Asymptotic Analysis of Distributed Estimation over Fading Multiple Access Channels

We consider a distributed estimation problem where sensors transmit their observations over fading channels to a fusion center (FC), where the parameter is estimated. We calculate the variance of the estimate when we have full, partial and no channel information at the sensors. We compare these with a benchmark obtained when the channels are AWGN. We show that while having no CSI at the sensors leads to bad performance, partial CSI at the sensors is sufficient to get reliable estimates of the parameter. Comparing the performance when the sensors have partial CSI, to when the sensors have full CSI, the deterioration of the variance of the estimator in the case of partial CSI at the sensors is upper bounded by a factor of 4/π, which is about a 2dB power loss.