Impact of Channel Estimation Error Upon Distributed Estimation Systems

We consider the distributed estimation of a random parameter in a wireless sensor network, in which sensors send their observations over orthogonal noisy channels to a fusion center (FC), whose task is to reconstruct the source. We adopt the mean squared error (MSE) as the performance criterion. Assuming training based channel estimation, we investigate the effect of imperfect channel state information (CSI) upon estimation performance. Under the constraint that the sum of data and training transmit power at each sensor is fixed, we study how the estimation performance is related to the power allocation between training and data. Extensive simulations are carried out to test the impact of imperfect CSI. Our results show that the channel estimation error decreases the estimation performance in terms of both the linear minimum mean square error (LMMSE) and the optimal weighted least squares (OWLS) fusion rule, and the former outperforms the latter. Besides, the performance gap between the optimal and the imperfect CSI varies from the data power ratio and signal-to-noise ratio (SNR).