Diffusion Constrained Adaptive Filtering Algorithm Based on Half-Quadratic Criterion for System Identification

Classical diffusion adaptive filtering algorithms are often designed to deal with unconstrained system identification. However, they are not suited to constrained system identification. This work develops a diffusion constrained adaptive filtering algorithm to address the above problem. We use the cost function based on the half-quadratic criterion (HQC) to enhance the robustness of the nodes against impulsive noise. We also utilize the strategy of data sharing between the neighboring nodes to promote the network convergence performance. To investigate the stochastic behavior, we further analyse the stability condition and the transient and steady-state performance of the proposed diffusion constrained HQC (DCHQC) algorithm under several commonly used statistical assumptions. Simulation results are given to show the advantages of DCHQC in the context of distributed constrained system identification and beamforming and to validate the theoretical expressions on the performance prediction.