On the effect of channel estimation error upon the performance of distributed detection systems

In this paper we consider fusion of decisions in a distributed detection system when the decisions are transmitted over Rayleigh fading channels. We assume noncoherent reception at the fusion center (FC) with a training based channel estimator which estimates amplitude of the channels between the sensors and the FC. We derive the likelihood-ratio-test (LRT) fusion rule that incorporates the channel amplitude estimates when the sensors use OOK or orthogonal modulations (e.g., binary FSK, binary PPM) to modulate their binary local decisions. We also derive a suboptimal fusion rule that approximates the LRT at low SNR. We study the effect of channel amplitude estimation error on the system performance with noncoherent reception using optimal and suboptimal fusion rules in the fusion center. As a benchmark we compare it with a fusion rule that assumes perfect channel amplitude information is available in the FC. Performance evaluation shows that as SNR increases the channel estimation error decreases and the performance of the rules converges to the performance of the corresponding rules with perfect channel amplitude at the FC.