter are exactly the same as before. Figure 4.23 shows the HFSS design of the out-of-phase Wilkinson power divider with the phase inverter attached at port 2. It is expected that the phase of port 2 is 180◦ out of phase Chapter 4. Potential Hardware Realization of a UWB Beamformer 81 −160 −165 Insertion Phase [Deg] −170 −175 −180 −185 −190 −195 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.22: Simulated phase inversion characteristics of the phase inverter. with respect to port 3. Figure 4.24 shows the simulated s-parameters of the out-of-phase Wilkinson power divider. The port reﬂection coeﬃcient |s11 | is approximately −15 dB at the centre design frequency of 3 GHz and it is below −10 dB from 1 GHz to 4 GHz. The magnitudes of s22 and s33 are very low, staying between −15 dB and −20 dB for most of the simulated frequencies. The port isolation, s32 , has the narrowest bandwidth but it is still reasonably wideband as it is below −10 dB from 1.6 GHz to 4.6 GHz. Figure 4.25 shows the simulated group delay of the out-of-phase Wilkinson power divider. Group delays are computed for s21 and s31 of the device. At the design centre frequency of 3 GHz, it has a delay of 569.5 ps for both output ports 2 and 3. For frequencies close to 3 GHz, the device has a small amount of dispersion as there are slight variations, approximately 5 ps, in both of its group delays. The large amount of group delay can be compensated but the dispersion can not. Figure 4.26 shows relative phase between the two output ports 2 and 3. In the vicinity of 3 GHz, from 2 GHz to 4 GHz, the relative phase is fairly constant. However, it consistently diﬀers by approximately 10◦ from −180◦ in that frequency range. This is thought to be attributed by the extra length of the air bridge needed for the polarity inversion. The lengths of the output ports Chapter 4. Potential Hardware Realization of a UWB Beamformer 82 were adjusted for the minimum variation in the relative phase and for it to be as close as possible to −180◦ . Figure 4.23: Layout of the out-of-phase Wilkinson power divider with the deﬁned port numbering. It has been shown that the Wilkinson power divider and the out-of-phase Wilkinson power divider have excellent performance characteristics. Operation of fairly wideband devices (1 GHz) has been demonstrated. In the next section, the simulated sparameters of these two devices are used in ADS unit cell simulation to compute its 5-port s-parameters, which can be used to determine the beam pattern of the beamformer. 4.4.3 Simulated Beam Characteristics of the Hardware Beamformer The simulated s-parameters of the Wilkinson power divider and the out-of-phase Wilkinson power divider are input into the ADS unit cell simulation for computation of the 5-port s-parameters of the unit cell. The circuit diagram of the unit cell is shown in Figure 4.13. Each square block represents a Wilkinson power divider whose s-parameters are that of the simulated ones obtained from HFSS. The phase shifters are set to values where Chapter 4. Potential Hardware Realization of a UWB Beamformer 83 0 −5 −10 S−Parameters [dB] −15 −20 −25 −30 |s11| −35 |s22| −40 |s33| |s21| −45 −50 |s32| 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.24: Simulated s-parameters of the out-of-phase Wilkinson power divider. 620 600 Delay [ps] 580 X: 3 Y: 569.5 560 540 520 Group Delay s21 Group Delay s31 500 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.25: Simulated group delay of the out-of-phase Wilkinson power divider. the phases of the signals are advanced such that there is no net delay. For example, phase shifter φ1 is a 2-port equation based s-parameter block with s21 = s12 = ejω374×10 where ω is frequency in radians. Phase shifter φ2 has s21 = s12 = ejω2(374×10 −12 ) −12 , , repre- senting a phase advancement of 2 times that of a single Wilkinson power divider. Phase shifter φ3 has a s21 = s12 = ejω(374+569.5)×10 −12 . The ampliﬁer with a gain of A is set to Chapter 4. Potential Hardware Realization of a UWB Beamformer 84 −150 −155 Phase Balance [Deg] −160 −165 −170 −175 −180 −185 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.26: Simulated phase balance between the output ports of the out-of-phase Wilkinson power divider. √ ( 2)3 to compensate for the voltage attenation of the signal due to the Wilkinson power dividers. For beamformer set to ψbf m = 40◦ corresponding to the ideal shunt capacitance C = 0.514 pF, the 5-port s-parameters of the unit cell are calculated. Figure 4.27 shows the ideal and simulated magnitude response of transfer function T F2 (s2 ) from 1 GHz to 5 GHz. The ideal transfer function T F2 (s2 ) is given by equation (4.7). The s43 of the simulated unit cell is taken to be the simulated transfer function. Around the design frequency of 3 GHz, the simulated |T F2 | is very close to the ideal one, ﬂuctuating only within 2 dB of the ideal curve even with the simulated s-parameters of the Wilkinson power dividers. Figure 4.28 shows the ideal and simulated phase responses of T F2 (s2 ). The phase between the ideal and simulated cases closely matched with each other around the design frequency. The simulated T F2 (s2 ) has frequencies with a magnitude response greater than unity at some frequencies. At those frequencies, the impulse response of the beamformer is not stable. It is easy to see that as the more unit cells are cascaded, the signal will get Chapter 4. Potential Hardware Realization of a UWB Beamformer 85 6 4 2 |TF2| [dB] 0 −2 −4 −6 −8 −10 −12 −14 Ideal Simulated 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.27: Magnitude of ideal transfer function T F2 (s2 ) and simulated one obtained from unit cell simulation. 