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We propose an improved proportionate affine projection algorithm (PAPA), which is realized by integrating a hybrid-norm constraint into the affine projection algorithm (APA) to estimate the cluster sparse signals that are happened in satellite and network echo channels. The proposed algorithm optimizes the hybrid <inline-formula> <tex-math notation="LaTeX">${l_{2,0}}$ </tex-math></inline-formula>-norm of the filter coefficients, and the PAPA is a special case of the proposed method. Moreover, an enhanced PAPA is modified for the cluster sparse channel estimations. Various simulation experiments are performed to verify that the proposed algorithms are superior to the APA, PAPA, and related sparse algorithms with different input signals and various parameters.

Mixed Norm Constrained Sparse APA Algorithm for Satellite and Network Echo Channel Estimation