New results on convergence of the discrete-time LMS algorithm applied to narrowband adaptive arrays

The discrete-time, Least-Mean-Squares (LMS) algorithm is often proposed for application to adaptive antenna arrays. In analyzing the mean-square error performance of LMS, however, previous results in the open literature have generally employed approximations which are valid only in the limit for very slow adaptation in an essentially stationary environment. In this paper we apply an exact mean-square error analysis for the application of discrete-time LMS to narrow-band adaptive arrays. The results provide considerable insight into the transient response of LMS under conditions of rapid adaptation, which is of importance in many practical applications.