A Computationally Efficient Algorithm for Distributed Adaptive Signal Fusion based on Fractional Programs

Spatial filtering procedures aim to optimally fuse the different signals collected in a sensor array, by exploiting their inter-channel correlations. If the sensors are physically distributed, as it is the case in a wireless sensor network, the inter-channel statistics cannot directly be measured or tracked, unless the data is transmitted to a central processor, which is not always possible due to energy or bandwidth constraints. The so-called distributed adaptive signal fusion (DASF) algorithm allows to solve such problems in a distributed fashion with a reduced communication burden. The DASF algorithm iterates over the different nodes of the network, each solving a local compressed version of the original (centralized) optimization problem. However, if the solver for these local optimization problems is in itself also iterative, the computational burden can become quite large as these iterations are nested within the DASF iterations. In this paper, we focus on Dinkelbach's iterative procedure to solve fractional programs, i.e., problems of which the objective function is a ratio of two continuous functions. We propose the fractional DASF (F-DASF) algorithm which interleaves the iterations of DASF with those of Dinkelbach's procedure, to reduce the computational burden without affecting the convergence properties of the original DASF algorithm.