Observation-Transformed Distributed Detection (TDD) Under Reporting Noise and Power Constraint

In distributed detection (DD), sensors typically report their sensed information to a fusion center (FC) either in its raw form or in a compressed form, where a final decision is made regarding the true hypothesis generating the data. In this paper, we focus on the scenario where the sensor reporting process is power-constrained, and the reporting channels are corrupted by additive noise. We propose an observation-transformed DD (TDD) framework, where the sensed data are transformed before being reported to the FC using the same power as the DD system without any observation transform. We demonstrate that the Bhattacharyya distance between the distributions of received signals under different hypotheses can be increased with proper design of the transforms. We then show that finding the optimal transform leads to a functional optimization problem, which can be solved using sequential quadratic programming (SQP). Suboptimal transforms are presented for maximizing the Bhattacharyya distance, as well as for maximizing the Kullback-Leibler divergence, and minimizing the Bayes error probability of detection for a single-sensor scenario. The results demonstrate that the proposed framework enhances detection performance and provides insights into the fundamental limits of power-constrained distributed detection in noisy environments.