Diffusion random-cloud least-mean squares for distributed adaptive networks

This paper proposes a diffusion random-cloud least-mean-squares (DRC-LMS) algorithm for distributed adaptive networks. The proposed method extends the conventional adapt-then-combine diffusion LMS recursion by inserting a local random-cloud exploration stage between the adaptation and combination steps. At each node, an LMS trial estimate is first computed. A finite cloud of candidate estimates is then generated around this trial point, and the candidate that minimizes a local short-window squared-error criterion is selected as the intermediate estimate to be exchanged with neighboring nodes. The cloud spread is gradually decreased over time, enabling local exploration during the transient phase while making the cloud-induced perturbations negligible near steady state. Mean and mean-square performance analyses are developed under a stationary linear regression model. The analysis shows that the proposed algorithm preserves the diffusion LMS transition structure, while the cloud-selection mechanism appears as a spread-controlled perturbation. The stability condition and steady-state network MSD are characterized, and the diffusion LMS steady-state behavior is recovered when the cloud-induced perturbation becomes negligible. Simulation results show that the proposed DRC-LMS algorithm improves the transient convergence behavior of diffusion LMS by means of controlled local random-cloud exploration, while preserving comparable steady-state mean-square deviation and the same communication load. These results confirm that the proposed adapt–explore–combine mechanism is effective for accelerating the early learning phase without requiring additional information exchange among neighboring nodes.