A model-based variable step-size strategy for proximal multitask diffusion LMS algorithm

Several practical applications, such as distributed spectrum sensing and channel identification in underwater communication networks with multiple sensors, can be modeled as a distributed network with jointly sparse structure. For such a network, the proximal multitask diffusion least mean square (LMS) algorithm has been proposed in the literature, and its performance has been studied thoroughly. Due to the trade-off between convergence speed and steady-state performance in the proximal multitask diffusion LMS algorithm, it is important but not trivial, to set the step-size parameter properly. To address this issue, a variable step-size strategy for the proximal multitask diffusion LMS algorithm is proposed in this paper. Based on the transient model of the proximal multitask diffusion LMS algorithm, and by minimizing an upper-bound of the excess mean-square error (EMSE) at each iteration on the basis of a white input assumption, we obtain a closed-form expression of the step-size parameter. Simulation results illustrate the effectiveness of the proposed strategy and highlight its performance through comparison with other existing variable step-size strategies, in the cases of white and moderately correlated inputs.