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

762. To avoid the complication, of a least-squares problem, let the matrix U berestricted to consist of r of the (N — 1) eigenvectors of R a ARA, whereA natural choice would be tolet the rank reducing transformation consist of the r principal eigenvectors of3. For a known covariance matrix R, an optimal approach that maximizes theoutput SINR for a given rank r, is suggested in [21, 22]: construct U from ther eigenvectors of Ra that maximize the quantitywhere qi, λi arerespectively eigenvectors and eigenvalues of Ra. In thereferences, this method is referred as the cross-spectral metric (CSM) method.4. Principal components decomposition, such as considered above, is datadependent. Fixed, reduced-rank transformations can be constructed byselecting the principal components of the discrete Fourier transform (DFT)or the discrete cosine transform (DCT). The cross spectral metric can also beused in conjunction with these fixed transforms [21, 22].Next, rank-reducing transformations are evaluated in the MVB framework.Consider the SINR at the MVB output, as given by Equation 4.3. When the transformationT is unitary, it has no effect on the output SINR, andany N x r rank reducing transformationSpecific examples are considered below.1. Consider how Case .1 of the GSC translates to the MVB framework. By substitutingEquation 4.10 in 4.8, we obtain the equivalent MVB weight vector