Multichannel adaptive array processing for optimal detection

An investigation of multichannel detection of known signals in noise of uncertain covariance resulted in an optimal adaptive array algorithm. The structure of the (Bayes) optimal system for this problem was determined by computing a likelihood ratio using a reproducing prior distribution for the uncertain covariance matrix. The problem could be reparameterized so that the uncertain quantities of interest were an adaptive weighting vector and the residual squared error. There was an optimal estimator for the weighting vector. The estimator was written recursively, resulting in a predictor-corrector algorithm for the required weighting vector. A comparison with the Widrow algorithm was performed. Additional comparisons were made with two variants of the LMS algorithm and the sample matrix inversion algorithm.