A practical method of obtaining constant convergence rates in LMS adaptive arrays

A practical, readily realizeable method of eliminating the old problem of widely disparate modal convergence rates in least mean squares (LMS) adaptive arrays is analyzed. The method is mathematically based on the Newton-Raphson iteration technique of finding zeros of a function. The practical realization is based on an extension of Compton\´s improved-feedback adaptive loop. It is shown how this modification results in constant and equal modal convergence rates in an adaptive array in conditions which cause widely disparate modal convergence rates in "standard" gradient-descent LMS algorithms, even in the presence of common circuit imperfections. The improved algorithm is compared to Compton\´s original improved-feedback loop and to a "standard" LMS adaptive array, all with equal open-loop time constants, then with individually optimized time constants. Preliminary experimental results are also shown to substantiate some of the analysis.