Statistical Analysis of Adaptive Maximum - Likelihood Signal Estimator

A classical problem in many radar and sonar applications is the adaptive detection/esti-mation of a given signal in the presence of zero mean Gaussian noise. Reed, Mallett, and Brennan (RMB) derived and analyzed an adaptive detection scheme where the noise adaptation and non-trivial nature of their analysis resulted from the use of a noise sample covariance matrix (SCM). The case now considered is that of adaptive signal estimation. Specifically, the exact probability density function (pdf) for the ML signal estimator, also referred to as the Minimum Variance Distortionless Response (MVDR) and as the Linearly Constrained Minimum Variance (LCMV) Beamformer, is derived when the esti-mator relies on a SCM for evaluation. The observation from which the signal ML estimate is made is assumed linear in the signal and corrupted by additive complex Gaussian noise. The SCM assumes a Complex Wishart (CW) distribution when each of the noise samples is i.i.d. Thus, by using the CW probabilistic model for the distribution of the estimated noise covariance it is shown that the pdf of the Adaptive ML (AML) signal estimator, i.e. the ML signal estimator which employs a SCM for evaluation, is in general the conflu-ent hypergeometric function known as Kummer's Function. The AML signal estimator remains unbiased, but asymptotically efficient; moreover, the AML signal estimator converges in distribution to the Gaussian non-adaptive beamformer output (known noise covariance). When the sample size of the estimated noise covariance matrix is fixed, there exist a dynamic tradeoff between Signal-to-Noise Ratio (SNR) and noise adaptivity as the dimensionality of array data is varied suggesting the existence of an optimal array data dimension which will yield the best performance. He is presently a Teaching Assistant and a candidate for the PhD at MIT. His research interest include statistical signal and array processing, detection/estimation, radar, controls, multivariate analysis and adaptive systems. His journal publications include