Adaptive equalizer using finite-bit power-of-two quantizer

The stochastic gradient algorithm using a simplified arithmetic is analyzed in this paper. A power-of-two quantizer is used for the input of the multiplier to reduce the multiplication to at most a simple shift. In spite of its simple implementation, the performance is shown to be comparable to the classical LMS algorithm. A linearized approximation to the quantizer is first derived, followed by the analysis of an exact nonlinear model. The derivation is based on the Gaussian assumption, and the effects of removing the Gaussian assumption are later considered. The roundoff error due to the finite-bit computation is calculated. Computer simulation results are provided to support the analysis.