Asymptotics and Power Allocation for State Estimation Over Fading Channels

State estimation of linear systems using analog amplify and forwarding with multiple sensors, for both multiple access and orthogonal access schemes is considered. Optimal state estimation can be achieved at the fusion center using a time-varying Kalman filter. We show that in many situations, the estimation error covariance decays at a rate of 1/M when the number of sensors M is large. We consider optimal allocation of transmission powers that 1) minimizes the sum power usage subject to an error covariance constraint, and 2) minimizes the error covariance subject to a sum power constraint. In the case of fading channels with channel-state information, the optimization problems are solved using a greedy approach, while for fading channels without channel state information (CSI) but with channel statistics available, a suboptimal linear estimator is derived.