Robust Transmit Beamforming for Parameter Estimation Using Distributed Sensors

In this letter, we study the problem of estimating a complex parameter in a wireless sensor network under individual power constraints and bounded channel uncertainty, where the channel state information is assumed to be imperfect at both the sensors and the fusion center. Transmit beamformers and a linear estimator that minimize the maximum mean square error are found. Although this problem is nonconvex, it can be relaxed to become a semidefinite programming problem by re-parameterization and semidefinite relaxation. Surprisingly, we find that relaxation is tight and a global optimal solution can be found. Finally, numerical simulations are performed to evaluate the performance of the robust estimator.