Multi-bit Distributed Detection of Sparse Stochastic Signals over Error-Prone Reporting Channels

We consider a distributed detection problem within a wireless sensor network (WSN), where a substantial number of sensors cooperate to detect the existence of sparse stochastic signals. To achieve a trade-off between detection performance and system constraints, multi-bit quantizers are employed at local sensors. Then, two quantization strategies, namely raw quantization (RQ) and likelihood ratio quantization (LQ), are examined. The multi-bit quantized signals undergo encoding into binary codewords and are subsequently transmitted to the fusion center via error-prone reporting channels. Upon exploiting the locally most powerful test (LMPT) strategy, we devise two multi-bit LMPT detectors in which quantized raw observations and local likelihood ratios are fused respectively. Moreover, the asymptotic detection performance of the proposed quantized detectors is analyzed, and closed-form expressions for the detection and false alarm probabilities are derived. Furthermore, the multi-bit quantizer design criterion, considering both RQ and LQ, is then proposed to achieve near-optimal asymptotic performance for our proposed detectors. The normalized Fisher information and asymptotic relative efficiency are derived, serving as tools to analyze and compensate for the loss of information introduced by the quantization. Simulation results validate the effectiveness of the proposed detectors, especially in scenarios with low signal-to-noise ratios and poor channel conditions.