Exponentially Weighted Step-Size Projection Algorithm for Acoustic Echo Cancellers

Shoji MAKINO  Yutaka KANEDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A   No.11   pp.1500-1508
Publication Date: 1992/11/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Acoustic System Modeling and Signal Processing)
digital signal processing,  adaptive filter,  adaptive algorithm,  echo canceller,  acoustics,  

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This paper proposes a new adaptive algorithm for acoustic echo cancellers with four times the convergence speed for a speech input, at almost the same computational load, of the normalized LMS (NLMS). This algorithm reflects both the statistics of the variation of a room impulse response and the whitening of the received input signal. This algorithm, called the ESP (exponentially weighted step-size projection) algorithm, uses a different step size for each coefficient of an adaptive transversal filter. These step sizes are time-invariant and weighted proportional to the expected variation of a room impulse response. As a result, the algorithm adjusts coefficients with large errors in large steps, and coefficients with small errors in small steps. 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. This algorithm also reflects the whitening of the received input signal, i.e., it removes the correlation between consecutive received input vectors. This process is effective for speech, which has a highly non-white spectrum. A geometric interpretation of the proposed algorithm is derived and the convergence condition is proved. A fast profection algorithm is introduced to reduce the computational complexity and modified for a practical multiple DSP structure so that it requires almost the same computational load, 2L multiply-add operations, as the conventional NLMS. The algorithm is implemented in an acoustic echo canceller constructed with multiple DSP chips, and its fast convergence is demonstrated.