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The issue considered in the current study is the problem of adaptive distributed estimation based on diffusion strategy which can exploit sparsity in improving estimation error and reducing communications. It has been shown that distributed estimation leads to a good performance in terms of the error value, convergence rate, and robustness against node and link failures in wireless sensor networks. However, the main focus of many works in the field of distributed estimation research is on convergence speed and estimation error, neglecting the fact that communications among the nodes require a lot of transmissions. In this work, the focus is on a solution based on sparse diffusion least mean squares (LMS) algorithm, and a new version of sparse diffusion LMS algorithm is proposed which takes both communications and error cost into account. Also, the computation complexity and communication cost for every node of the network, as well as performance analysis of the proposed strategy, is provided. The performance of the proposed method in comparison with the existing methods is illustrated by means of simulations in terms of computational and communicational cost, and flexibility to signal changes.

Wireless sensor networks (WSNs) could benefit a lot from compressive sensing (CS). Inherent physical structure of sensors of WSNs (battery-powered devices) demands computational-efficient algorithms with no heavy burden on a small subset of the sensors, i.e. fusion sensors. This could be achieved by distributed algorithms in which computation is distributed among all sensor nodes. On this basis, in this study, the authors have proposed a distributed and cooperative sparse recovery algorithm in which each sensor decodes a sparse signal by running a recovery algorithm with the cooperation of its neighbours. The proposed algorithm has a general structure and can be adapted to many optimisation algorithms in the context of the CS. This algorithm is completely distributed and requires an acceptable computational complexity that is suitable for WSNs. A detailed proof of convergence behaviour of the proposed algorithm is also presented. The superiority of the proposed algorithm compared with similar methods in terms of recovery quality and convergence rate is confirmed through simulation.