Joint compression, detection, and routing in capacity constrained wireless sensor networks

This paper considers an important class of sensor networks where the ultimate goal is not necessarily to collect each individual measurement but rather a potentially smaller set of statistics. Considering link capacity constrained topologies, we derive results that optimally allocate rate/distortion to information collected by the sensors. As a key contribution, we determine how the flow of information emanating from the sensors should be managed, yielding optimal routing algorithms and jointly optimized networks. Our analysis encompasses the typical scenarios that are widely observed in sensor networks, and over these scenarios, we quantify the gains offered by sending the statistics rather than the measurement data itself. Our results reveal bottleneck situations over various scenarios, where directly performing bandwidth allocation over the statistics does not provide the desired gains. We start the analysis from a simple scenario, where a fixed node aggregates all the information in the sensor network and relays the information to a remote control center. We obtain close form expressions and illustrate how allocating bandwidth for each individual measurement (Case-1) performs compared to allocating it for each desired statistic (Case-2) in different bottleneck situations. Then, we extend this scenario to the case where we optimally select a number of aggregators from a cloud of sensor nodes. In this second scenario, under well defined bandwidth constraints, we look at the optimum clustering problem, in which the goal is to select the best aggregation nodes to minimize the total distortion of the desired statistics at the remote control node. We provide an algorithmic solution that returns the optimum aggregation points and the optimum size of each cluster under some mild assumptions. We finally turn our attention to the general routing problem and provide an algorithm that performs routing and bandwidth allocation jointly. We also study the performance and behavior of bandwidth allocation for both Case-1 and Case-2.