Distributed Detection and Bandwidth Allocation with Hybrid Quantized and Full-Precision Observations over Multiplicative Fading Channels

A hybrid detector that fuses both quantized and full-precision observations is proposed for weak signal detection under additive and multiplicative Gaussian noise. We first derive a locally most powerful test (LMPT)–based hybrid detector from the composite probability distribution of the compound observations received by the fusion center, and then analyze its asymptotic detection performance. Subsequently, we optimize the sensor-wise quantization thresholds to achieve near-optimal asymptotic performance at the local sensor level. Moreover, we propose a mixed-integer linear programming approach to solve the optimization problem of transmission bandwidth allocation accounting for bandwidth constraints and error-prone channels. Finally, simulation results demonstrate the superiority of the proposed hybrid detector and the bandwidth allocation strategy, especially in challenging error-prone channel conditions.