Simulation results: A simplied asynchronous DS-CDMA system with BPSK spreading (ideal code, carrier and symbol synchronisation) was simulated using the SPW” software. The channel model consisted of inter-user interference and AWGN. The short spreading codes corresponding to spreading ratios (processing gains) of 127 and 255 were Gold and Kasami (the large set) sequences, respectively. Gold sequences of period 2w-1 were used as long codes. Relative code delays and carrier phases were selected randomly, and they were the same in the simulation of both short and long codes, i.e. just the codes were changed. Long simulation times limited the simulation of small BER and large Eb/Nnvalues. The BER results are shown in Figs. 2 and 3. It can be seen that the system performance using long codes is 4 . 5 - 1.OdB worse, when the Eb/Nois -10dB (IOdB i s a typical value in digital cellular telephone applications). The worse BER performance results from uncontrolled partial crosscorrelation properties. 10‘’ MER, A.: ‘Multi-rate DS-CDMA A promising m s s technique for third-generation mobile radio systems’. Proc. PIMRC ’93, 1993, (Yokohama), pp. 114-1 18 BEKIR, N.E.: ‘Bounds on the distribution of partial correlation for PN and Gold sequences’, PhD Dissertation, Univ. of Southern California, Los Angeles CA, 1978, p. 74 Pseudo-syndrome method for supervising Viterbi decoders at any coding rate C. Berrou and C. Douillard Indexing terms. Viterbi decoding, Codes and coding t 0 2 A new technique for the supervision and synchronisation of Viterbi decoders, using the novel concept of the pseudo-syndrome, is presented. This technique is applicable with slight additional complexity, whatever the coding rate, to all decoders which contain the function of search for the maximum likelihood path. Simulation results are presented in the particular case of a K = 7 enoxleddecoder for different rates. ............. j ............................ ;....... ........................... .- . . . 4 signal-to-noise Node synchronisation: Various ambiguities in the input symbols of 6 8 ratio Eb/NO, dB Fig. 3 BER of DS-CDMA system when spreading ratio is 255 _ _ _ _ Kasami sequences (the large set) of length 255 __ Gold sequences of length 1073741823 . . . . . Theoretical single user BPSK curve Spreading ratio: 255, number of simultaneous usen: 20 Conclusion: The loss in the BER performance is tolerable, because long codes provide several benefits that are desirable in the design a Viterbi decoder may have to be removed, for instance the relative positions of the symbols after depuncturing and/or demultiplexing. This problem is referred to as node synchronisation; solving it generally consists in scanning all the possible cases of synchronisation by relying on a supervision algorithm, able to discriminate between the in-sync (good synchronisation) and the outof-sync (bad synchronisation) behaviour of the decoder. Among other techniques, node synchronisation based on the computation of a syndrome has been proposed. The syndrome is a Boolean [1,2] or possibly a soft [3] value which is representative of the validity of the decoder input samples as symbols compatible with convolutional generation. The syndrome is easily identified for an R = 1/2 coding rate; for instance, with constraint length K = 7 and encoding polynomials 133 and 171, it is formed (as a Boolean) by the exclusive-OR of ten symbols considered in hard decision. For higher rates, a larger number of s);snbols is necessary to build the syndrome, and its reliability becomes very sensitive to the channel noise. The pseudo-syndrome method is inspired by this, but with reduced complexity and improved performance. state 00 of a large cellular CDMA network. The benefits are [3]: the number of available individual codes is extremely large, the flexibility with respect to multiple bit rates and variable spreading ratios is high, there is no need for inter-user or inter-cell synchronisation, and the code does not change when the mobile station crosses the cell boundary (the handover situation). Slightly worse BER performance can be improved with powerful error correction coding as in [2]. IEE 1994 27 April 1994 Electronics Letters Online No: 19940706 K. H. A. KLrkkPinen (University of Oulu. Department of Electrical Engineering, Telecommunication Lubaratory, Linnanmaa SI, 90570 Oulu. Finland) M. J. Laukkanen (Nokia Cellular Systems, Teknologiantie 4. 90570 Ouh. Finland) H. K. Tarnanen (University of Turku, Department of Mathematical Sciences, 20500 Turku, Finland) References on the maximum cross correlation of (3), pp. 397-399 signals’, IEEE Trans., 1974, IT-U), 2 GILHOUSEN, K.S., JACOBS, I.M., PADOVANI, R., WEAVER, L.A., WHEATLEY, C.E. and VITERBI, AI.: ‘System and method for generating signal waveforms in a CDMA cellular telephone system’. Patent No. WO 9200639, 1992 1 WELCH, L.R.: ‘Lower bounds 1036 ~~ . - ( ~ . o , . ~ ( ~ k.