80 Ideal Simulated 60 40 ∠ TF2 [Deg] 20 0 −20 −40 −60 −80 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.28: Phase of ideal transfer function T F2 (s2 ) and simulated one obtained from unit cell simulation. ampliﬁed cell after cell, leading to instability. Hence, it is not meaningful to calculate the response at those unstable frequencies and only the stable frequencies (2.5 GHz to 3.5 GHz) are calculated. Figure 4.29 shows the 2-D transfer function of the beamformer in the frequency range from 2.5 GHz to 3.5 GHz for ψbf m = 40◦ and N = 15, using the Chapter 4. Potential Hardware Realization of a UWB Beamformer 86 5-port s-parameters of the unit cell. This ﬁgure shows a good beam pattern whose main lobe is centred at approximately 40◦ across a reasonably wide bandwidth of 1 GHz. A slight variation in the peak the main lobe can be observed due to the variations of |T F2 | across frequency, shown in Figure 4.27. To evaluate this gain variation, Figure 4.30 shows the corresponding gain beam pattern, it oﬀers a high gain between 11 dBi to 12.7 dBi over 1 GHz of bandwidth. Figure 4.29: 2-D far-ﬁeld pattern from 2.5 GHz to 3.5 GHz of the new beamformer with simulated s-parameters of the in-phase and out-of-phase Wilkinson power dividers. Colour scale in dB. Since the simulated response oﬀers high gain over a reasonably wide bandwidth using the simulated s-parameters of the in-phase and out-of-phase Wilkinson power dividers, the next step is to evaluate whether real Wilkinson power dividers have suﬃciently good performance to achieve beamforming. The next section evaluates the performance of the beamformer with fabricated Wilkinson power dividers to assess their feasibility of the hardware UWB beamformer. Chapter 4. Potential Hardware Realization of a UWB Beamformer 87 15 2.5 GHz 3 GHz 3.5 GHz 10 Gain [dBi] 5 0 −5 −10 −15 −20 −80 −60 −40 −20 0 20 Angle From Broadside ψ° 40 60 80 Figure 4.30: Beam pattern for various frequencies in Figure 4.29. 4.4.4 Fabrication and Measurement of Wilkinson Power Dividers The simulated s-parameters of the in-phase and out-of-phase Wilkinson power dividers oﬀer promising performance. However, the beam pattern obtained in the previous section was only based on the simulated s-parameters of the two power dividers. In this section, a Wilkinson power divider is fabricated and its s-parameters are measured. The Wilkinson power divider was fabricated using a milling machine to produce a desired metal pattern. It was fabricated on Rogers RO4360 substrate with a dielectric constant of 6.15. Three female SMA connectors were soldered at the ports of the power divider so that its s-parameters can be measured using a PNA. A surface mount chip resistor of 100 Ω was soldered between the output conductors of the power divider as the isolation resistor. There were four air bridges soldered across the two ground planes at the points of discontinuities to suppress the unwanted slotline mode from propagating on the CPW transmission lines. Figure 4.31 shows the fabricated Wilkinson power divider. The port numbering deﬁnitions are the same in both simulated and measured case. Figure 4.32 shows the simulated and measured s-parameters of the Wilkinson power Chapter 4. Potential Hardware Realization of a UWB Beamformer 88 divider, which matches very well. The measured |s21 | and |s31 | are slightly lower compare to the simulated values as there are losses in the substrate in the fabricated device. The higher the frequency, the more lossy the CPW transmission lines are. However, it isn’t until 5 GHz that the loss is suﬃciently large to reduce |s21 | by 2 dB. Figure 4.31: Fabricated Wilkinson power divider. Figure 4.33 shows the measured group delay of the device to check its dispersion characteristics. The group delay is computed for both s21 and s31 . At the centre frequency of 3 GHz, the group delay is 447.9 ps and varies by 25 ps as the frequency deviates ±1 GHz away from the design frequency. 70 ps of delay is added in the simulated group delay to account for the extra length of the SMA connectors soldered. This is not a source of concern as it simply introduces an extra delay shifting the group delay higher and it does not contribute to dispersion. Overall, the device has good dispersion characteristics in simulations and measurements. Figure 4.34 shows the measured phase balance between the two output ports of the power divider. The phase balance is calculated to be ∠(s21 /s31 ) at each frequency. The Chapter 4. Potential Hardware Realization of a UWB Beamformer 89 0 −5 S−Parameters [dB] −10 −15 −20 −25 |s11| |s22| −30 |s33| |s21| −35 |s32| −40 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.32: Measured (solid) and simulated (dashed) s-parameters of the Wilkinson power divider. 