Principles of Modern Radar - Volume 2 1891121537

750 CHAPTER 17 Advanced Processing Methods for Passive Bistatic Radar SystemsTABLE 17-1Computational Loads for Optimum and Suboptimum Algorithms for 2D-CCF EvaluationAlgorithm Complex Multiplications Complex AdditionsCorrelation FFT 2N log 2 (N) + N f [N + N log 2 (N)] 2N log 2 (N) + N f [N log 2 (N)]Direct FFT N τ [N + N log 2 (N)] N τ [N log 2 (N)]Batches algorithm N τ [N + n B log 2 (n B )] N τ [N + n B log 2 (n B )]Decimation using CIC filters N τ [N + 5N D + N D log 2 (N D )] N τ [N + N D + N D log 2 (N D )]Channelization technique 2N log 2 (n C ) + N + N log 2 (N) 2N log 2 (n C ) + N log 2 (N)the N complex multiplications and a single inverse FFT (IFFT) must be performed. Theresulting computational load is reported in Table 17-1. This algorithm can be implementedin parallel for the N f Doppler bins of interest.Direct FFTThis algorithm is based on the observation that, at the l-th time bin, the samples alongDoppler frequency of the 2D-CCF correspond to the samples of the DFT of the sequencex l [n] = s surv [n]sref ∗ [n −l] obtained as the product of the surveillance signal and the delayedconjugated reference signal, [4]:χ[l,m] = X l [m] = DFT{x l [n]} (17.6)Similar to the previous case, for each one of the N τ bistatic delays, the DFT isevaluated, and N–N f output samples are discarded. The resulting algorithm is sketchedin Figure 17-3b. Since its iterations involve the range dimension, this algorithm can beparallelized over the range bins and can be limited to the N τ range bins of interest.Therefore, at each iteration only N complex multiplications and a single FFT must beperformed (in contrast to the correlation FFT algorithm it does not require the preliminaryevaluation of the signals DFT). The resulting computational load is reported in Table 17-1for comparison.As is apparent from Table 17-1, the computational load for both algorithms increaseswith the number of integrated samples as N log 2 (N). However, the final cost of the correlationFFT is essentially determined by the number N f of considered Doppler bins,while the cost of the direct FFT is essentially determined by the number N τ of rangebins included in the 2-D map. Thus, the algorithm with the lowest number of operationsdepends on the extent of the 2D-CCF over the range and Doppler dimensions required forthe specific application: if N τ < N f the direct FFT algorithm requires less computationthan the correlation FFT.As an example, Table 17-2 reports the numerical evaluation of the computationalload of both the correlation FFT and the direct FFT for an FM-based PBR (the mainparameters of the considered study case are also listed in the table). It is easily verifiedthat, as N τ∼ = 3/5 · N f , the direct FFT algorithm requires almost half the computationalload of the correlation FFT. Notice that this is not always the case. For example, let usconsider a PBR based on DVB-T transmissions aimed at the surveillance of the samearea described in Table 17-2 in both range and velocity dimensions. In this case, a signalbandwidth of 8 MHz might be assumed at a carrier frequency of 500 MHz (ultra highfrequency [UHF] band). These requirements result in a 2D-CCF consisting of N τ = 6400range bins and N f = 256 Doppler bins (assuming that the integration time has beenproperly modified to yield the same velocity resolution). The benefits of the correlation