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Sociedade Brasileira de Telecomunicações

A Block-Sparsity Induced NLMS Algorithm with Bias Compensation

Adaptive filtering algorithms are flexible mechanisms that adapt themselves to the environment statistics in which they are immersed. It is known that in practice several transfer functions are sparse, in the sense that their energy is concentrated in a few (sometimes clustered) coefficients. In this paper, a new normalized adaptive algorithm tailored to identifying block-sparse systems using a mixed ℓ2,0-norm of the adaptive coefficients is devised. Since the presence of noise in the input signal may induce an additional asymptotic bias in the estimation procedure, a compensation scheme is also advanced to address such an issue. At last, the computational burden is controlled by the adoption of a selective partial-update strategy. Simulated results indicate that the proposed algorithms present good performance compared to state-of-the-art alternatives, and allows the designer the choice of a convenient point regarding the trade-off between computational cost and convergence rate.

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