520 500 480 X: 3.002 Y: 447.9 Delay [ps] 460 440 420 400 380 Group Delay s21 360 Group Delay s31 340 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.33: Measured (solid) and simulated (dashed) group delay of the Wilkinson power divider. phase balance is within 2.4◦ of the desired value over the frequency range of interest. Chapter 4. Potential Hardware Realization of a UWB Beamformer 90 4.4.5 Fabrication and Measurement of Out-Of-Phase Wilkinson Power Dividers Figure 4.35 shows the fabricated out-of-phase Wilkinson power divider. This out-of-phase Wilkinson power divider was also fabricated on Rogers RO4360 substrate. The phase inverter was attached at port 2 to invert the phase of the signal at this port relative to port 3, creating a balun. The same 100 Ω isolation resistor was soldered between the conductors at port 2 and port 3. Figure 4.36 shows the simulated and the measured s-parameters of the out-of-phase Wilkinson power divider. Overall, the s-parameters between the simulated and measured match very well. The measured |s11 | has a better performance than the simulated one. In addition, the measured isolation bandwidth, s32 , is better than the simulated bandwidth. The measured |s21 | is slightly more lossy than the simulated one due to the loss in the substrate. The measured |s22 | has a worse performance than |s33 | as the phase inverter circuit is connected at port 2. Figure 4.37 shows the measured group delay of s21 and s31 of the out-of-phase Wilkin- 2.5 Measured Simulated 2 Phase Balance [Deg] 1.5 1 0.5 0 −0.5 −1 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.34: Measured (solid) and simulated (dashed) phase balance of the Wilkinson power divider. Chapter 4. Potential Hardware Realization of a UWB Beamformer 91 Figure 4.35: Fabricated out-of-phase Wilkinson power divider. 0 −5 −10 S−Parameters [dB] −15 −20 −25 −30 |s11| −35 |s22| −40 |s33| |s21| −45 −50 |s32| 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.36: Measured (solid) and simulated (dashed) s-parameters of the out-of-phase Wilkinson power divider. son power divider. Both curves match very well near the design frequency of 3 GHz with a group delay of approximately 600 ps. As in the earlier case, the simulated group delay is oﬀset to match with the measured group delay. The fabricated out-of-phase power Chapter 4. Potential Hardware Realization of a UWB Beamformer 92 divider is slightly more dispersive compared to the simulated one as there are fabrication imperfections. The measured group delay has 20 ps of variance from approximately 2 GHz to 3.5 GHz. The beamformer is expected to have the best performance within this frequency range. Figure 4.38 shows the measured phase balance of this out-of-phase Wilkinson power divider. The ideal phase balance between output port 2 and port 3 is −180◦ across all frequencies. Here, the measured performance is close to that of the ideal phase balance from approximately 2 GHz to 4 GHz where it is relatively ﬂat. It is only about 8.5◦ away from the ideal −180◦ in this frequency range. This phase balance error is thought to be contributed mostly by the air bridges soldered in the phase inverter circuit at port 2. The air bridges were soldered to be as close to the ground plane as possible without making contact with any other metal. However, there was still a gap left contributing to the extra length that the signal must travel through. 700 680 660 Delay [ps] 640 620 600 580 560 540 Group Delay s21 520 500 Group Delay s31 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.37: Measured (solid) and simulated (dashed) group delay of the out-of-phase Wilkinson power divider. Chapter 4. Potential Hardware Realization of a UWB Beamformer 93 −150 Measured Simulated −155 Phase Balance [Deg] −160 −165 −170 −175 −180 −185 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.38: Measured (solid) and simulated (dashed) phase balance of the out-of-phase Wilkinson power divider. 4.4.6 Calculated Beam Pattern Using Real Microwave Devices The simulated and measured performance of both the in-phase and out-of-phase Wilkinson power dividers match very well with simulation results. One can expect that the beamformer pattern obtained using the measured s-parameters of the two power dividers to have similar characteristics as the one obtained by using simulated s-parameters. The ADS unit cell simulation can compute the 5-port s-parameters given the measured sparameters of the two power dividers. Then, the beam pattern can be calculated for any number of unit cells in cascade. Figures 4.41 and 4.42 show the magnitude and phase of T F2 (s2 ) obtained from the ADS unit cell simulation when the measured s-parameters of the power dividers are used instead of simulated ones. |T F2 (s2 )| matches very well with the ideal one from approximately 2.5 GHz to 4 GHz where it is the most ﬂat. For frequencies outside of this band, there are peaks in the magnitude of the transfer function that are greater than unity. Those frequencies do not produce stable operation