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

5support consists of a population of independent, identically distributed vectors witha multivariate Gaussian distribution, the number of samples required to achieveperformance within 3 dB of the optimal, is approximately K 2N, where N is thedimension of the vectors. The main drawback of the SMI detector is that its samplesupport K is proportional to the array degrees of freedom N. Recent publicationshave shown the advantages of various forms of reduced-rank processing over thefull-rank SMI [16, 17, 18].A taxonomy of reduced-rank methods is shown in Figure 1.1. Two main architecturesare noted: the reduced-rank minimum variance beamformer (RR-MVB),and the reduced-rank generalized sidelobe canceler (RR-GSC). A third method,loaded SMI (indicated by a dashed line), refers to adding a constant term to thediagonal of the covariance matrix to improve its numerical conditioning. LSMIbehaves as a reduced-rank method [19, 20]. The RR-MVB architecture is shownin Figure 1.2. Given a rank reducing transformation T, adaptation can take placein the subspace spanned by the principal components of the transform (interferencesubspace methods) [18], or in the complementary subspace (noise subspace methods)[16, 17]. The transforms are either fixed (such as discrete Fourier transform - DFT,or discrete cosine transform - DCT) or data dependent (Karhunen-Loeve transform- KLT). The RR-GSC architecture is shown in Figure 1.3. The rank-reducing transformationis applied in the branch used for estimating the interference component.Another class of RR-GSC methods are based on the cross-spectral metric (CSM)[21, 22].It is interesting to note that reduced-rank methods are generally evaluatedaccording to the error they produce with respect to full-rank adaptive processing.When the true covariance matrix is known, reduced-rank processing is suboptimal.However, our interest in those methods stems from the fact that in limiteddataset regimens reduced-rank methods actually outperform full-rank adaptive