Power allocation in estimation fusion with phase asynchronization at the fusion center

We consider power allocation problem in wireless sensor networks with phase synchronization error at the fusion center. The sensors amplify-and-forward their measurements (using uncoded analog transmission) to a remote fusion center over wireless fading channels. The residual phase error at the fusion center is modeled by the Tikhonov distribution. The global optimal power allocation algorithm is proposed. The power allocation problem can be changed into the matrix eigenvector problem. And the closed-form solutions for power amplification coefficients and Linear Minimum Mean Square Error (LMMSE) are obtained. Monte Carlo simulations are carried out to verify the performance of the proposed methods. Simulation results show that the proposed scheme outperforms the optimal scheme without considering phase error and uniform power allocation algorithm.