of the beamformer, as discussed earlier, and are omitted from the frequency range considered for this proof-of- Chapter 4. Potential Hardware Realization of a UWB Beamformer 94 Figure 4.39: 2-D far-ﬁeld pattern of the beamformer using real in-phase and out-of-phase Wilkinson power dividers. Colour scale in dB. concept calculation. The phase of T F2 (s2 ) also matches closely with the ideal one near the design frequency of 3 GHz shown in Figure 4.42. Figure 4.39 shows the 2-D far ﬁeld-pattern of the beamformer using the measured sparameters of the two Wilkinson power dividers. This 2-D far-ﬁeld pattern was calculated for ψbf m = 40◦ and N = 15 unit cells. A highly directive beam is clearly visible in this ﬁgure. Figure 4.40 shows the gain beam pattern of this beamformer for various frequencies. It oﬀers a very highly directive beam ranging from 10.6 dBi to 12.9 dBi, aimed at approximately ψbf m = 40◦ over a 1.5 GHz bandwidth. 4.4.7 Feasibility Discussion This proof-of-concept design has shown that an UWB beamformer could be realized by using real physical components to achieve a highly directive tunable beam pattern and it Chapter 4. Potential Hardware Realization of a UWB Beamformer 95 15 2.5 GHz 3 GHz 3.5 GHz 4 GHz 10 Gain [dBi] 5 0 −5 −10 −15 −20 −80 −60 −40 −20 0 20 Angle From Broadside ψ° 40 60 80 Figure 4.40: Beam pattern for various frequencies of the beamformer with real in-phase and out-of-phase Wilkinson power dividers. 10 8 6 |TF2| [dB] 4 2 0 −2 −4 −6 −8 Ideal Simulated 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.41: Magnitude of ideal transfer function T F2 (s2 ) versus the one obtained from ADS unit cell simulation using real in-phase and out-of-phase Wilkinson power divider. could potentially be used as a part of a real UWB wireless communication system. The proof-of-concept beamformer has a good performance over about a 1.5 GHz bandwidth from 2.5 GHz to approximately 4 GHz. Although it does not cover the entire UWB Chapter 4. Potential Hardware Realization of a UWB Beamformer 96 100 Ideal Simulated 80 60 ∠ TF2 [Deg] 40 20 0 −20 −40 −60 −80 −100 1 1.5 2 2.5 3 3.5 Frequency [GHz] 4 4.5 5 Figure 4.42: Phase of ideal transfer function 2 versus the one obtained from ADS unit cell simulation using real in-phase and out-of-phase Wilkinson power divider. frequency range, it is still quite wideband. It meets the FCC deﬁnition of UWB transmission as it exceeds the absolute bandwidth of 500 MHz and the fractional bandwidth of 20%. Throughout the design process of the proof-of-concept beamformer, some design considerations have presented themselves and they are summarized here. 1. Wideband power dividers and baluns that operate over the entire UWB frequency range need to have an excellent performance in order for the beamformer to operate over a such wide frequency range. Furthermore, these devices must be designed with dispersion as a priority in addition to keeping port reﬂection coeﬃcient low and output port isolation high. Designing such devices is very challenging. 2. The signal propagation delay needs to be matched within each unit cell in order for the signals to be processed properly. This means that the lengths of the transmission lines need to be properly designed. In addition, the inputs of the unit cells (port 1) must be properly delayed to compensate the delays of the previous cells, as shown in Figure 4.14. Hence an extra piece of transmission line of appropriate length is needed at the input of each unit cell. Chapter 4. Potential Hardware Realization of a UWB Beamformer 97 3. Two voltage ampliﬁers are needed to scale signal at the two nodes shown in Fig√ ure 4.13 of values 2 and ( 2)3 . While these gain values can be easily achieved via an active ampliﬁer, their dispersion characteristics must be controlled. Either the dispersion of the ampliﬁers needs to be minimized or their dispersion must be compensated by microwave circuits. The dispersion of an UWB low-noise ampliﬁer was measured to gather a sense of the dispersion characteristics of tpyical UWB ampliﬁers in general. It showed a group delay variance of about 25 ps over the UWB band, which is potentially tolerable by the analog beamformer. 4. A varactor diode can be used as the variable capacitor needed to tune ψbf m to a desired angle, shown in Figure 4.13. A control voltage line must be routed to bias the varactor in order for it to have the desired capacitance. A DC chock circuit must be deployed so that the voltage bias line does not interfere with the RF signal path. The non-ideal characteristics of a varactor diode is expect to distort the beam pattern as the device inductance at high frequencies could be considerable. 5. Figure 4.43 shows the eﬀect capacitance needed Cef f , which includes any parasitic capacitance due to the device itself, soldering of its leads, etc. as a function of the angle that the beamformer is set to ψbf m . The required eﬀective capacitance ranges from 0 pF (open circuit) to almost 1 pF. Depending on the manufacturing process of the varactor diodes, such a small capacitance could be diﬃcult to achieve as the parasitic capacitance would increase the eﬀective capacitance. The eﬀective capacitance as a function of the control voltage must be characterized. Chapter 4. Potential Hardware Realization of a UWB Beamformer 98 0.8 0.7 0.6 Ceff [pF] 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 ψ°bfm Figure 4.43: Cef f as a function of ψbf m . 