Robust Linear Beamforming in Wireless Sensor Networks

A typical wireless sensor network (WSN) has multiple sensors, each of which obtains noisy observation of one common physical event and sends the observation to a fusion center (FC) for post-processing. This paper provides a comprehensive research on robust linear transceiver design in the presence of imperfect channel-state information (CSI) in multi-input multi-output (MIMO) WSNs. For the CSI uncertainty, the classical ellipsoid model is assumed, where channel estimation errors live in an ellipsoid. Two robust beamforming problems are considered: 1) the worst-case mean-square-error (MSE) minimization with limited power and 2) sum-power minimization with guaranteed worst-case MSE. For both problems, centralized and decentralized solutions are developed. Moreover, an interesting fundamental relation between the metrics of signal-to-noise ratio (SNR) and MSE has been presented, which extends our proposed solutions to handle the transceiver design when SNR is considered. Extensive numerical results are presented to confirm our findings.