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

CHAPTER 4REDUCED-RANK PROCESSINGThe signal model presented in the previous chapter suggests that STAP could benefitfrom the application of reduced-rank (RR) methods. Such methods incur a loss inthe SNR, but their main advantage lies in their statistical stability. In this chapter,the term SNR is defined as the signal-to-noise and interference ratio. First consideredare RR methods with known covariance matrix, subsequently RR performance withunknown covariance is analyzed. The analysis is carried out in the frameworks of theminimum variance beamformer (MVB) and the generalized sidelobe canceller (GSC)processors. Calibration errors are known to affect the performance of adaptive arrays.A method of studying these errors is also presented.4.1 Reduced-Rank Processing with Known CovarianceA diagram of the reduced-rank MVB is shown in Figure 4.1. The full-rank MVBweight vector is obtained as a solution to the optimization problem:are snapshots of the secondary data, and s is the steeringvector. With RR-MVB, the vector xk is pre-processed by a full column rank N x rmatrix transformation T. The RR data is then the r x 1 vector zk THxk , the RRcovariance matrix is THRT, and the RR steering vector is t THs. The RR-MVBweight vector is given bywhere k is a scalar chosen to satisfy the unit gain constraint in the direction ofthe desired signal. Notice that the value of k does not affect the output signal-tointerferenceplus noise ratio (SINR). The output SINR may be written as73