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

82The density of the CSNR f (p) can then be computed as in Equation 4.23. Thedensity of PCPs CSNR is similar in form to that of the SMI method, with thedifference that in Equation 4.18 the signal dimensionality N is replaced by theThe relation between Equations 4.26 and 4.27 is explored in Appendix C.In the introduction it was mentioned that LSMI is essentially a reduced-ranktechnique. Indeed, a CSNR distribution similar to Equation 4.27 is found in [20].To complete the analysis of data dependent transforms, we now consider thecase of the weight vector constrained to the interference subspace. We will refer tothis method as principal components SMI (PC-SMI). Ignoring a constant gain, thePC-SMI weight vector is given bywhere A., is a diagonal matrix of the r principal eigenvalues of R, and the columnsof Q r are the associated eigenvectors. Consistent with the earlier discussion onthe topic, r is chosen larger than the actual interference subspace rank p. Directanalysis of PC-SMI's performance is very difficult since the CSNR is a function ofboth random eigenvalues and random eigenvectors. However, an approximation canbe obtained based on the following argument. Letare respectively the eigenvectors and eigenvalues of therank p interference, r = p + 1, and 4r, -Ar are the index r (in descending order)eigenvector and eigenvalue. Then the PC-SMI weight vector can be expressed