Diffusion leaky LMS algorithm: Analysis and implementation

The diffusion least-mean-square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such algorithms may change when they are implemented for acoustic echo cancellation (AEC) systems. To overcome this problem, a leaky dLMS algorithm is proposed in this work, which is characterized by its numerical stability and small steady-state error for noisy speech signals. Then, we perform some stability and convergence analyses of the proposed algorithm for Gaussian inputs and verify the theory results by simulations. As an added contribution in this paper, we further develop a new variable leakage factor (VLF) strategy for the leaky dLMS algorithm to overcome the parameter selection of adaptation. Finally, implementations of the proposed algorithms in the context of system identification and stereophonic AEC (SAEC) network are performed. Simulation results illustrate that the leaky diffusion algorithms achieve improved performance as compared with the existing algorithms.