We investigate distributed estimation based on measurements from multiple wireless sensors. For the same target, different sensors have different observations, which are modeled by additive observation noises of different variances. The observations are transmitted using (analog) amplify-and-forward transmissions from the sensors over non-ideal wireless channels to a fusion center, where they are combined to generate an estimate of the observed target. Our goal is to minimize total end-to-end distortion under certain power constraints, assuming the Best Linear Unbiased Estimator (BLUE) is used. We analyze the system outage performance, and show an achievable diversity gain of order K, which is the number of sensors. We also show that by turning off bad sensors, i.e., sensors with bad channels, we achieve adaptive power gain without losing diversity gain, where the adaptive power gain is similar to the array gain achieved in Multiple Input Single Output (MISO) systems when channel conditions are known to the transmitter.