1 Distributed Function Computation in Wireless Sensor Networks ∗

A wireless sensor network is often built for a specific purpose, and sensors are required to collaborate to accomplish a common task. Many of these tasks can be regarded as computations of functions of the sensor measurements. In this chapter, we study such a function computation problem in wireless sensor networks under two different scenarios. In Section 1.2, we consider a wireless sensor network consisting of n sensors. Each sensor has a recorded bit, which has been set to either “0” or “1,” and the statistics of sensor measurements are assumed to be unavailable. The network has a special node called the fusion center whose goal is to compute a symmetric function of these measurements. We also assume the wireless channels are binary symmetric channels with a probability of error p. Under this setting, we study distributed function computation algorithms which use multi-reception diversity to combat channel noise and data aggregation to reduce the number of transmissions. We first show a trivial lower bound on the transmission energy consumption, and then propose a distributed algorithm whose energy consumption is only a factor of log logn more than the lower bound. In Section 1.3, we consider a different scenario where n sensors are densely deployed, and the sensor measurements are highly correlated. It is assumed that the statistics of sensor measurements are known, and the sensors can hear each other. Further, we assume that each sensor measurement can take one of m values, and each sensor also has m signals to represent those measurements. Different signal is assumed to associate with different transmission cost. The goal of the the network is to transmit information to the fusion center so that the fusion center can compute a function based on the sensor measurements. Assume that real-time function computation is required, so at each time slot, the measurement should be reported immediately. We propose a stochastic control approach to exploit the correlation of sensor measurements to achieve the minimum cost real-time function computation.