Diffusion augmented complex-valued LMS algorithm with shared measurements and its performance analysis

The diffusion augmented complex-valued LMS (DACLMS) algorithm was proposed for distributed estima-tion over networks to deal with noncircular signals. This paper develops an improved DACLMS by sharing measurements between nodes within the same neighborhood. To predict its stochastic behavior, including the transient mean weight error, standard mean-square error (MSE), and complementary MSE (CMSE), is analyzed under some frequently-used statistical assumptions. A joint consideration of the MSE and CMSE performance is also analyzed to provide extra insight to the stochastic behavior of the proposed algo-rithm. Furthermore, the closed-form expressions for the steady-state MSE and CMSE are subsequently derived based on the transient analysis results. Since the proposed steady-state performance analysis does not assume that the network has the same data statistics at all nodes, it is applicable to the DA-CLMS without shared measurements and more general than the existing steady-state analysis. Simulation results are finally provided to verify the accuracy of the theoretical expressions and the effectiveness of the proposed algorithm.(c) 2022 Elsevier B.V. All rights reserved.