|Christ D. Richmond
Massachusetts Institute of Technology
305 Memorial Drive, Room 512B
Cambridge, MA 02139
tel: (617) 225-9832 or (617) 981-0346
Abstract Recently, non-Gaussian signal and array processing has received increased attention. The power resolution of available technologies based on sophisticated statistical processing techniques brings into question the classic assumption of data normality. Hence, there exists a need for statistical performance analyses which address in a relatively general sense a plurality of possible non-Gaussian distributions, especially in adaptive array scenarios which often involve estimation of the data covariance via the sample covariance matrix (SCM). The theory of complex multivariate elliptically contoured (MEC) distributions provides one such vehicle to perform such analyses. In this presentation we replace the classic assumption of data normality with one of MEC distributed data and reexamine many of the important Gaussian-based results of adaptive array detection and signal estimation. In particular, Kelly's Generalized Likelihood Ratio Test is shown to be optimal over a broad class of MECs. The PFA and CFAR loss are shown invariant over this entire MEC class, and PD is data distribution dependent. Exact statistical analyses of the SCM based LCMV and GSC beamformers, which include pdfs for their SCM-based weightings, beam responses, and beamformer outputs are given. All results suggest significant robustness implications to adaptive array processing in non-Gaussian environments.
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