Exponentially Weighted Stepsize NLMS Adaptive Filter Based on the Statistics of a Room Impulse Response

This paper proposes a new normalized least-mean-squares (NLMS) adaptive algorithm with double the convergence speed, at the same computational load, of the conventional NLMS for an acoustic echo canceller. This algorithm, called the ES (exponentially weighted stepsize) algorithm, uses a different stepsize (feedback constant) for each weight of an adaptive transversal filter. These stepsizes are time-invariant and weighted proportional to the expected variation of a room impulse response. The algorithm is based on the fact that the expected variation of a room impulse response becomes progressively smaller along the series by the same exponential ratio as the impulse response energy decay. As a result, the algorithm adjusts coefficients with large errors in large steps, and coefficients with small errors in small steps. A transition formula is derived for the mean-squared coefficient error of the proposed algorithm. The mean stepsize determines the convergence condition, the convergence speed, and the final excess mean-squared error. The algorithm is modified for a practical multiple DSP structure, so that it requires only the same amount of computation as the conventional NLMS. The algorithm is implemented in a commercial acoustic echo canceller and its fast convergence is demonstrated.