Conference on Mathematics and Applications of Data/Image Coding, Compression, and Encryption IV SPIE’s International Symposium on Optical Science and Technology, San Diego, CA, July 29 – August 3, 2001 Data Compression via Pulse-to-Pulse Redundancy for Radar Emitter Location∗ Mark L. Fowler† and Zhen Zhou Department of Electrical Engineering State University of New York at Binghamton Binghamton, NY 13902 ∗ This work was supported by the Lockheed Martin Corporation under Contract UA-199865. † Correspondence: [email protected] ABSTRACT An effective method for geolocation of a radar emitter is to intercept its signal at multiple platforms and share the data to allow measurement of the time-difference-of-arrival (TDOA) and the frequency-difference-of-arrival (FDOA). This requires effective data compression. For radar location we show that it is possible to exploit pulse-to-pulse redundancy. A compression method is developed that exploits the singular value decomposition (SVD) to compress the intercepted radar pulse train. This method consists of five steps: (i) pulse gating, (ii) pulse alignment, (iii) matrix formation, (iv) SVD-based rank reduction, and (v) encoding. Matrix formation places aligned pulses into rows to form a matrix that has rank close to one and SVD truncation gives a low rank approximate matrix. We show that (i) compression is maximized if the matrix is made to have two-thirds as many rows as columns and (ii) truncation to a rank-one matrix is feasible. We interpret this as extracting a prototype “pulse trainlet.” The maximum compression ratio is expressed in terms of the number of pulses and the number of samples per pulse and point out a particularly interesting and important characteristic – the compression ratio increases as the total number of signal samples increases. Theoretical and simulation results show that this approach provides a compression ratio up to about 30:1 in practical signal scenarios. Keywords: data compression, singular value decomposition, emitter location, time-difference-of-arrival, TDOA, frequency-difference-of-arrival, FDOA 1. INTRODUCTION A common way to locate electromagnetic emitters is to measure the time-difference-of-arrival (TDOA) and the frequency-difference-of-arrival (FDOA) between pairs of signals received at geographically separated platforms.1,2,3 The measurement of TDOA/FDOA between these signals is done by coherently cross-correlating the signal pairs.2,3 This requires that the signal samples of the two signals are available at a common platform, which is accomplished by transferring the signal samples over a data link from one platform to the other. An important aspect of this that is not widely addressed in the literature is that the available data link rate often is insufficient to accomplish the transfer within the time requirement unless some form of lossy data compression is employed. To mitigate this, various data compression approaches have been proposed,4−9 although they have not been designed to fully exploit the characteristics of radar signals. For the case of white Gaussian signals and noises, Matthiesen and Miller4 established bounds on the rate-distortion performance for the TDOA/FDOA problem and compared them to the performance achievable using scalar quantizers, where distortion is measured in terms of lost SNR due to the mean square error (MSE) of lossy compression. However, these results are not applicable when locating radar emitters because the signals encountered are not Gaussian. A method using block adaptive scalar quantization was proposed5 and analyzed6 to show that it was marginally effective for various signal types. Wavelet-based methods have been proposed7 and demonstrated8 to give compression ratios on the order of 6 to 7 for some radar signals. A method that optimally trades between decimation and quantization has been developed for non-radar-like signals and shown to perform better than either method alone.9 However, none of these previously proposed methods exploits the inherent pulse-to-pulse redundancy characteristic of most radar signals. For the radar case, the fact that (at least) one platform must be operating at an SNR high enough to detect pulses can be exploited as a first step towards reducing the transferal by not sending the samples between detected pulses (i.e., gating).Conference on Mathematics and Applications of Data/Image Coding, Compression, and Encryption IV SPIE’s International Symposium on Optical Science and Technology, San Diego, CA, July 29 – August 3, 2001 However, even with this reduction due to gating, the transferal time is still excessive given the rates for current and projected data links. In the method proposed here, once the pulses have been gated they are formed into a matrix in such a way that the resulting matrix has an effective rank of one, due to the redundancy between pulses. Then the singular value decomposition (SVD) is used to exploit this redundancy to achieve significant levels of compression ratio that exceed what is possible using the previously proposed general methods.4 – 9 The two signals to be correlated are the complex envelopes of the received RF signals. The two noisy received signals to be processed are notated as )()()(ˆ)()()(ˆkvkdkdknksks+=+= (1) where s(k) and d(k) are the complex baseband signals of interest and n(k) and v(k) are complex white Gaussian noises. The signal d(k) is a delayed and doppler shifted version of s(k). The signal-to-noise ratios (SNR) for these two signals are denoted SNR and DNR, respectively‡. To cross correlate these two signals one of them (assumed to be here) is compressed, transferred to the other platform, and then decompressed before cross-correlation, as shown in Figure 1. Signal has SNR of after lossy compression/decompression. )(ˆks)(ˆksc cSNR CompressCrossCorrelate)(ˆkd)(ˆkscTDOAFDOA)(ˆksPlatform #1Platform #2Data LinkDecompressSNRDNRSNRc Figure 1: System Configuration for Compression 2. FORMING THE PULSE MATRIX 1. Pulse Gating and The Unaligned Pulse Matrix The emitter location system consists of three or more platforms, each outfitted with identical receiving and processing equipment. Once signal data is collected at all of the platforms, the SNR is estimated at each platform and the one with the highest SNR is chosen as the