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

81The performance of the GSC processor with a fixed rank-reducing transformationis analyzed in [55].4.2.2 Analysis of Data Dependent TransformsThe case when T is data dependent cannot be directly derived from the SMI distribution.In this case T is a random matrix and its effect on the CSNR needs to beevaluated statistically. The weight vector may be constrained to lie either in thenoise subspace or the interference subspace.The method resulting from the noise subspace constraint is referred to as inversePCI in [16] and as eigencanceler in [17]. The weight vector is given byThe CSNR density function for the eigencanceler was derived in [56]. The derivationis based on the asymptotic expansion of the distribution of the principal componentsof the covariance matrix. Therein it is shown that, unlike the SMI density in Equation4.18, for the eigencanceler the density depends on the covariance matrix. It is notedin reference [56], the expression in Equation 4.25 below was developed under theassumption that the projection of the steering vector s on the true interferencesubspace is negligible compared to its projection on the true noise subspace, i.e.,pb 1. Retracing some of the steps in [56], it is not difficult to show that when thisassumption is not imposed, the CSNR can be expressed in the form p = pbpr (as inand the density of pr given byINR this expression simplifies to