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In this paper we 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. We consider a training based channel estimator with which the fusion center (FC) estimates the complex channels between the sensors and the FC. We 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. We study the effect of channel estimation error on the system performance. As a benchmark we compare it with a fusion rule that assumes perfect channel state information (CSI). Performance evaluation shows that as SNR increases the channel estimation error decreases and the system performance approaches to the clairvoyant scenario where perfect CSI is assumed at the FC.