Effects of Mutual Coupling upon the LMS Adaptive Antenna Array Algorithm

The Least Mean Squares (LMS) algorithm has been frequently used for adapting the weighting multipliers of array elements which form the resulting antenna pattern. While significant performance gain has been reported for such applications as forming a pattern maximum in the direction of a desired signal and adaptively nulling strong jammers, many of the current results have assumed no mutual coupling between array elements. This paper examines the effects of mutual element coupling upon two properties of the LMS algorithm: (1) convergence rate, and (2) steady state pattern. Analysis is developed which displays the effects of mutual coupling explicitly via the elemental coupling coefficients. It is shown that both amplitude and phase of the elemental coupling in general degrades the convergence rate of the LMS algorithm and causes the pattern maximum to appear at a look-direction other than the angle of desired signal arrival. Several examples then illustrate LMS performance in representative coupled environments.