Optimal Sensor Decision Rules for Quantized-but-Uncoded Distributed Detection

In conventional codeword-based distributed detection (CDD), sensors quantize their observations and report codewords to the fusion center (FC) where a final decision is made regarding the truthfulness of the hypotheses. Recently, quantized-but-uncoded DD (QDD) has been proposed, where sensors, after quantization, transmit summarized values instead of codewords to the FC. QDD can adapt well to the power constraint and offers better detection performance than CDD. However, the added degree of freedom in parameter selection in QDD comes with high complexity in optimal system design. The contribution of this letter is a proof showing that in QDD, the optimal sensor decision rules for binary decisions are likelihood-ratio-quantizers (LRQ), regardless of the reporting channel conditions, provided that the sensor observations are conditionally independent given the hypotheses. This property largely simplifies the design of QDD. Performance comparison is presented for CDD, QDD, and a benchmark system that reports original sensor observations, when both sensing and reporting channel noise exist.