Distributed Adaptive Signal Fusion for Fractional Programs

TL;DR

This paper introduces a distributed adaptive signal fusion algorithm tailored for fractional programs, reducing computational complexity while ensuring convergence and optimality in sensor networks.

Contribution

It develops a novel fractional DASF algorithm that exploits problem structure to lower computational costs in distributed fractional programming.

Findings

The fractional DASF algorithm converges and is optimal.

Numerical simulations show reduced computational load.

The method outperforms straightforward DASF applications.

Abstract

The distributed adaptive signal fusion (DASF) framework allows to solve spatial filtering optimization problems in a distributed and adaptive fashion over a bandwidth-constrained wireless sensor network. The DASF algorithm requires each node to sequentially build a compressed version of the original network-wide problem and solve it locally. However, these local problems can still result in a high computational load at the nodes, especially when the required solver is iterative. In this paper, we study the particular case of fractional programs, i.e., problems for which the objective function is a fraction of two continuous functions, which indeed require such iterative solvers. By exploiting the structure of a commonly used method for solving fractional programs and interleaving it with the iterations of the standard DASF algorithm, we obtain a distributed algorithm with a significantly reduced computational cost compared to the straightforward application of DASF as a meta-algorithm. We prove convergence and optimality of this "fractional DASF" (FDASF) algorithm and demonstrate its performance via numerical simulations.