Distributed Detection in EH-Powered Mobile WSNs: Adaptive Transmission over Temporally Correlated MIMO Channels with Limited Feedback

Abstract

We address distributed detection problem in a mobile wireless sensor network, where each deployed sensor stores randomly arriving energy units in a finite-size battery. Sensors transmit their symbols simultaneously to a mobile fusion center (FC) with $M > 1$ antennas, over temporally correlated fading channels. To characterize the time variation of the fading channel, we adopt a Markovian model and assume that the fading channel time-correlation is defined by the Jakes-Clark's correlation function. We consider limited feedback of channel gain, defined as the Frobenius norm of MIMO channel matrix, at a fixed feedback frequency from the FC to sensors. Modeling the randomly arriving energy units during a time slot as a Poisson process, and the quantized channel gain and the battery dynamics as homogeneous finite-state Markov chains, we propose an adaptive transmission scheme such that the $J$-divergence based detection metric is maximized at the FC, subject to an average per-sensor transmit power constraint. The proposed scheme is parameterized in terms of the scale factors (our optimization variables) corresponding to the channel gain quantization intervals. This scheme allows each sensor to adapt its transmit power in each time slot, based on its current battery state and the latest available channel gain feedback.