Power Allocation for Distortion Outage Minimization in Clustered Wireless Sensor Networks

In this paper we study a clustered wireless sensor network observing a Gaussian random field. Within a cluster, multiple sensors amplify and forward their measurements using uncoded analog transmission to the clusterhead (CH). In turn the clusterheads transmit also amplify and forward their received signals to a Fusion Centre (FC) located at some distance using an orthogonal multiple access scheme such as frequency division multiple access (FDMA). The distortion of the signal reconstructed at the FC is required to be within a certain threshold D_max. Due to random fading suffered by the channels from the CH´s to the FC, the distortion achieved at the FC can exceed D_max in which case a distortion outage occurs. We propose a novel optimal power allocation scheme at the CH transmitters that minimizes this distortion outage probability subject to an average total power constraints across the CH´s. While this optimal scheme performs very well, it requires full (instantaneous) channel state information (CSI) at the receiver (FC) as well as the CH transmitters. We also study some sub- optimal power allocation methods based on the knowledge of the statistics of the fading channels between the CH´s and the FC at the transmitters (and full CSI at the FC). Simulation studies show that the statistical power allocation methods perform poorly compared to the full CSI based algorithm, which points to the need for designing efficient power allocation algorithms based on quantized channel feedback from the FC to the CH´s.