80 Chapter 5 Conclusions UWB is a fast growing technology that has attracted much research eﬀorts as it is applicable for a wide variety of applications. In wireless communications in particular, UWB signaling scheme oﬀers a promising potential for extremely high data rates due to the extremely wide bandwidth available for signal transmission. However, the transmit power is restricted to a very low level to minimize interference with many existing communication systems that already operate within the UWB frequency band. This creates a challenging research problem because the received signal power could be on the same order of magnitude as the power of interfering signal. Furthermore, multiple UWB users could be transmitting broadband signals in the same channel that create more interference making signal recovery even more diﬃcult. The multipath in the channel further degrades the quality of the received signal as multiple copies of the transmitted signal, all with diﬀerent amplitudes and phases are added. UWB beamformers provide a ﬁltering process based on the location of the transmitter, enhancing the desired signal arriving from a desired direction and attenuate interference signals from other directions. The work presented in this thesis has shown that UWB beamformers are eﬀective tools in combating interference and multipath issues. In this thesis, an UWB IIR beamformer has been characterized in a real wireless UWB 99 Chapter 5. Conclusions 100 channel. The beamformer was characterized in three diﬀerent methods – far-ﬁeld pattern with real array of UWB antennas, interference rejection capability and Monte Carlo BER simulations. In the far-ﬁeld pattern measurement of the beamformer, it was shown that with real UWB antennas as the receiving array, the beam pattern is very robust even in the worse case antenna coupling scenario. The measured far-ﬁeld pattern was very close to that of the ideal pattern in all cases. In the interference rejection experiment, it was shown that the beamformer provided clear spatial discrimination based on the angle of arrival of the received signal, clearing demonstrating its spatial selectivity in a real wireless channel. The BER simulations have clearly shown the interference suppression capability that the beamformer can provide in a real UWB communication system. The BER ﬂoor was lowered by several orders of magnitude in many cases. Diﬀerent beamformer conﬁgurations were tested to assess the impact of the beamformer’s parameters. Limitations of the beamformer were also shown. The beamformer performance degrades when it is scanned to large angles from broadside. It was shown that this undesired eﬀect can be mitigated by pre-tuning the beamformer to a diﬀerent angle. The design of a proof-of-concept hardware beamformer was proposed. This hardware beamformer processes the signal in the continuous-domain and does not have the computational complexity associated with high-speed digital signal processing. Real physical microwave components were fabricated in order to assess the feasibility of the hardware beamformer. A few design considerations resulted from design processes of the hardware beamformer – the beamformer placed rather stringent requirements on the dispersion, port reﬂection coeﬃcient and port isolation of the combining devices used in the beamformer network. Despite such stringent requirements, it was shown that the proof-of-concept beamformer had a good performance over 1.5 GHz of bandwidth with a relatively narrowband Wilkinson power dividers. This showed that the beamformer was potentially feasible to realize in hardware and could potentially be part of a real UWB wireless communication system. Chapter 5. Conclusions 5.1 101 Contributions There are two major contributions listed below have resulted from this thesis: • L. Liang and S. V. Hum, “Experimental characterization of UWB beamformers based on multidimensional beam ﬁlters (in press),”, IEEE Transaction on Antennas and Propagation, vol. 59, no. 1, January 2011. • L. Liang and S. V. Hum, “Experimental Veriﬁcation of an Adaptive UWB Beamformer Based on Multidimensional Filtering in a Real Radio Channel,” IEEE Antennas and Propagation Society International Symposium (AP-S 2010), July 2010. 5.2 Future Work There are lot of aspects of the hardware beamformer that remain as future work. They are outlined below. 1. In the derivation of the beamformer only a one-dimensional physical array size was considered. This derivation can be extended to include another dimension to allow for a 2-D physical array as the receiving array. Such a beam pattern would then be a steerable pattern in all 3 dimensions. However, the complexity of the beamformer would be increased as a more sophisticated interconnection between the networks would be required, placing even greater constraints on the design of those networks. 