Accumulator quantization noise in the single-weight complex LMS adaptive algorithm

Quantization noise effects in a digital implementation of the complex scalar LMS adaptive algorithm are analyzed by modelling the accumulator input quantizer as a memoryless nonlinearity. The probability density function of the quantizer input, conditioned on the weight, is derived. The density is applied to finding the first and second conditional moments at the quantizer output. These are used to derive difference equations that approximate the dynamical behavior of the first and second weight moments. These difference equations, when solved numerically, compare favorably with simulation results.