A steady-state analysis of the LMS adaptive algorithm without use of the independence assumption

Current analysis of the LMS algorithm makes use of an “independence assumption” stating statistical independence of successive input vectors. This assumption conflicts with the inherent deterministic coherence of the vector input signal and, as such, is the source of conceptual and didactic difficulties. Nevertheless, due to its analytic convenience and its moderate agreement with experimental results, it is in widespread use. A theory of the steady-state behaviour of the LMS algorithm is presented that avoids the independence assumption with its inherent problems and yields a number of new results. Simulations support the analytic conclusions. A study is also included of the parameter or weight fluctuations for the well-known LMS algorithm applied to the common adaptive FIR filter structure