Optimal Matching in Wireless Sensor Networks

We design a wireless sensor network (WSN) in terms of rate and power allocation in order to send without loss the data gathered by the nodes to a common sink. Correlation between the data and channel impairments dictate the constraints of the optimization problem. We further assume that the WSN uses off-the-shelf compression and channel coding algorithms. More precisely source and channel coding are separated and distributed source coding is performed by pairs of nodes. This raises the problem of optimally matching the nodes. We show that under all these constraints the optimal design (including rate/power allocation and matching) has polynomial complexity (in the number of nodes in the network). A closed form solution is given for the rate/power allocation, and the matching solution is readily interpreted. For noiseless channels, the optimization matches close nodes whereas, for noisy channels, there is a tradeoff between matching close nodes and matching nodes with different distances to the sink. This fact is illustrated by simulations based on empirical measures. We also show that the matching technique provides substantial gains in either storage capacity or power consumption for the WSN with regard to the case where the correlation between the nodes is not used.