RADAR J l l T E R SUPPRESSION BY SELF- R EFER ENCE MATCH ED FILTER H.Szu and J. P. Garcia simulation processing two radar pulses we have demonstrated the ability to detect target signals over 20dB down from the clutter. Indexing terms: Radar, Signal processing The effectiveness of moving target indicator (MTI) processing degrades substantially in- the presence of even moderate phase jitter or phase noise. A technique originally developed for processing images viewed through turbulent media is applied to correct for phase jitter in MY1 radar processing. Introduction: The well known moving target indicator (MTI) processing technique takes advantage o r the fact that the phase of the radar clutter signal is constant while the phase of the target signal varies. This permits clutter to be subtracted over multiple radar pulses while preserving the target signal. The main requirement for MTI processing is a stable phase of the radar signal. This requirement, however, is not always realisable [I]. Some types of clutter exhibit phase variation over time. In addition to this environmental source of phase jitter there is also system-based phase jitter. Very high power amplifiers exhibit nondeterministic phase instabilities. When these cases apply, the result is seriously degraded clutter cancellation (Fig. I). Adaptive MTI has been successful in dealing with some cases of phase noise but may not be suflicient when the phase is changing within a subpulse. I " ' +b ~~~~~'~~~~~~~~~~~~~~~~~~~~~~~~~~ d Fig. 2 Steps in SRMFIMTI processing a Centroiding b Calculation of master subpulse c Sectioning of master subpulse d Registration w.r.1. maste; subpulse Fig. 1 T w o radar pulses (jour subpulses per pulse) representing clutter return, and diflerence showing how phase jitter degrades M T l cancellation a Two radar pulses b Difference An image processing technique known as the self-reference matched filter [2] (SRMF) can compensate for image distortion of an object viewed through a turbulent medium. In a sense this technique is a two dimensional analogue of processing a time series signal subject to nondeterministic phase jitter. In a simple elegant manner, a variation of the SRMF is used to implement MTI processing on two or more jittered radar pulses over consecutive scans. Just as in conventional MTI, the SRMF-based MTI processing is performed after the radar signals have been mixed down to the video frequency. All the subpulses from both pulses are processed together. This technique involves seven steps: (i) centroiding the subpulses (Fig. 2a) The length of a section is defined as a predetermined count of zero crossings. The count starts at the first zero amplitude point on the first positive to negative transition. Then for every subsequent positive to negative transition encountered, the counter is incremented until it attains some predetermined value. The distance along the waveforms from the initial zero crossing to the final zero crossing determines the length of the section. Implicit to this approach is that every section begins and ends at a common phase on the waveform. In the final step of the processing, subpulses comprising the second pulse are weighted by -1 so that once both pulses are phase matched, the second pulse will effectively cancel out the first pulse. The intensity of the residue when no signal is present will depend on the spectrum of the phase jitter such that higher frequency phase shifts will cause higher intensity residues. Simulation: A computer simulation was written to demonstrate the above theory. The phase jitter as a function of frequency X u ) was modelled with the real part having a llf form [4] where (ii) shifting the subpulses so that their centroids coincide (iii) summing the shifted subpulses to produce a master subpulse (Fig. 2b) (iv) dividing the master subpulse into sections and then centroiding these sections (Fig. 2c) (v) repeating this procedure with the individual subpulses (vii) performing a weighted summation of the processed subpulses in which subpulses from half of the pulses are weighted by -1. Fig. 2d represents the shifting of the subpulse sections so that their centroids are coincident with the centroids of the analogous sections on the master pulse. From an SRMF/MTI ELECTRONlCS LETTERS 10th June 1993 Vol. 29 No. 12 The phase as a function of frequency was chosen to be a uniform random distribution between -n/2 and n/2. Subsequent to computing Im {Xu)} from the phase, Xu) was transformed to the time domain bv a comulex DFT. Fie. 3 f (t) = k, A@)exp [ - i(w, t + 4)l + k, 4)exp C - i(w, t + 4 + 431 where k, is the weighting coefficient for the clutter (k, is arbitrarily set to unity), k , is the weighting coeficient for the target, A(t) is the square weighting function, w, is the radar 1045 video frequency, 4 is the phase term, and 4, is the target phase. Two phase jitter functions were numerically generated presently existing radar systems could be inexpensively upgraded to MTI systems with only minor modifications to their signal processing electronics and software. Acknowledgments: This work was supported in part by the NSWC Dalgren Division Independent Research Program. Fig. 3 Randomly generated phase jitter function and subsequently used in generating two radar square modulated pulse signals by letting 4 = x(t) for each pulse. Each pulse consists of four subpulses like the pulses shown in Fig. 1. The frequency of