Sparse Distributed Estimation via Heterogeneous Diffusion Adaptive Networks

Recently, diffusion networks have been proposed to identify sparse linear systems which employ sparsity-aware algorithms like the zero-attracting LMS (ZA-LMS) at each node to exploit sparsity. In this brief, we show that the same optimum performance as reached by the aforementioned networks can also be achieved by a "heterogeneous" network with only a fraction of the nodes deploying ZA-LMS-based adaptation, provided that the ZA-LMS-based nodes are distributed over the network maintaining some "uniformity." Reduction in the number of sparsity-aware nodes reduces the overall computational burden of the network. We show analytically and also by simulation studies that the only adjustment needed to achieve this reduction is a proportional increase in the value of the optimum zero attracting coefficient.