Performance of distributed estimation over multiple access fading channels with partial feedback

We consider a wireless sensor network for distributed estimation over Rayleigh fading channels. The sensors transmit their observations over fading channels to a fusion center, where a source parameter is estimated. Since the sensor transmissions add incoherently over a multiple access channel, we consider partial channel knowledge at the sensors to improve performance. We calculate the variance of the estimate when the channel phase is quantized uniformly and fed back to the sensors. We show that as few as 3 bits of feedback is sufficient for a loss in performance of about 5%. We also show that the performance is robust in the presence of feedback errors.