the pulses corresponds to the video frequency of the radar. This was selected to be 30 MHz, and the R F frequency and the pulse width were chosen to be 3 G H z and l o p , respectively. For the simulation, each subpulse was divided into 10 sections in which the section length was defined by four zero counts. Fig. 4a and b show the average of 0IEE 1993 13th April I993 H. Szu and J. P. Garcia (Naual Surface Warfare Center, Code R44, I0901 New Hampshire Ave., Silver Spring, M D 20903-5000, U S A ) References ‘Introduction to radar systems’ (McGraw-Hill, New York, 1980). pp. 129-138 2 SZU, H. H., and BLODOETT, 1. A.: ‘Self reference spatiotemporal image-restoration technique’, J. Opt. Soc. Am., 1982, 12, (12), pp. 1666-1669 3 szu, H. H., BMDOETT, I. A., and SICA, L.: ‘Local instances of good seeing’, Opt. Commun., December 1980, JS, (3). pp. 317-322 4 OOLDMAN, s. 1.: ‘Phase noise analysis in radar systems using personal computers’ (John Wiley & Sons, New York, 1989), Chaps. 1-2 1 SKOLNIK, M. 1.: C DISCRETE ITERATIVE LEARNING CONTROLLER d L. Y. X. Ma, T. S.Low and S. K. Tso Fig. 4 Radar simulation a Average subpulse of first pulse b Average subpulse of second pulse c Output ofSRMF/MTI processing d Difference of first and second average subpulse Indexing terms: Algorithms, Control systems, Controllers the four subpulses in the two radar pulses. Fig. 4c is the output of the SRMF/MTI processing over the two pulses with no target (k, = 0). Fig. 4d is the difference of the two average subpulses without processing. As can be seen, the SRMF/MTI greatly enhances the effectiveness with which the pulses cancel each other. Next the above SRMF processing was repeated with an artificial target inserted into the radar signals. The phase of the artificial target is of the form bt = bo + k , t , where represents some constant phase shift and k , t represents the linear time dependent phase shift where k, is the target velocity divided by the carrier wavelength. A target was chosen to be travelling with a head-on velocity component of IOOOm/s that translates to a phase shift of 2rr x 10000rad/s in the radar signal. Fig. 5 shows the result of an artificial target d 1678151 Fig. S Radar simulation with target - 2 0 d B downfrom clutter a Average subpulse of first pulse b Average subpulse of second pulse c Output of SRMF/MTI processing d Differenceo f first and second average subpulse having k, = 1/100th the magnitude of k,. The integration of the SRMF/MTI output residue for the 1/100th (-20dB) target is over twice that of the output with no target. This indicates that for the above phase jitter, the target signal just exceeds the threshold of detectability based on the criteria of a signal-to-noise ratio of unity. This simulation demonstrates the potential of the above technique. Using the SRMF, certain 1046 An effective discrete learning control method is proposed for improving the tracking performance of linear systems repeating the task from cycle to cycle. With this method, the current cycle data are intentionally introduced into the learning control law. Analysis of the convergence is conducted completely in the discrete-time domain. The fast convergence performance is further substantiated by simulation results. Introduction: Iterative learning control was originally proposed for robot applications [l], which enables us to find the control torque that makes the robot follow the desired trajectory exactly over a finite time interval through the repetition of trials. The usefulness of this kind of scheme has already been illustrated by experiments for manipulator trajectory control [2, 31. Recently, this new type of control scheme has received much attention [4-61 for application in dynamic systems whose operations are required to repeat from cycle to cycle with unchanged reference commands. It is noted that the existing learning control algorithms [l, 2, 4-61 have mostly been developed and analysed in the continuous-time domain. However, from an implementation point of view, it would be more reasonable to discuss an iterative learning control scheme fully in the discrete-time domain because the storage of the past data in digital memory is definitely required for any practical learning control implementation. It is well known that many control algorithms in continuous time are still available in discrete time provided that the sampled theorem is guaranteed. Conceptually, there certainly exists some restriction such as the sampled theorem to determine the sample period in the learning control system so that the scheme is still effective, or the convergence is also guaranteed in the discrete time domain. Unfortunately, these issues are seldom discussed in the literature. Another weakness of existing learning schemes is that the current cycle information does not enter into consideration in the design of the scheme. Obviously, a feedback path of information in the current cycle will definitely play an important role in learning, even though past cycle information is to be used. In this Letter, the learning control algorithm is developed realistically in the discrete-time domain and the current cycle information is directly introduced into the proposed iterative learning controller. The convergent analysis is also completely based on a discrete system so that we can obtain a ELECTRONICS LETTERS 10th June 1993 Vol. 29 No. 12

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