Diffusion LMS algorithms with multi combination for distributed estimation: Formulation and performance analysis

We propose diffusion least-mean-square (LMS) algorithms that use multi-combination step. We allow each node in the network to use information from multi-hop neighbors to approximate a global cost function accurately. By minimizing this cost and dividing multi-hop range summation into 1-hop range combination steps, we derive new diffusion LMS algorithms. The resulting distributed algorithms consist of adaptation and multi-combination step. Multi combination allows each node to use information from non-adjacent nodes at each time instant, thereby reducing steady-state error. We analyzed the output to derive stability conditions and to quantify the transient and steady-state behaviors. Theoretical and experimental results indicate that the proposed algorithms have lower steady-state error compared to the conventional diffusion LMS algorithms. We also propose a new combination rule for the multi-combination step which can further improve the estimation performance of the proposed algorithms.