2. Although the Wilkinson power divider provided an excellent performance over a reasonably wide bandwidth, new UWB power dividers must be designed in order for the beamformer to operate over the entire UWB frequency range. A balun must also be designed to provide a balanced output signals over UWB frequencies. Such wideband microwave devices are not trivial to design and were beyond the scope of this MASc thesis. Since it was found that the dispersion plays an important role in the performance of the beamformer, the dispersion characteristics must be Chapter 5. Conclusions 102 a design priority in all the microwave components used in addition to the low port reﬂection coeﬃcient and high output port isolation. 3. A variable capacitor must be used in the realization of the hardware beamformer as an ideal low-pass RC network is used in this thesis. A varactor diode is a good candidate to generate the variable capacitance needed in the microwave circuit as it is economically aﬀordable. MEMs capacitors can be used as an alternative but are relatively expensive and immature compared to varactor diodes. However, MEMs capacitors are much more linear. 4. There are two voltage ampliﬁers needed in the microwave realization of the unit cell. In the realization of the unit cell, these voltage ampliﬁers must be carefully characterized for their gain and dispersion, since both could be function of frequency. Since the bandwidth of the UWB frequencies are very wide, the gain and dispersion characteristics could vary signiﬁcantly from one end of the spectrum to another. A method to manage this must be developed. 5. A fabrication of an unit cell with the physical microwave components, varactor diode and ampliﬁers is needed to measure its 5-port s-parameters, which can be used to calculate the corresponding beam pattern of the beamformer and assess its tunability over a wide frequency range. An array of unit cells can be fabricated and cascaded to realize a full implementation of the UWB hardware beamformer. Appendix A Fabrication and Measurements of BAVAs A.1 Fabrication of BAVAs A Rogers RT/duroid 6002 high frequency laminate (r = 2.94, tan δ = 0.0012 @ 10 GHz, thickness h = 1.524 mm) was used as the substrate in the fabrication of the BAVA. This substrate has very low loss and it is well-suited for the milling process where the copper is removed from the substrates. The BAVAs were constructed in two pieces as shown in Figure A.1. On the bottom piece (Piece 1), there are two layers of metal shown here in red and blue on the opposite side of the substrate. The top piece (Piece 2) is to be aligned and bonded to the bottom piece via a bonding ﬁlm placed in between the two substrates. A multipress machine was used to during this bonding process in which the pressure and temperature was controlled to the speciﬁed values required by the bonding speciﬁcations. The bonding procedure is outline below. 1. Apply constant pressure of 138 N/cm2 . 2. Increase temperature to 210◦ C for 30 minutes. 103 Appendix A. Fabrication and Measurements of BAVAs 104 3. Decrease temperature to below 70◦ C for curing. 4. Release pressure. Figure A.1: BAVA fabricated in two piece as shown. The exponential antenna patterns on each of the metal layers were fabricated via a combination of etching and milling processes. The etching process is a chemical process where the copper is removed using an acid solution. The metal pattern is produced by placing a photoresistive mask with the same shape as the desired metal pattern but the mask material is immune to the acid protecting the copper from dissolving the copper. The etching process for copper removal and it was used to remove large areas of copper. However, the etching process does not allow an accurate alignment between metal layers. Hence the ﬁner details of the metal pattern were produced by a milling machine after the large amount of copper was removed. This allows for rapid fabrication while maintaining the same high-precision fabrication oﬀered by the milling machine. The combination of etching and milling process is described below. 1. A course etching mask is created from the antenna design. The course mask only has features and contours that approximate the overall shape of the actual design. 2. A photoresist was laminated on substrate. Appendix A. Fabrication and Measurements of BAVAs 105 3. Ultraviolet was shone over the entire substrate which causes the photoresist to harden. The remaining photoresist was washed away. 4. An acid washer then dissolves the unprotected copper leaving the desired metal pattern. 5. Since etching process removed large areas of copper, the design was placed under a milling machine to mill out the remaining ﬁner details of the metal pattern. Alignment holes wee made in the course mask such that when the design was placed on the milling machine, the machine can use the alignment holes for positioning references. A.2 Measurement of BAVAs Four BAVAs were fabricated using the same process and their characteristics were measured then compared to that of the simulated. The measured characteristics were: • s11 • Absolute gain in the E-plane and H-plane. • 4-port s-parameters in an array conﬁguration. Figure A.2 through Figure A.7 shows the measured s11 of all fabricated antennas and measured 4-port s-parameters of the BAVAs arranged in a linear array with element spacing of 12 mm, and the E and H plane antenna pattern cuts of the antennas. Note that this element spacing produces the highest coupling values as the antennas elements are at the smallest. 