Principles of Modern Radar - Volume 2 1891121537

10.6 STAP Processing Architectures and Methods 489covariance matrix estimate, ˆR adpca/k , corresponds to the data vector for M channels andÑ pulses, for example, [ x T k/s (n − 1) xT k/s (n) xT k/s (n + 1) ] Tfor Ñ = 3.Pre-Doppler STAP is not as popular as post-Doppler STAP, since its performancedoes not generally benchmark as well relative to the joint domain optimal solution. Thisapproach is primarily of interest when the the clutter within the CPI is expected to mildlydecorrelate. In such cases, pre-Doppler STAP typically adjusts the adaptive weights morefrequently in time than a post-Doppler STAP method, which may prove beneficial.10.6.3 Reduced-Rank STAPRR-STAP is a weight calculation strategy involving an eigendecomposition of theinterference-plus-noise covariance matrix and then selection of the dominant interferencesubspace to essentially form an orthogonal projection matrix [21,22]. The orthogonal projectionmatrix coherently removes the clutter signal prior to the application of a matchedfilter. RR-STAP is a viable strategy because the clutter signal tends to be of low numericalrank. RR-STAP methods are computationally demanding due to the required eigendecompositionbut generally show improved convergence over SMI, with training vector supportreducing from twice the processor’s DoFs (e.g., 2NM) to twice the interference rank foran average adaptive loss of 3 dB.It is shown in [21] that the STAP weight vector of (10.66), with the arbitrary scaling,β, can be writtenw k = βR −1k s s−t ( f sp, ˜f d ) = β NM∑[sλ s−t ( f sp , ˜f d ) −0m=1]λ k (m) − λ 0ϑ k (m)q k (m)λ k (m)(10.92)where λ 0 = min ({λ k (m)} ∀m ) is the noise-floor eigenvalue level, and ϑ k (m) = qk H(m)s s−t ( f sp , ˜f d ) is the projection of the m-th eigenvector onto the quiescent pattern. As seenfrom (10.92), the STAP response appears as a notching of the space-time beampatterngiven by s s−t ( f sp , ˜f d ) by the weighted, interference eigenvectors. When λ k (m) = λ 0 ,nosubtraction occurs, since the corresponding eigenvector lies in the noise subspace. Thus,running the sum from m = 1tom = r c , where r c ≪ NM is the clutter rank, yieldsa more robust adaptive response, with better sidelobe pattern behavior and more rapidconvergence; this implementation of (10.92) is called reduced rank.A special case of (10.92) occurs when λ k (m) ≫ λ 0 for all m = 1:r c . Under suchcircumstances, we have from (10.92)w k ≈ β λ 0[I NM −r c∑m=1q k (m)q H k (m) ]s s−t ( f sp , ˜f d ) (10.93)The term in brackets in (10.93) is an orthogonal projection; it removes all subspacesaligning with the q k (m) defining the interference subspace. Naturally, after applying theorthogonal projection, s s−t ( f sp , ˜f d ) beamforms the data in space and time. This approachto reduced-rank processing is called principal components inverse (PCI) [22].As noted, RR-STAP is a weight calculation strategy. Equations (10.92) and (10.93)can be used with RD-STAP methods if desired.