An Efficient Water-Filling Solution for Linear Coherent Joint Estimation

We consider a sensor network with distributed sensors observing multiple sources and transmitting local observations over a Gaussian multiple access channel to a fusion center where the signals are coherently combined. We develop a joint estimation method based on the linear analog forwarding scheme at each local node, which can be cast as a nonlinear optimization problem. By minimizing the gap to the performance benchmark, we obtain a closed-form solution that follows the water-filling strategy. Numerical results are given to demonstrate the average estimation performance in a fading communication environment.