PDFS, CONFIDENCE-REGIONS, AND RELEVANT STATISTICS FOR A CLASS OF SAMPLE COVARIANCE-BASED ARRAY PROCESSORS

In this paper, we add to the many results on sample covariance matrix (SCR I) dependent array processors by i) weakening the traditional ass umption of Gaussian data and ii) providing for a class of array proces sors additional performance measures that are of value in practice, Th e data matrix is assumed drawn from a class of multivariate elliptical ly contoured (MEG) distributions. The performance measures include the exact probability density functions (pdf's), confidence regions, and moments of the weight vector (matrix), beam response, and beamformer o utput of certain SCM-based (SCB) array processors. The array processor s considered include the SCB: i) maximum-likelihood (ML) signal vector estimator ii) linearly constrained minimum variance beamformer (LCMV) iii) minimum variance distortionless response beamformer (MVDR) iv) g eneralized sidelobe canceller (GSC) implementation of the LCMV beamfor mer. It is shown that the exact joint pdf's for the weight vectors/mat rices of the aforementioned SCB array processors are a linear transfor mation from a complex multivariate extension of the standardized t-dis tribution. The SCB beam responses are generalized t-distributed, and t he pdf's of the SCB beamformer outputs are given by Kummer's function. All but the beamformer outputs are shown to be completely invariant s tatistics over the class of MEC's considered.