On Adaptive Transmission for Distributed Detection in Energy Harvesting Wireless Sensor Networks With Limited Fusion Center Feedback

Abstract

We consider a wireless sensor network tasked with solving a binary distributed detection problem. Sensors communicate directly with a fusion center (FC) over orthogonal fading channels, with additive Gaussian noise. Each sensor can harvest randomly arriving energy units and store them in a battery. Also, it knows its quantized channel state information (CSI), acquired via a limited feedback channel from the FC. Modeling the randomly arriving energy units during a time slot as a Poisson process and the battery dynamics as a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -state Markov chain (where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> is the battery size), we propose a channel-dependent transmit power control strategy such that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${J}$ </tex-math></inline-formula> -divergence based detection metric is maximized at the FC, subject to an average transmit power per sensor constraint. The proposed strategy is parametrized in terms of the channel gain quantization thresholds and the scale factors corresponding to the quantization intervals. This strategy allows each sensor to adapt its transmit power based on its battery state and its qunatized CSI. Finding optimal strategy requires solving a non-convex optimization problem that is not differentiable with respect to the optimization variables. We propose near-optimal strategies based on random search methods that have a low-computational complexity and provide a close-to-optimal performance.