Sensor networks over information fields: optimal energy and node distributions

Wireless sensor networks are typically deployed over an information field to sense and gather information from a distributed physical process. Resource allocation problems considered in the literature often ignore the underlying information field and rather consider a uniform distribution of information. We propose an information field model that partitions the observation space into a grid, with independent information being generated at each point in the grid. Given this model, we find the optimal node distribution over the field that maximizes the network information capacity or the total information gathered over the lifetime of the network. The optimal node distribution is obtained by considering the equivalent problem of optimal energy distribution and flow over the information field that maximizes the information capacity.