Principles of Modern Radar - Volume 2 1891121537

10.6 STAP Processing Architectures and Methods 483MMSE estimate of d o/k asˆd o/k = w H MMSE/k x 0/k (10.81)where the MMSE weight vector follows from the well-known Wiener-Hopf equation [2,9]The lower leg covariance matrix isR x0/k = Ew MMSE/k = R −1x 0/kr x0/k d (10.82)[ ]x 0/k x0/kH = B G R k BG H (10.83)while the cross-correlation between lower and upper legs is[ ]r x0/k d = E x 0/k do/k∗ = B G R k s s−t ( f sp , ˜f d ) (10.84)The GSC filter output is theny k = d o/k − ˆd o/k = ss−t H ( f sp, ˜f d )x k − wMMSE/k H x 0/k()= ss−t H ( f sp, ˜f d ) − wMMSE/k H B G x k . (10.85)From (10.85) and prior discussion, it is seen that the corresponding space-time weightvector isw GSLC = s s−t ( f sp , ˜f d ) − B H G w MMSE/k (10.86)We compute the output SINR as the ratio of output signal power to interference-plus-noisepower, as in (10.56). The signal-only output power of the GSC isP s = E [ w GSLC¯s H k¯sH k w ] [GSLC = E sHs−t ( f sp , ˜f d )¯s k¯s k H s s−t ( f sp, ˜f d ) ]= σs2 ∣ ss−t H ( f sp, ˜f d )s s−t ( f sp , ˜f d ) ∣ 2 = σs 2 (NM)2 (10.87)and the output interference-plus-noise power is]P i+n = E[wGSLC H x k/H 0xk/H H 0w GSLC = wGSLC H R kw GSLC (10.88)In practice, just as for the maximum SINR filter and the MV beamformer, the adaptiveprocessor substitutes v s−t as a surrogate for s s−t ( f sp , ˜f d ) and ˆR k as an estimate of R k .The multistage Wiener filter exploits the GSC structure, providing an iterative, signaldependent,rank reduction strategy that enhances adaptive filter convergence [20].10.6 STAP PROCESSING ARCHITECTURESAND METHODSSection 10.5 discussed several approaches to optimally and adaptively weight a space-timedata vector, x k . The resulting space-time weighting invariably involves a steering vectormatched to the target response over the space-time aperture and an inverse covariancematrix to mitigate colored interference, such as clutter.