Distributed Cross-Relation-Based Frequency-Domain Blind System Identification using Online-ADMM

In this paper, we propose a distributed cross-relation-based adaptive algorithm for blind identification of single-input multiple-output (SIMO) systems in the frequency domain, using the alternating direction method of multipliers (ADMM) in a wireless sensor network (WSN). The network consists of a fixed number of nodes each equipped with a processing unit and a sensor that represents an output channel of the SIMO system. The proposed algorithm exploits the separability of the cross-channel relations by splitting the multichannel identification problem into sub-problems containing a subset of channels, in a way that is determined by the network topology. Each node delivers estimates for the subset of channel frequency responses, which are then combined into a consensus estimate per channel using general-form consensus ADMM in an adaptive updating scheme. Using numerical simulations, we show that it is possible to achieve convergence speeds and steady-state misalignment values comparable to fully centralized low-cost frequency-domain algorithms.