A memory improved proportionate affine projection algorithm for sparse system identification

For cluster sparse system identification, it is known that the cluster sparse improved proportionate affine projection algorithm (CS-IPAPA) outperforms the standard IPAPA. However, since CS-IPAPA does not retain past proportionate factors, its performance can be further improved. In this paper, a modification to CS-IPAPA is proposed by utilizing the past instant proportionate elements based on its projection order. Steady-state performance of the proposed memory cluster sparse improved proportionate affine projection algorithm (MCS-IPAPA) is studied by deriving the condition for mean stability. Different simulation setups show that the proposed algorithm outperforms different versions of IPAPA in terms of convergence rate, normalized misalignment (NM) and tracking, for different types of inputs like colored noise, white noise, and speech signal. By incorporating past proportionate factors, the proposed MCS-IPAPA significantly reduces computational complexity for higher projection orders.