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In this paper, the authors consider the problem of fusing decisions in a distributed detection system when the local binary decisions made at the sensors are transmitted over wireless links subject to fading and noise. They consider a training based channel estimator with which the Fusion Center (FC) estimates the complex channels between the sensors and the FC. They derive the Likelihood-Ratio-Test (LRT) fusion rules that incorporate the complex channel estimates for the cases where the sensors employ BPSK, OOK, binary FSK, and binary PPM signaling to modulate their binary local decisions. They study the effect of channel estimation error on the system performance. As a benchmark they compare it with a fusion rule that assumes perfect Channel State Information (CSI).
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