Smooth Approximation l0-Norm Constrained Affine Projection Algorithm and Its Applications in Sparse Channel Estimation

Abstract EN

We propose a smooth approximation l0-norm constrained affine projectionalgorithm (SL0-APA) to improve the convergence speed and the steady-state error of affine projectionalgorithm (APA) for sparse channel estimation.

The proposed algorithm ensures improved performance interms of the convergence speed and the steady-state error via the combination of a smooth approximationl0-norm (SL0) penalty on the coefficients into the standard APA cost function, which gives rise to a zeroattractor that promotes the sparsity of the channel taps in the channel estimation and hence acceleratesthe convergence speed and reduces the steady-state error when the channel is sparse.

The simulationresults demonstrate that our proposed SL0-APA is superior to the standard APA and its sparsity-awarealgorithms in terms of both the convergence speed and the steady-state behavior in a designated sparsechannel.

Furthermore, SL0-APA is shown to have smaller steady-state error than the previously proposedsparsity-aware algorithms when the number of nonzero taps in the sparse channel increases.