106 Appendix A. Fabrication and Measurements of BAVAs 0 −5 −10 −15 |s11| [dB] −20 −25 −30 −35 −40 −45 −50 Antenna 1 Antenna 2 Antenna 3 Antenna 4 Simulated 2 4 6 8 Frequency [GHz] 10 12 Figure A.2: |s11 | of all fabricated antennas and that of the simulated. 107 Appendix A. Fabrication and Measurements of BAVAs 0 −5 −10 S−Parameters [dB] −15 −20 −25 −30 −35 |s21| −40 |s31| |s41| −45 −50 |s32| 2 3 4 5 6 7 Frequency [GHz] 8 9 10 8 9 10 (a) 0 −5 −10 S−Parameters [dB] −15 −20 −25 −30 −35 −40 |s22| |s33| −45 −50 |s44| 2 3 4 5 6 7 Frequency [GHz] (b) Figure A.3: Measured (solid) and simulated (dashed) 4-port s-parameters of the BAVA array with element spacing 12 mm. 108 Appendix A. Fabrication and Measurements of BAVAs 2 Ghz 2.5 Ghz −10 −100 0 0 −10 −20 100 10 Gain [dBi] 0 −20 −100 ° −10 0 ψ° 5 Ghz −10 −100 0 −10 −100 ° 0 100 −20 Gain [dBi] −10 −100 0 ψ° 100 −100 0 100 ψ Simulated Directivity Measured Gain 0 −10 −20 100 ° 10 0 0 ψ° 6 Ghz −10 ψ 7 Ghz 10 −100 0 ° ψ 6.5 Ghz Gain [dBi] −10 10 0 −20 100 0 −20 0 100 ° ψ 5.5 Ghz Gain [dBi] Gain [dBi] Gain [dBi] −10 100 10 10 0 0 ψ 4.5 Ghz 0 −20 100 10 −100 −100 ° Gain [dBi] Gain [dBi] Gain [dBi] 0 −20 −20 100 10 −100 −10 ψ 4 Ghz 10 −20 0 0 ° ψ 3.5 Ghz −20 3 Ghz 10 Gain [dBi] Gain [dBi] 10 −100 0 ψ° 100 Figure A.4: E-plane cut for antenna 1. 109 Appendix A. Fabrication and Measurements of BAVAs 2 Ghz 2.5 Ghz −10 −100 −10 −100 0 ψ° 5 Ghz −10 −100 −10 −100 Gain [dBi] −10 −100 0 ψ° 100 −100 0 ψ° 6 Ghz 100 −100 0 ψ° 100 10 −10 −100 0 ψ° 7 Ghz 100 0 −10 −20 Simulated Directivity Measured Gain 0 −10 −20 0 100 ψ° 4.5 Ghz −10 10 0 −100 0 −20 0 100 ψ° 5.5 Ghz 0 −20 0 100 ψ° 6.5 Ghz −10 10 Gain [dBi] Gain [dBi] Gain [dBi] 0 0 −20 100 10 10 Gain [dBi] 0 ψ° 4 Ghz 0 −20 100 10 −20 −100 Gain [dBi] 0 −20 −10 10 Gain [dBi] Gain [dBi] 10 −20 0 −20 0 100 ψ° 3.5 Ghz 10 Gain [dBi] 0 −20 3 Ghz 10 Gain [dBi] Gain [dBi] 10 −100 0 ψ° 100 Figure A.5: H-plane cut for antenna 1. 110 Appendix A. Fabrication and Measurements of BAVAs 2 Ghz 2.5 Ghz −10 −100 −10 −100 0 ψ° 5 Ghz −10 −100 −10 −100 −100 0 100 ψ° 4.5 Ghz 0 −10 −20 0 100 ° ψ 5.5 Ghz −100 0 ψ° 6 Ghz 100 −100 0 ψ° 100 10 0 −10 −20 0 100 ψ° 6.5 Ghz −10 10 Gain [dBi] Gain [dBi] Gain [dBi] 0 0 −20 100 10 −100 0 ψ° 7 Ghz 100 0 −10 −20 10 Gain [dBi] 10 Gain [dBi] 0 ψ° 4 Ghz 0 −20 100 10 0 −10 −20 −100 Gain [dBi] 0 −20 −10 10 Gain [dBi] Gain [dBi] 10 −20 0 −20 0 100 ψ° 3.5 Ghz 10 Gain [dBi] 0 −20 3 Ghz 10 Gain [dBi] Gain [dBi] 10 −100 0 ψ° 100 Antenna 1 Antenna 2 Antenna 3 Antenna 4 0 −10 −20 −100 0 ψ° 100 Figure A.6: E-plane cut for all fabricated antennas. 111 Appendix A. Fabrication and Measurements of BAVAs 2 Ghz 2.5 Ghz −10 −100 −10 −100 0 ψ° 5 Ghz −10 −100 −10 −100 −100 0 100 ψ° 4.5 Ghz 0 −10 −20 0 100 ° ψ 5.5 Ghz −100 0 ψ° 6 Ghz 100 −100 0 ψ° 100 10 0 −10 −20 0 100 ψ° 6.5 Ghz −10 10 Gain [dBi] Gain [dBi] Gain [dBi] 0 0 −20 100 10 −100 0 ψ° 7 Ghz 100 0 −10 −20 10 Gain [dBi] 10 Gain [dBi] 0 ψ° 4 Ghz 0 −20 100 10 0 −10 −20 −100 Gain [dBi] 0 −20 −10 10 Gain [dBi] Gain [dBi] 10 −20 0 −20 0 100 ψ° 3.5 Ghz 10 Gain [dBi] 0 −20 3 Ghz 10 Gain [dBi] Gain [dBi] 10 −100 0 ψ° 100 Antenna 1 Antenna 2 Antenna 3 Antenna 4 0 −10 −20 −100 0 ψ° 100 Figure A.7: H-plane cut for all fabricated antennas. Appendix B CPW Wilkinson Power Divider Dimensions The fabricated Wilkinson power divider is shown in Figure B.1 along with its cross section views. The dimensions are deﬁned in Table B.1. (a) (b) Figure B.1: (a) Wilkinson power divider with (b) cross section views. Dimension h G50 G70 W50 W70 Value 1.524 0.155 0.155 0.936 1.6 L70 S 15.196 0.8 Table B.1: Fabricated CPW Wilkinson power divider dimensions in mm. 112 Bibliography [1] L. Yang and G. B. Giannakis, “Ultra-wideband communications: an idea whose time has come,” IEEE Signal Process. Mag., vol. 21, no. 6, pp. 26–54, Nov. 2004. [2] J. Bourqui, M. Okoniewski, and E. C. Fear, “Balanced antipodal Vivaldi antenna for breast cancer detection,” in Europ. Conf. Antennas Propag., Nov. 2007, pp. 1–5. [3] S. V. Hum, H. L. P. A. Madanayake, and L. T. Bruton, “UWB beamforming using 2-D beam digital ﬁlters,” IEEE Trans. Antennas Propag., vol. 57, no. 3, pp. 804–807, Mar. 2009. [4] S. Barker and G. M. Rebeiz, “Distributed MEMS true-time delay phase shifters and wide-band switches,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 11, pp. 1881–1890, Nov. 1998. [5] E. Adabi and A. M. Niknejad, “Broadband variable passive delay elements based on an inductance multiplication technique,” in Radio Freq. Integr. Circ. Symp., Apr. 2008, pp. 445 –448. [6] T.-S. Chu, J. Roderick, and H. Hashemi, “An integrated ultra-wideband timed array receiver in 0.13 μm CMOS using a path-sharing true time delay architecture,” IEEE J. Solid-State Circuits, vol. 42, no. 12, pp. 2834–2850, Dec. 2007. 