Augmented complex-valued normalized subband adaptive filter: Algorithm derivation and analysis

In this paper, a novel augmented complex-valued normalized subband adaptive filter (ACNSAF) algorithm is proposed for processing the noncircular complex-valued signals. Based on the augmented statistics, the proposed algorithm is derived by computing a constraint cost function. Due to contain all second-order statistical properties, the ACNSAF algorithm can process the circular and noncircular complex-valued signals simultaneously. Moreover, the stability and mean square steady-state analysis of the proposed algorithm is derived by using the energy conservation principle. Computer simulation experiments on complex-valued system identification, prediction and noise cancelling show that the proposed algorithm achieves the improved mean square deviation and prediction gain compared to the ACNLMS algorithm. And the simulation results are consistent with the analysis results.