Optimal bit allocation for distributed estimation in wireless sensor networks

This paper studies the optimal bit allocation problem for distributed estimation in wireless sensor networks (WSNs) where a total bit rate constraint is imposed. We derive the mean-square error (MSE) for a quasi-minimum mean-square error (quasi-MMSE) estimator in terms of the bit rate allocation and obtain an upper bound of the MSE. Then a suboptimal bit allocation scheme, which minimizes this MSE upper bound, is presented. This bit allocation scheme shows that the number of optimal quantization levels is inversely proportional to the sensor noise variance. Moreover, we investigate the identical problem for more general estimators, a numerical value solution under a total bit rate constraint is obtained by minimizing the Bayesian Cramer-Rao lower bound (BCRB). Then we study this problem for a case where the quantization law has a high-resolution and obtain an optimal analytic solution. It is shown that for the high-resolution case, the suboptimal bit allocation solution for quasi-MMSE estimator is an optimal in the sense that the BCRB of the estimator is minimized. Simulation results show the efficiency of the optimal bit allocation strategy.