Optimized constant-rate encoding for decentralized parameter estimation with wireless sensor networks

In this paper, we address the problem of the estimation of an underlying parameter of interest with a wireless sensor network. We assume that sensors encode (i.e. quantize) their observations at a common constant rate which, on the one hand, determines the quantization noise at the encoders and, on the other, the outage probabily experienced in the sensor-to-fusion center fading channels. We then identify the encoding rate that minimizes the distortion in the fusion center (FC) estimates or, in other words, the optimal trade-off in terms of quantization noise vs. the number of observations actually decoded at the FC. We solve the problem analytically for two cases of interest, namely, (i) networks with an asymptotically-large number of sensor nodes; and (ii) scenarios where the underlying parameter can be sampled at a low rate. Results are given in terms of expected distortion vs. network size, outage probability and SNR. The loss with respect to a system with variable encoding rates is analyzed as well.