Principles of Modern Radar - Volume 2 1891121537

812 CHAPTER 17 Advanced Processing Methods for Passive Bistatic Radar SystemsFIGURE 17-43Array patterns forarray configurationin Figure 17-41b.0−5−10−15Uniform TaperRadial TaperArray pattern (dB)−20−25−30−35−40−45−50−150 −100 −50 0 50 100 150θ (deg)Optimum Filter Assuming that the disturbance covariance matrix M is known, the optimumweights vector that maximizes the signal-to-disturbance ratio is given by [63]w H (θ 0 ) = s H θ (θ 0) M −1 (17.46)where θ 0 is the direction toward which the beam is pointed. In practical applications,the covariance matrix M is replaced with its estimated version obtained from the receiveddata. This is quite appropriate in the PBR case given that the level of both thedirect signal and its multipath reflections is well above that of the useful signal. Aftercombining the received signals according to (17.46), an adaptive temporal cancellationmight be performed only to cancel disturbance residuals not adequately suppressed bythe spatial adaptive filter. Then the 2D-CCF is evaluated, and a proper CFAR threshold isapplied to obtain a detection map. When applying the optimum filter in the presence ofa strong multipath reflection from a given direction, a null is imposed in the synthesizedadaptive pattern at this direction. This also cancels all target echoes coming from thesame DOA.Principal Eigenvalue Approach A way to circumvent the weakness of the optimum filterfor targets at the same DOA of strong multipaths is to reduce the number of DOF availableto the spatial adaptivity so that only a single null can be imposed by the adaptive spatialfilter. Since the direct signal is by far the strongest component of the overall disturbance, it isobvious that its effect dominates the spatial covariance matrix and specifically determinesits principal eigenvector q max . Therefore, by estimating only the principal eigenvector ofthe spatial disturbance covariance matrix, it is possible to strongly attenuate the directsignal by projecting the target steering vector s θ (θ) on the subspace orthogonal to sucheigenvector. The resulting weights vector is given byw H PE (θ 0) = sθH (θ 0) ( I − q max qmaxH )(17.47)Obviously, the disturbance subspace can be extended by including the eigenvectorscorresponding to the highest eigenvalues. This technique leaves some multipath reflections