Widely Linear Complex-Valued Diffusion Subband Adaptive Filter Algorithm

The adaptive algorithms applied to distributed networks are usually real-valued diffusion subband adaptive filter algorithms. However, it cannot be used for processing the complex-valued signals. In this paper, a novel augmented complex-valued diffusion normalized subband adaptive filter (D-ACNSAF) algorithm is proposed for distributed estimation over networks. In order to deal with the noncircular complex-valued signals, the D-ACNSAF algorithm uses the widely linear model for a diffusion network. Due to the second-order statistical properties of signal, the D-ACNSAF algorithm can process the circular and non-circular complex-valued signals simultaneously. Moreover, the stability and mean-square steady-state analysis of the proposed algorithm are derived based on the spatial-temporal energy conservation principle. Computer simulation experiments on complex-valued system identification and prediction show that the proposed algorithm has better performance (lower mean-square deviation and faster convergence rate) than diffusion complex least-mean-square and diffusion augmented complex least-mean-square algorithms. And the simulation results are consistent with the analysis results.