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Analysis of partial diffusion recursive least squares adaptation over noisy links

Partial diffusion-based recursive least squares (PDRLS) is an effective way of lowering computational load and power consumption in adaptive network implementation. In this method, every single node distributes a fraction of its intermediate vector estimate with its immediate neighbours at each iteration. In this study, the authors examine the steady-state performance of PDRLS algorithm in the presence of noisy links by means of an energy conservation argument. They consider the mean-square-deviation (MSD) as the performance metric in the steady-state and derive a theoretical expression for PDRLS algorithm with noisy links. The authors’ analysis reveals that unlike the established statements on PDRLS scheme under ideal links, the trade-off between MSD performance and the number of selected entries of the intermediate estimate vectors, as a sign of communication cost, is mitigated. They further examine the convergence behaviour of the PDRLS algorithm. The obtained results show that under certain statistical assumptions for the measurement data and noise signals, under noisy links the PDRLS algorithm is stable in both mean and mean-square senses. Finally, they present some simulation results to verify the theoretical findings.