This paper presents the use of nonlinear distributed estimation in a wireless system transmitting over channels with random gains. Specifically, we discuss the development of estimators and analytically determine their attainable variance for two conditions: 1) when full channel state information (CSI) is available at the transmitter and receiver; and 2) when only channel gain statistics and phase information are available. For the case where full CSI is available, we formulate an optimization problem to allocate power among each of the transmitting sensors while minimizing the estimate variance. We show that minimizing the estimate variance when the transmitter is operating in its most nonlinear region can be formulated in a manner very similar to optimizing sensor gains with full CSI and linear transmitters. Furthermore, we show that the solution to this optimization problem in most scenarios is approximately equivalent to one of two low-complexity power allocation systems.