A New Penalized Improved Proportionate Affine Projection Algorithm for Block Sparse Systems

Abstract

Adaptive signal processing is a growing area of research, and there is a constant drive to improve adaptive algorithms for sparse system identification, such as echo cancellation. A new improved proportionate affine projection algorithm penalized with the l₀-norm, is proposed for system identification of sparse systems whose impulse response coefficients are grouped in blocks, or block-sparse system identification. The l₀-norm penalty is integrated into the cost function of the Block sparse Improved proportionate affine projection algorithm (BS-IPAPA) to derive the proposed algorithm l₀-norm BS-IPAPA (l₀-BS-IPAPA). The mean stability condition is derived. Simulation results reveal that the l₀-BS-IPAPA outperforms its competing algorithms, namely IPAPA, l₀-IPAPA, BS-IPAPA, and l₀-APA with regard to misalignment, tracking, and convergence rate performance for identification of block-sparse systems. For a colored input single cluster channel, an improvement of about 31% in the initial convergence rate is achieved by the l₀-BS-IPAPA over the BS-IPAPA. Similarly, for a colored input double cluster channel, the proposed algorithm is 14% better than the BS-IPAPA. Studies comparing the performance for higher projection order and dispersive systems are illustrated. To enhance the performance of the l₀-BS-IPAPA further, its variable step-size version is derived and studied. A transient study of the proposed l₀-BS-IPAPA against varying SNRs is conducted. An average 3 dB improvement in echo return loss enhancement is achieved by the proposed algorithm over the BS-IPAPA for real-world datasets. A comparative study is made between the computational overload of the proposed and its competing algorithms.