Abstract
Sensing, processing and communication must be jointly optimized for efficient operation of resource-limited wireless sensor networks. We propose a novel source-channel matching approach for distributed field estimation that naturally integrates these basic operations and facilitates a unified analysis of the impact of key parameters (number of nodes, power, field complexity) on estimation accuracy. At the heart of our approach is a distributed source-channel communication architecture that matches the spatial scale of field coherence with the spatial scale of node synchronization for phase-coherent communication: the sensor field is uniformly partitioned into multiple cells and the nodes in each cell coherently communicate simple statistics of their measurements to the destination via a dedicated noisy multiple access channel (MAC). Essentially, the optimal field estimate in each cell is implicitly computed at the destination via the coherent spatial averaging inherent in the MAC, resulting in optimal power-distortion scaling with the number of nodes. In general, smoother fields demand lower per-node power but require node synchronization over larger scales for optimal estimation. In particular, optimal mean-square distortion scaling can be achieved with sub-linear power scaling. Our results also reveal a remarkable power-density tradeoff inherent in our approach: increasing the sensor density reduces the total power required to achieve a desired distortion. A direct consequence is that consistent field estimation is possible, in principle, even with vanishing total power in the limit of high sensor density.