Impact of Wireless Channel Uncertainty upon Distributed Detection Systems

We consider a distributed detection system, in which sensors send their decisions over orthogonal noisy channels to a fusion center (FC). We study how the optimal integrated fusion rule and its low signal-to-noise ratio (SNR) approximation, as well as the suboptimal non-integrated fusion rule, are related to the physical layer specifications (reception, modulation, channel model, and availability of channel state information (CSI) at FC). In particular, we consider training and non-training based systems and investigate the effect of imperfect CSI on the fusion rules, detection performance and error exponent, assuming that the sum of training and data symbol transmit powers is fixed. Our results show that the detection performance of the system with noncoherent reception is maximized when training symbol transmit power is zero. This performance is attainable with the statistics-based likelihood ratio test (LRT) rule for random channel model and the generalized LRT rule for deterministic channel model. For a system with BPSK modulation and coherent reception, subject to Rayleigh fading, the detection probability and error exponent are maximized when half of transmit power is allocated for training symbol. For Rician fading, however, optimal power allocation between training and decision symbols depends on the SNR and Rice factor. Comparing the integrated and non-integrated fusion rules, we show that the former always outperforms the latter.