A Sparse Aware Arctangent Framework Based LHCAF Algorithm for System Identification

In the past, an efficient arctangent framework-based logarithmic hyperbolic cosine adaptive filter (ALHCAF) for system identification was proposed for effective performance under the impact of impulsive noise. However, a zero attractor (ZA) penalty term was missing to utilize the sparseness characteristics of the system. In this work, we provide a norm adaptation (NA) penalised ALHCAF approach to sparse system identification. The NA-ALHCAF approach is an extension of the ALHCAF algorithm that includes a p − norm penalty term in the ALHCAF algorithm’s cost function. This penalty term performs as a collaboration of l
0
and l
1
norms and utilizes the sparseness properties of physical systems by serving as a zero attractor. Simulation results obtained from identifying an echo path suggest that the NA-ALHCAF approach outperforms current sparse-aware LHCAF algorithms concerning the steady-state error or convergence rate.