Estimation of Spatially-Correlated Random Fields With Compressed Observations

In this paper, we focus on the use of wireless sensor networks for the estimation of spatially-correlated random fields. We explicitly take communication aspects into account and propose a number of distributed pre-coding (beamforming) schemes allowing for an over-the-air compressed representation of the set of spatially correlated observations. Those observations are then encoded in a number of consecutive sensor-to-Fusion Center (FC) transmissions. The ultimate goal is to minimize the distortion in the reconstructed random field and, simultaneously, keep the number of transmissions low (i.e., the compression ratio high). Specifically, we first propose a family of distributed pre-coding schemes based on the Karhunen-Loève (KL) and partial KL transforms and we derive closed form expressions of the optimal power allocation strategies. Aspects such as residual phase synchronization errors or the fact that some sensors might be idle (inactive) are specifically taken into account in the analysis. Next, we propose an iterative and greedy scheme by which the pre-coder design and power allocation problems can be jointly solved for the general case. We assess the performance of the proposed pre-coding schemes by means of computer simulations. Other uncompressed transmission schemes are used as a benchmark.