Distributed Cross-Relation-Based Frequency-Domain Blind System Identification Using Online-Admm

Abstract

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.

Distributed Adaptive Norm Estimation for Blind System Identification in Wireless Sensor Networks

“…In this section, we briefly outline the adaptive SIMO BSI algorithm proposed in [9], setting the scene for the distributed averaging scheme proposed herein. We refer the reader to [9] for the full derivation of the algorithm.…”

“…We can define the symmetric adjacency matrix C with elements Cij = 1 if {i, j} ∈ E and 0 otherwise. It may be noted that in [9], the pairs {i, j} ∈ E are ordered, which yields a directed graph and leads to two sets of neighborhoods ("transmit" and "receive") and therefore a non-symmetric adjacency matrix. For the sake of brevity, we limit the explanations in this paper to the undirected case.…”

“…Source code available at https://github.com/ SOUNDS-RESEARCH/icassp2023-adapt-dist-avg blind system identification (BSI) has been addressed with adaptive cross-relation-based (CR) algorithms [7,8]. In this context, we recently introduced an adaptive CR-based algorithm [9] using the alternating direction method of multipliers (ADMM) [10].…”

“…However, the CR-based BSI task necessitates a non-triviality constraint on the full system to be identified (we refer the reader to, e.g., [11,12] for details), which manifests itself as one or more variables that require network-wide shared information for their computation. The algorithm in [9] relies on node-wise values being relayed throughout the network. In contrast, to overcome the need for the network to be fully connected, [7,8] use an average consensus [13] approach where a secondary recursion estimates the global variable for each signal frame.…”

“…In this paper, we extend our algorithm in [9] with a distributed averaging-based [13] estimation scheme for the global variable. This approach allows us, similarly to [14,15], to compute the global variable without needing a fully connected network or broadcasting.…”