Some of important issues in acoustic echo cancellation (AEC) using adaptive filters are the sparseness of the acoustic path impulse responses and strong dependency of the convergence performance of adaptive algorithm to the eigenvalue spread of the input signal correlation matrix. These issues result in a performance degradation of the adaptive AEC systems. In this paper, to improve the performance of the LMS/Newton adaptive algorithm in AEC, the matrix inverse computation is modified. To this end, the matrix inversion lemma is employed such that the contribution of the matrix inverse in the weight update is initially high and as a result, the dependency of the adaptive algorithm to the eigenvalue spread is low during the initial convergence. In addition, for the step-size adjustment, an improved proportionate method is applied such that during the convergence, the contribution of those weights having higher amplitudes in the adaptation process is gradually varied to become identical at the end of convergence. The proposed adaptive proportionate method, results in both convergence rate and steady-state performance improvement for identification of sparse acoustic impulse responses. Simulation results using a colored speech-like signal shows the steady-state misalignment of the proposed algorithm is typically 6.5 dB lower than that of the LMS/Newton algorithm. Moreover, the convergence of the proposed algorithm is typically 3.6 sec faster than that of the PNLMS algorithm, to achieve a misalignment of -17 dB. Theoretical misalignment analyses in the transient and steady state are presented and verified with simulation results.
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