A full mean-square analysis of CNSAF algorithm for noncircular inputs

Abstract

A full performance analysis of complex normalized subband adaptive filter (CNSAF) algorithm will provide guidelines for designing the adaptive filter. However, because of the noncircular characteristic of complex-value signal, the complementary mean-square performance analysis of the CNSAF algorithm has not been presented in the literature. In order to give the detailed theoretical expressions of the CNSAF algorithm, the present study first analyzes the mean-square deviation (MSD) with the energy-conservation method, and then the complementary mean-square derivation (CMSD) behavior is given using pseudo-energy-conservation method. Analytical expressions are obtained for the transient MSD and CMSD of the CNSAF algorithm. Also, the steady-state MSD and CMSD are predicted based on the closed-form expressions. Besides, the analysis results are not constrained by the distribution of input signals. Finally, simulation results obtained for diffferent inputs present a good consistence with the analytical results.