Cross correlation P-vector influence on LMS convergence

The principal weakness of Least Mean Squares (LMS) algorithm is that adaptation can be sometimes slow. Convergence is known to depend mainly on eigenvalue spread of the input signal, through the time constants of the various convergence modes. However, most LMS convergence analysis do not consider the influence of cross correlation between input and desired output signals, which plays also a significant role on convergence and is the main topic of this paper. The extreme cases of high and low statistical similarity between input and desired output are analysed in detail. Furthermore, an LMS-based adaptive system that seizes the convergence properties explored is also introduced. This system is shown to achieve better performance (that is, faster convergence while maintaining the steady-state error level) than LMS when input and desired output present low or moderately low statistical similarity.