Analysis and implementation of variable step size adaptive algorithms

Stochastic gradient adaptive filtering algorithms using variable step sizes are investigated. 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 used to calculate the mean-square-error evolution. The initial convergence rate and the steady-state error are also investigated. 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 variable 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