A Novel Widely-Linear Complex-Valued Diffusion VSS-LMS Algorithm for Distributed Network and Its Performance Analysis

To address the shortcomings of the widely-linear complex-valued distributed adaptive filtering algorithm that cannot combine convergence speed and steady-state performance when using a fixed step-size strategy. In this paper, by making the partial derivative of the square of the sum of a priori error and a posteriori error with respect to step-size equal to zero, we propose a novel variable step-size (VSS) strategy, which is formulated as a function of a priori error and a posteriori error. In addition, a corresponding adaptive filtering algorithm is proposed by using the VSS strategy. Then in the process of parameter update, the moving average method is used to avoid large perturbations in iteration of the algorithm. Secondly, the theoretically analysis of the transient and steady-state performance of the proposed algorithm is provided. Finally, in the numerical simulation experiments, the effect of each parameter on the algorithm is tested, the result of the comparison with the fixed-step algorithm illustrates that the proposed algorithm has more superiority, and the high degree of matching between theory and experiment also verifies the feasibility and accuracy of the theoretical analysis method.