Principles of Modern Radar - Volume 2 1891121537

490 CHAPTER 10 Clutter Suppression Using Space-Time Adaptive Processing10.6.4 Angle and Doppler EstimationA maximum likelihood estimate for target bearing and Doppler integrates seamlessly withSTAP clutter mitigation steps. The approach described here follows [29].Consider the alternative hypothesis of (10.52)x k = ¯s k + x k/H0 = αs s−t ( f sp , ˜f d ) + x k/H0 (10.94)where ¯s k = αs s−t ( f sp , ˜f d ) is the target space-time response, α is a complex constant, andx k/H0 = c k + j k + n k is the interference-plus-noise (total noise) vector. The objective isto estimate p = [ ] Tf sp ˜f d with ˆp. Since xk/H0 ∼ CN(0, R k ), the joint probability densityfunction is1 ()p(x k |p) =π M |R k | exp −(x k − αs s−t (p)) H R −1k (x k − αs s−t (p)) (10.95)Given the likelihood function defined by (10.95), we first require an estimate for thecomplex constant. Equation (10.95) is maximal whenQ(α,p) = (x k − αs s−t (p)) H R −1k (x k − αs s−t (p)) (10.96)is minimal. Differentiating (10.96) and setting the result to zero yieldsˆα =Substituting (10.97) into (10.96) leads toQ( ˆα,p) = xk H R−1 k x k −sH s−t (p)R−1 k x kss−t(p)R H −1k s s−t(p)∣∣xk HR−1ks ∣s−t(p)∣ 2ss−t(p)R H −1k s s−t(p)(10.97)(10.98)Differentiating (10.98) with respect to p and setting the result to zero yields the maximumlikelihood estimate, ˆp. Consequently, the estimator is [29]⎛[ ]∣ˆf sp⎜∣ss−t Hˆp = = arg max(p)R−1 k x k∣ 2 ⎞⎟⎝ˆ˜f [ ] Tdsfsp ˜f s−t(p)R H −1k s ⎠ (10.99)s−t(p)dp=The maximum likelihood estimate takes the form of an adaptive matched filter (AMF) normalized[17,18] STAP cost surface where in practice, v s−t ( f sp , ˜f d ) replaces s s−t ( f sp , ˜f d ),and ˆR k replaces R k . Implementing the estimator requires a very fine grid search to findthe peak of the likelihood function and occurs after the STAP detects a target.10.6.5 Processing Block DiagramFigure 10-20 shows a radar detection block diagram incorporating STAP, post-detectionintegration (PDI), CFAR thresholding, and bearing and Doppler estimation as the primarysignal processing operations.The multichannel array receives multiple pulses of data for range cell k, as describedin preceding sections. After downconversion to an intermediate frequency and ADC, thedigital processor converts the data to complex baseband and performs pulse compression