Distributed estimation over fading macs with multiple antennas at the fusion center

We consider a distributed estimation problem over fading multiple-access channels. Several sensors transmit a parameter to a fusion center using an amplify-and-forward scheme. The fusion center has multiple antennas and uses the transmissions from the sensors to estimate the parameter. In this paper we will assume that the sensors have full channel state information and formulate an optimization problem that needs to be solved to select the best sensor gains. We also propose bounds on the performance and two practical methods that can be implemented in this scenario. By comparing the performance, it is shown that though there is benefit in having multiple antennas at the fusion center, when full channel information is available at the sensors, the gain in performance is at most a factor of 2.