Space/time/frequency methods in adaptive radar - New Jersey ...

784. Similar to Case of the GSC, the rank reducing transformation T may beconstructed from the principal components of a fixed transform such as theDFT or the DOT.To reiterate, when the true covariance matrix R is known, reduced-rankprocessing is suboptimal. The strength of reduced-rank methods is revealed forunknown covariance. This case is considered in the next section.4.2 Reduced-Rank Processing with Unknown CovarianceIn practice, the space-time covariance matrix is not known and it needs to beestimated from the secondary data. This is an application for which reduced rankmethods can take advantage of their improved statistical stability. Let the numberof snapshots from the secondary dataset (sample support) be equal to K. Thenthe estimated covariance matrix is given bythe performance of reduced-rank processors is analyzed as a function of the samplesupport K.A widely accepted measure of performance for radar systems is the probabilityof detection. In adaptive radar, detection probability is a function of theweight vector. Likewise, the weight vector is derived from estimates of the covariancematrix of the secondary data, and as such, its elements are random variables. Thismakes the detection probability dependent on the outcome of the sample covariancematrix. Insight can be gained by expressing detection probability as a function ofthe conditioned SNR (CSNR). The CSNR is defined as the effective SINR obtainedby the application of a particular method, normalized by the optimal SINR (knowncovariance matrix, full-rank case):