Sparsity aware minimum error entropy algorithms

Sparse estimation has received a lot of attention due to its broad applicability. In sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through sparse adaptive filters. In previous studies, most works use the mean square error (MSE) based cost to develop sparse filters, which is rational under the assumption of Gaussian distributions. However, Gaussian assumption does not always hold in real-world environments. To address this issue, we incorporate in this work l₁-norm and reweighted l₁-norm into the minimum error entropy (MEE) criterion to develop new sparse adaptive filters, which may perform much better than the MSE based methods especially in non-Gaussian situations, since the error entropy can capture higher-order statistics of the errors . Furthermore, a new approximator of l₀-norm based on the Correntropy Induced Metric (CIM) is also used as a sparsity penalty term (SPT). Simulation results show the excellent performance of the proposed algorithms.