113 Bibliography 114 [7] M. Y. Frankel, P. J. Matthews, and R. D. Esman, “Fiber-optic true time steering of an ultrawide-band receive array,” IEEE Trans. Microw. Theory Tech., vol. 45, no. 8, pp. 1522–1526, Aug. 1997. [8] D. B. Ward, R. A. Kennedy, and R. C. Williamson, “Antenna array pattern synthesis via convex optimization,” J. of Acoust. Soc. of America, vol. 97, pp. 1023–1034, Feb. 1995. [9] W. Liu and S. Weiss, “Design of frequency invariant beamformers for broadband arrays,” IEEE Trans. Signal Process., vol. 56, no. 2, pp. 855–860, Feb. 2008. [10] D. B. Ward, R. A. Kennedy, and R. C. Williamson, “FIR ﬁlter design for frequency invariant beamformers,” IEEE Signal Process. Lett., vol. 3, no. 3, pp. 69–71, Mar. 1996. [11] D. Scholnik and J. Coleman, “Optimal design of wideband array patterns,” in Record of IEEE Int. Radar Conf., 2000, pp. 172 –177. [12] H. Lebret and S. Boyd, “Antenna array pattern synthesis via convex optimization,” IEEE Trans. Signal Process., vol. 45, no. 3, pp. 526 –532, Mar. 1997. [13] W. Liu, R. Wu, and R. Langley, “Design and analysis of broadband beamspace adaptive arrays,” IEEE Trans. Antennas Propag., vol. 55, no. 12, pp. 3413 –3420, Dec. 2007. [14] T. Sekiguchi and Y. Karasawa, “Wideband beamspace adaptive array utilizing FIR fan ﬁlters for multibeam forming,” IEEE Trans. Signal Process., vol. 48, no. 1, pp. 277 –284, Jan. 2000. [15] K. Nishikawa, T. Yamamoto, K. Oto, and T. Kanamori, “Wideband beamforming using fan ﬁlter,” in Proc. IEEE Int. Symp. on Circuits and Syst., vol. 2, May 1992, pp. 533 –536 vol.2. 115 Bibliography [16] L. Bruton and N. Bartley, “Highly selective three-dimensional recursive beam ﬁlters using intersecting resonant planes,” IEEE Trans. Circuits Syst., vol. 30, no. 3, pp. 190 – 193, Mar. 1983. [17] L. T. Bruton, “Three-dimensional cone ﬁlter banks,” IEEE Trans. Circuits Syst. I, vol. 50, no. 2, pp. 208–216, Feb. 2003. [18] A. V. Oppenheim and R. W. Schafer, Discrete-time signal processing. Prentice Hall, 2006. [19] T. S. Rappaport, Wireless communications principle and practice. Prentice Hall, 1996. [20] G. Janssen and J. Vriens, “High resolution coherent radio channel measurements using direct sequence spread spectrum modulation,” in Proc. Electrotechnical Conf., May 1991, pp. 720–727 vol.1. [21] D. Cassioli and A. Durantini, “A time-domain propagation model of the UWB indoor channel in the FCC-compliant band 3.6 – 6 GHz based on PN-sequence channel measurements,” in 59th Vehicular Technol. Conf., vol. 1, May 2004, pp. 213 – 217 vol.1. [22] W. Ciccognani, A. Durantini, and D. Cassioli, “Time domain propagation measurements of the UWB indoor channel using PN-sequence in the FCC-compliant band 3.6 – 6 GHz,” IEEE Trans. Antennas Propag., vol. 53, no. 4, pp. 1542 – 1549, Apr. 2005. [23] S. Howard and K. Pahlavan, “Measurement and analysis of the indoor radio channel in the frequency domain,” IEEE Trans. Instrum. Meas., vol. 39, no. 5, pp. 751 –755, Oct. 1990. Bibliography 116 [24] V. Hovinen, M. Hamalainen, and T. Patsi, “Ultra wideband indoor radio channel models: preliminary results,” in IEEE Conf. on Ultra-wideband Syst. and Technol., 2002, pp. 75 – 79. [25] J. Kunisch and J. Pamp, “Measurement results and modeling aspects for the UWB radio channel,” in IEEE Conf. on Ultra-wideband Syst. and Technol., 2002, pp. 19 – 23. [26] W. Wiesbeck, G. Adamiuk, and C. Sturm, “Basic properties and design principles of UWB antennas,” Proc. of the IEEE, vol. 97, no. 2, pp. 372 –385, Feb. 2009. [27] S. Rapuano, P. Daponte, E. Balestrieri, L. De Vito, S. Tilden, S. Max, and J. Blair, “ADC parameters and characteristics,” IEEE Trans. Instrum. Meas., vol. 8, no. 5, pp. 44 – 54, Dec. 2005. [28] H. L. P. A. Madanayake, S. V. Hum, and L. T. Bruton, “A systolic array 2-D IIR broadband RF beamformer,” IEEE Trans. Circuits Syst. II, vol. 55, no. 12, pp. 1244 –1248, Dec. 2008. [29] L. Wu, Z. Sun, H. Yilmaz, and M. Berroth, “A dual-frequency Wilkinson power divider,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1, pp. 278 –284, Jan. 2006. [30] S. Wong and L. Zhu, “Ultra-wideband power dividers with good isolation and improved sharp roll-oﬀ skirt,” Microw., Antennas Propag., vol. 3, no. 8, pp. 1157 –1163, Dec. 2009. [31] A. Abbosh, “Ultra wideband inphase power divider for multilayer technology,” Microw., Antennas Propag., vol. 3, no. 1, pp. 148 –153, Feb. 2009. Bibliography 117 [32] H. Oraizi and A.-R. Shariﬁ, “Design and optimization of broadband asymmetrical multisection wilkinson power divider,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 2220 – 2231, May 2006. [33] L. Fan and K. Chang, “Uniplanar power dividers using coupled CPW and asymmetrical CPS for MICs and MMICs,” IEEE Trans. Microw. Theory Tech., vol. 44, no. 12, pp. 2411 –2420, Dec. 1996. [34] T. Wang and K. Wu, “Size-reduction and band-broadening design technique of uniplanar hybrid ring coupler using phase inverter for M(H)MIC’s,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 2, pp. 198 –206, Feb. 1999. [35] J.-S. Lim, D.-J. Kim, Y.-C. Jeong, and D. Ahn, “A size-reduced CPW balun using a “X”-crossing structure,” in Europ. Conf. Antennas Propag., vol. 1, Oct. 2005.

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