Principles of Modern Radar - Volume 2 1891121537

752 CHAPTER 17 Advanced Processing Methods for Passive Bistatic Radar SystemsFIGURE 17-4Sketch ofsuboptimumalgorithms for2D-CCF evaluation.(a) Batchesalgorithm.(b) Channelizationtechnique.for l = 1 : N tx l [n] = s surv [n]s* ref [n − l]for r = 0 : n B − 1N B − 1y l [r] = ∑ x l [rN B + p]p = 0for r = 1 : N C(r)(r)S surv [k] = FFT{s surv [p]}(r)(r)S ref [k] = FFT {s ref [p]}(r) (r)Y[k, r] = S surv [k]S *ref [k]Y l [m] = FFT{y l [r]}X[k, m] = FFT{Y[k, r], over r}(n C FFT s )c [l,m] = Y l [m](possibly discardsamples)c [l, m] = IFFT{X[k, m], over k}(N C FFT s )(a)(b)that represents the DFT of the decimated sequence y l [r](r = 0,...,n B − 1), obtained bysumming the product sequence x l [n] = s surv [n] · sref ∗ [n − l] for each batch. The resultingalgorithm is sketched in Figure 17-4a, and its computational load is reported in Table 17-1as a function of the number of batches assuming that n B N B = N.The number of batches should be selected so that n B ≥ N f , and, in particular, nosample is discarded at the FFT output if equality holds. Within this limit, a smaller n Bprovides a lower computational load but also yields a higher integration loss for fastmovingtargets whose Doppler shift is not properly compensated [28]. In fact, for a constantmodulus signal the SNR loss for a target at range bin l and Doppler bin m can be writtenL[l,m] =−20 log 10{n BNsin ( πm / )}n Bsin ( πm / N )(17.9)As is apparent, it depends only on the considered Doppler bin and reaches its maximumat the highest Doppler value considered in the 2D-CCF, while no loss is experienced atzero Doppler.As an example, Figure 17-5a shows maximum SNR loss (for the highest Dopplerfrequency) and computational load (number of complex multiplications) as a function ofthe number of batches n B for the study case described in Table 17-2. When operating withn B between 500 and 2500, the batches algorithm yields a computational load about 17times smaller than the direct FFT, with an SNR loss below 1 dB in the worst case. Thisis confirmed by Table 17-2 reporting the results of the batches algorithm for n B = 500providing a reduction in computation by a factor 18.2. Notice that the same 1 dB losswould be experienced by the direct FFT operating with a number of integrated samplesreduced by a factor of 1.2. However, in this case for the same SNR loss, the computationalload would be reduced by only a factor of 1.2.