Goal-Oriented Distributed L-MMSE Estimation in Wireless Fading Channels By Gaussian Information Bottleneck

This paper studies the use of the Gaussian Information Bottleneck (GIB) in integrated sensing and communication (ISAC) systems for distributed estimation of a target Gaussian source. Multiple sensors acquire noisy measurements and communicate wirelessly with a centralized fusion and estimation center (FC). To economize transmission resources, each sensor first exploits the GIB to locally compress its observations, and then, by a vector quantization (VQ) matched to the GIB, digitally transmits them over a (capacity limited) fading channel. The FC exploits the received messages to infer the target source by a linear minimum mean-squared error (L-MMSE) estimator. By a simple (dynamic) resource optimization algorithm, we show that the proposed solution can nicely trade performance estimation with compression, approaching the performance of a fully (uncompressed) centralized estimator, while significantly saving transmission rate and/or power.