Diffusion least-mean squares over distributed networks in the presence of MAC errors

This paper presents the formulation and steady-state analysis of the distributed estimation algorithms based on diffusion cooperation scheme, in which all nodes in the network communicate employing a non-ideal channel access mechanism. We formulate and study a two-node network and derive the closed-form expressions of the steady-state mean-square deviation (MSD). We also assess the mean performance and stability condition. The proposed analytical framework enables us to investigate the effects of the medium access control (MAC) layer performance on the behavior of the diffusion least-mean squares (LMS) algorithm in terms of the convergence speed and the steady-state error that is validated by performing Monte Carlo simulations. Simulation and analysis confirm that a high probability of collision at the MAC level, results in lower convergence speed and higher steady-state MSD for distributed estimation algorithm.