Bayesian Decision Making Via Over-the-Air Soft Information Aggregation

This work formulates a collaborative decision-making framework that exploits over-the-air computation to efficiently aggregate soft information from distributed sensors. This new AirCompFDM protocol approximates the sufficient statistic (SS) of optimum binary hypothesis testing at a server node in this distributed sensing environment under different operation constraints. Leveraging pre/post-processing functions on over-the-air aggregation of sensor log-likelihood ratios, Air-CompFDM significantly improves bandwidth efficiency with little detection loss, even from modest numbers of participating sensors and imperfect phase pre-compensation. Without phase pre-compensation, the benefit of over-the-air sensor aggregation diminishes but still can mitigate the effect of channel noise. Importantly, AirCompFDM outperforms the traditional bandwidth-hungry polling scheme, even under low SNR. Furthermore, we analyze the Chernoff information and obtain the approximate effect of sensor aggregation on the probability of detection error that can help develop advanced detection strategies.