Principles of Modern Radar - Volume 2 1891121537

478 CHAPTER 10 Clutter Suppression Using Space-Time Adaptive ProcessingGiven the loss factor terms, SINR can be writtenSINR ( f sp , ˜f d) = SNR(fsp) × Ls,1 ( f sp , ˜f d ) × L s,2 ( f sp , ˜f d ), (10.63)where SNR( f sp ) is the angle-dependent signal-to-noise ratio. Target velocities closest tothe dominant clutter component and exhibiting SINR loss above some acceptable value,viz. L s,1 ( f sp , ˜f d )·L s,2 ( f sp , ˜f d ) ≥ ε, determine the MDV. For example, suppose we calculateSNR to be 13 dB, thereby yielding P D = 0.87 for P FA = 1E − 6 according to (10.59)and Figure 10-12. If our minimum detection requirement is P D = 0.5 for this same falsealarm rate, then SINR must be greater than or equal to 11.25 dB. This indicates a tolerablecombined SINR loss of 1.75 dB, or ε = 0.668.The UDSF is that percent of the Doppler space yielding acceptable SINR loss basedon detection performance requirements [5].10.4.1.3 Improvement FactorIF is another common metric, given asIF =SINR out=∣ wk Hs s−t( f sp , ˜f d ) ∣ 2 (σc 2 + σ n 2)SINR element wk HR (10.64)kw kwhere σc 2 is the total clutter power received by a single subarray on a single pulse [4].In the noise-limited case, (10.64) defaults to the space-time integration gain (nominally,NM). IF closely relates to the preceding SINR loss definitions.10.5 STAP FUNDAMENTALSA selection for the weight vector, w k , is a key issue remaining from the discussion inthe prior section. This section briefly discusses three approaches to choose the weightvector: the maximum SINR filter, the minimum variance beamformer, and the generalizedsidelobe canceller. While the formulations are different, each equivalently maximizesoutput SINR.10.5.1 Maximum SINR FilterThe optimal space-time weight vector maximizes the output SINR and takes the formw k = βR −1k s s−t( f sp , ˜f d ), for arbitrary scalar β [3]. To see this, express (10.56) asSINR = σ 2 s∣ ⌢ w H k⌢∣s∣ 2⌢w H ⌢k w k≤ σ 2 s⌢w H ⌢ ⌢k w k s H ⌢s⌢w H (10.65)⌢k w kwhere w k = R −1/2 ⌢k w k and s s−t ( f sp , ˜f d ) = R 1/2 ⌢k s. For covariance matrices of interest,R k = R 1/2k R1/2 k . Analogous to the matched filter case, by choosing w ⌢ k = ⌢ s we find theleft-hand side of (10.65) achieves the upper bound. Substituting the prior expressions gives⌢w k = ⌢ s ⇒ R 1/2k w k = R −1/2k s s−t ( f sp , ˜f d ) ⇒ w k = R −1k s s−t( f sp , ˜f d ) (10.66)Scaling the weight vector by β does not alter the output SINR.