Shrinkage tuning based on an unbiased MSE estimate for sparsity-aware adaptive filtering

Effective utilization of sparsity of the system to be estimated is a key to achieve excellent adaptive filtering performances. This can be realized by the adaptive proximal forward-backward splitting (APFBS) with carefully chosen parameters. In this paper, we propose a systematic parameter tuning based on a minimization principle of an unbiased MSE estimate. Thanks to the piecewise quadratic structure of the proposed MSE estimate, we can obtain its minimizer with low computational load. A numerical example demonstrates the efficacy of the proposed parameter tuning by its excellent performance over a broader range of SNR than a heuristic parameter tuning of the APFBS.