A wireless sensor network monitoring a target signal source by distributed sensors is considered and the effects of imperfect channel state information at the sensor node receivers are studied. The sensor nodes are assumed to have independent observations of the target signal which are sent to a common fusion center through reliable links. If the channel gains between the target and the sensors (channel state information) are known exactly, the estimation problem reduces to least-squares estimation. If the channel gains are only known in distribution and by pilot-assisted training (imperfect channel state information), least-squares estimation is inefficient. This work investigates the properties of the optimum estimator with imperfect channel state information and assesses its performance versus suboptimum least-squares estimation and perfect channel state information (genie-aided) estimation.