Instantaneous error analysis of the least mean square algorithm

An analysis is presented which complements classical stochastic methods and helps to clear up ambiguities in convergence characteristics. By including the approximation of replacing the mean squared error with the instantaneous error, fundamental to the practical implementation, it is shown that the LMS algorithm attempts to minimise the instantaneous error and that the squared norm of the incident vector defines the conditions for stability at each iteration. Interesting features of the convergence, usually obscured by the complex mathematical treatments, are highlighted