‘k.l) +l /p?i 7 k‘ 191.111 0 (0.0) tl.0 11 Fig. 1 Convolutional code with K = 3, polynomials 5 (symbol X ) and 7 (symbol Y). and associated decoding trellis Pseudo-syndrome: Consider in Fig. 1 the convolutional code with K = 3, polynomials 5 (symbol X ) and 7 (symbol Y), and the decoding trellis. Suppose for instance that, at time k , the maxi- mum likelihood path is associated with state 00. If this state was actually the state of the encoder, at the corresponding time, then the symbols (X,,,,Y,,,) ‘expected‘ by the decoder is not just any couple. If a hard decision is considered, it must be either (0,O) or (1,l); these couples are also compatible with state 01. For the other two states, couples (0,l) and (1,O) are relevant. It is therefore possible to build a parity relation between the maximum likelihood state at time k and the symbols coming at time k + l . By denoting v = K-1 (code memory), let S, = (&, S,-,, ...SnJ,be the maximum likelihood state at time k. Let also, for a 1/2 rate encoder, GX = @xv, gx,.,, ...gxo) and GY = @yv, gyv.,, ...gyri) be the polynomials associated with the generation of sym- ELECTRONICS LE7TERS 23rd June 1994 Vol. 30 - No. 13 ~~ Pseudo-syndrome method applied Io K = 7 (polynomials 133, 171) enco&r/&co&r: Psk is calculated as X,+,OY,+@ S,,,Q SI.*. Fig. 2 shows the probability of having PS, equal to 1, as a function of the signal to noise ratio E J N , for rates R = 1/2, 2/3, 3/4, 5/6 and 8/9. In the out-of-sync situation, PI { P S , = 1) = 0.5; the dashed line represents the probability minus the standard deviation s of the measure, when L is 1024, for a large number of measures. In the in-sync case, the dashed l i e , for the extreme rates, represents probability plus standard deviation. From these curves, we can see that very reliable discrimination may be achieved at low E J N , . Moreover, it happens that the gaps between these curves are close to the gaps between the curves yielding the binary error rate (BER). This means it is quite possible to adopt the same threshold for all coding rates, corresponding roughly to the same BER. Conclusion: A very simple supervision/synchronsationmethod has heen proposed for Viterbi decoders which already possess the ability to search for the maximum likelihood path or state. This method, based on the calculation of the so-called pseudo-syndrome, offers very reliable discrimination between in-sync and out-of-sync cases. The associated circuit and its parameters can he independent of the coding rate. It has been implemented successfully in the first turbo encoder/decoder [6lfor supervision needs. Acknowledgments: The authors thank A. Glavieux for his relevant remarks on the presentation of this Letter, and COMATLAS for their support. 0 IEE 1994 27 April 1994 Electronics Letters Online No: 19940737 C. Bemu and C. Douillard (Telecom Bretagne, Integrated Circuits Lab., BP 832, 29285 BREST Cedex, France) References MCELIECE, R. 1.. and SWANSON. L.: 'Node synchronisation for the Viterbi decoder', IEEE Trans., 1984, COM-32,(5) pp. 524-531 SODHA,J., and TArr,D.: 'Node synchronisation for high rate convolutional codes', Electron. Lett., 1992, 28, pp. 81&812 SODHA.J., and TAIT,D.: 'Soft-decision syndrome based node synchronisation', Electran. Lett., 1990, 26, pp. 1108-1 109 BERROU, c . , GLAVIEUX. A., and PHITIMAISHIMA, P.: 'Near Shannon l i t errorcorrecting coding and decoding: Turbo-codes'. Proc. IEEE Int. Conf. on Communications (ICC'93), Geneva, Switzerland, 1993, pp. 1064-1070 BERROU. c . , and GLAYIEUX, A.: 'Turbo-codes: General principles and applications'. 6th Int. Tirrenia Workshop on Digital Communications, 1993 'CAS5093: Turbo encoder/decoder'. Data sheet, COMATLAS, Chateaubourg, France,Nov. 1993 1 LORDEN, G., 2 3 4 5 o.5 -- I ! ! 6 out-of-sync decoder ~=0.016 -R=~e~a__~_,5=0.01q--_ Wideband trapezoidal stri grating for elimination of specular rJection T. Mathew, D. S. Stephen, C. K. Aanandan, P. Mohanan and K. G. Nair Indexing terms: Grotingfilters. Radar cross-sections, Electromagnetic wave-diffraction A trapezoidal strip grating surface that eliminates specular reflections almost over the entire X-band frequency range for TM polarisation is reported. This new grating structure ovemmes the bandwidth limitation of conventional rectangular strip grating surfaces. Eb"O Fig. 2 Pr (PS, = 1 ) in out-of-sync and in-sync conditions o decoder of K = 7 (133, 171) code for rates R = 1/2, 2/3, 3/4, 5/6 and && Quantisation of 4 bits -mean value - - _ _mean value minus (out-of-sync) or plus (in-sync, R = 112 and 8/9) standard deviation s for L = 1024 ELECTRONICS LETTERS 23rd June 1994 Vol. 30 Inrroduction: Blazed reflection gratings, capable of scattering plane electromagnetic waves to first order diffracted waves have been studied extensively [I, 21. The most common blazed grating consists of rectangular corrugations on a conducting surface. Reflector backed rectangular strip gratings have been reported that can be used to simulate the effects of cormgated surfaces [3]. They No. 13 1037

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