Complementary performance analysis of general complex-valued diffusion LMS for noncircular signals

Abstract

Abstract A novel transient and steady-state complementary mean square analysis of the general diffusion complex least mean square (G-DCLMS) algorithm, including diffusion complex LMS (DCLMS) and the diffusion augmented complex LMS (DACLMS) algorithm is proposed. Considering the second order noncircular input and noise, we first propose the network complementary mean square error (NCMSE) and the complementary covariance matrix of weight error vector for G-DCLMS algorithm. Then, we quantify the real and imaginary components of the network MSE and network MSD of G-DCLMS independently using the proposed analysis approach, jointly with current network standard mean square error analysis method. Based on the similarity conjecture and the approximate uncorrelating transform (AUT), we develop a stability bound on the step-size to guarantee the stability of the proposed complementary covariance matrix of weight error vector, and also obtain the steady-state performance of the proposed NCMSE of G-DCLMS. The simulation results verify the effectiveness of the newly proposed analysis approach.