ANALYSIS AND IMPLEMENTATION OF VARIABLE STEP-SIZE ADAPTIVE ALGORITHMS

Stochastic gradient adaptive filtering algorithms using variable step sizes are investigated in this paper. The variable step size algorithm improves the convergence rate while sacrificing little in steady-state error. Expressions describing the convergence of the mean and mean squared values of the coefficients are developed and are used to calculate the mean square error evolution. The initial convergence rate and the steady-state error are also investigated. In addition, the performance of the algorithm is studied when a power-of-two quantizer algorithm is used, and finite word-length effects are considered. The analytical results are verified with simulations encompassing various applications. Two CMOS implementations of the variable step size, power-of-two quantizer algorithm are presented to demonstrate that the performance gains are attainable with only a modest increase in circuit complexity.