DERIVED PDF OF MAXIMUM-LIKELIHOOD SIGNAL ESTIMATOR WHICH EMPLOYS AN ESTIMATED NOISE COVARIANCE

A probability density function (pdf) for the maximum likelihood (ML) s ignal vector estimator is derived when the estimator relies on a noise sample covariance matrix (SCM) for evaluation. By using a complex Wis hart probabilistic model for the distribution of the SCM, it is shown that the pdf of the adaptive ML (AML) signal estimator (alias the SCM based minimum variance distortionless response (MVDR) beamformer outpu t and, more generally, the SCM based linearly constrained minimum vari ance (LCMV) beamformer output) is, in general, the confluent hypergeom etric function of a complex matrix argument known as Kummer's function . The AML signal estimator remains unbiased but only asymptotically ef fficient; moreover, the AML signal estimator converges in distribution to the ML signal estimator (known noise covariance). When the sample size of the estimated noise covariance matrix is fixed, it is demonstr ated that there exists a dynamic tradeoff between signal-to-noise rati o (SNR) and noise adaptivity as the dimensionality of the array data ( number of adaptive degrees of freedom) is varied, suggesting the exist ence of an optimal array data dimension that will yield the best perfo rmance.