Exact PDFs for sample covariance based array processors with elliptically contoured data

Practical application of array processors typically requires the use of a sample covariance matrix (SCM). We add to the many results on SCM based (SCB) array processors by weakening the traditional assumption of data Gaussianity and subsequently providing for a class of array processors additional performance measures of value in practice. The snapshot data matrix is assumed complex multivariate elliptically contoured (MEC) distributed. The performance measures include the exact probability density functions (PDFs) and moments of the SCB weightings and beam responses of the following array processors: (1) maximum-likelihood signal vector estimator, (2) linearly constrained minimum variance beamformer (LCMV), (3) minimum variance distortionless response beamformer, and (4) generalized sidelobe canceller implementation of the LCMV beamformer. The SCB weightings for these array processors are complex multivariate standardized t-distributed and the SCB beam responses are generalized t. All results are completely invariant over the class of MECs considered