Convergent Behavior Of Modulus-restoring Adaptive Arrays In Gaussian Interference Environments

Abstract

The convergent behavior of the general class of modulus-resioral (M0RE) algorithms, which encompasses the class of constant-modulus algorithms (CMAs) are derived for the case where the MORE algorithms adapt a sensor array excited by a single non-Gaussian signal of interest (SOI) and full-rank Gaussian noise and co-channel interference. The class of modulus-mapping cost functions (MMCFs) are introduced, and stationary solutions of the MMCFs are obtained for arbitrary SOI modulus, and for arbitrary background-interference covariance distribution. It is shown (subject to mild restrictions) that the MMCFs will in general have two classes of stationary solutions in the single-SOI environment: signal-capture solutions where the desired signal is captured with maximum attainable SINR, and noise-capture solutions where the desired signal is nulled by the array. These solutions are also shown to be either rainima or saddle points of the MMCF, depending only on the variation in the desired-signal modulus.