On the steady-state mean squared error of the fixed-point LMS algorithm

This communication studies the quantization effects on the steady-state performance of a fixed-point implementation of the Least Mean Squares (LMS) adaptive algorithm. Based on experimental observations, we introduce a new intermediate mode of operation and develop a simplified theoretical approach to explain the behaviour caused by quantization effects in this mode. We also review the stall mode and provide a new expression that predicts the discontinuous behaviour of the steady-state mean squared error as a function of the input signal power. Combined with a previous analysis of quantization effects in stochastic gradient mode, this study provides analytical expressions for the steady-state mean squared error for the full range of step-size values. We present experimental results that are in a good agreement with theoretical predictions to validate our model.