Optimal network size and encoding rate for random field estimation withwireless sensor networks

In this paper, we address the problem of random field estimation with wireless sensor networks in the absence of CSI at the sensor nodes. We assume that sensors encode their observations at a common and constant rate which, on the one hand, determines the quantization noise at the encoders and, on the other, the outage probability experienced in the sensor-to-fusion center fading channels. These effects, arising from the power and bandwidth constraints that we impose, along with the spatial sampling process itself result into some distortion that we attempt to minimize by carefully selecting the optimal number of sensor nodes and the aforementioned encoding rate. On the basis of a (tight) upper bound, we derive closed-form expressions of the corresponding optimal values. Computer simulation results are mostly given in terms of optimal encoding rate and network size for different operating conditions (SNR, spatial variability of the random field) and reconstruction distortion vs. network size.