Steady State Mean Square Analysis of Convex Combination of ZA-APA and APA for Acoustic Echo Cancellation
This paper proposes a new approach for the cancellation of acoustic echo in a loud speaker enclosed microphone system. The acoustic echo is often sparse in nature and the level of sparseness also changes with time. The input in such applications, is speech which is highly correlated. Thus there is a requirement of an adaptive filter which can work in both sparse and non sparse environment and perform well even for correlated inputs. We present convex combination of conventional affine projection algorithm (APA) with small step size and projection order and zero attraction APA (ZA-APA) for echo cancellation. Steady state excess mean square (EMSE) error analysis revealed that the proposed algorithm converges to conventional APA in non sparse environment and to ZA-APA in case of sparse environment and in semi sparse condition, the steady state EMSE value is at least same as the lesser filter‘s steady state error or even smaller depending on the value of the constant chosen. Simulation is performed in the context of acoustic echo cancellation and the validity of the proposed algorithm is proved from the simulation results.
KeywordsAffine projection algorithm Convex combination Steady state mean square error Zero attraction Convergence
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