Statistical analysis of adaptive beamforming methods
Abstract
A statistical measure of the performance of an adaptive beamforming technique for a multisensor linear array is developed. The sample complex vector signal processes, Z sub K as observed at sample times sub K an element of (OT) is used to calculate a positive, definite, maximum likelihood estimate (M.L.E.) R of the signal process covariance matrix R. Then, an estimated measure of the performance of the array in terms of its ability to suppress an interfering signal is developed from an a priori specified process matrix E(R), its sample. M.L.E. estimate R1 and a form of the Wishart distribution. In particular, such an estimated measure of performance in terms of suppressing an interfering signal with an angle of arrival (AOA) of theta 2 relative to a beam AOA of Theta 1 is the statistic represented by the absolute difference of the L2 norms. Block averaging as required in the sample estimation of 1/R1 provides statistically consistent estimates of the process parameters necessary to the efficient interference suppression of unwanted signals by the beamformer process. Exponential averaging does not provide numerically or statistically consistent estimates of the requisite process parameters either for deterministic or stochastic sample process.
 Publication:

Final Report Electromagnetic Systems Labs
 Pub Date:
 May 1988
 Bibcode:
 1988esli.rept.....M
 Keywords:

 Beams (Radiation);
 Linear Arrays;
 Signal Analyzers;
 Signal Detectors;
 Statistical Analysis;
 Adaptation;
 Consistency;
 Efficiency;
 Maximum Likelihood Estimates;
 Sonar;
 Suppressors;
 Vector Analysis;
 Communications and Radar