Analysis of simplified gradient adaptive lattice algorithms using power-of-two quantization

Two gradient adaptive lattice (GAL) algorithms that have been simplified by replacing multipliers and dividers with shifting operations using power-of-two quantization are presented and analyzed. A convergence model is developed for each algorithm, from which the convergence of the mean of the filter coefficients is analyzed. An expression for the asymptotic variance of the filter coefficients of the different algorithms is developed. Both an exact analysis under a Gaussian input assumption and an analysis using a linear approximation of the power-or-two quantizer are compared to simulation results