Rate-Constrained Distributed Estimation in Wireless Sensor Networks

In this paper, we consider the distributed parameter estimation in wireless sensor networks where a total bit rate constraint is imposed. We study the optimal tradeoff between the number of active sensors and the quantization bit rate for each active sensor to minimize the estimation mean-square error (MSE). To facilitate the solution, we first introduce a concept of equivalent 1-bit MSE function. Next, we present an optimal distributed estimation algorithm for homogeneous sensor networks based on minimizing the equivalent 1-bit MSE function. Then, we present a quasi-optimal distributed estimation algorithm for heterogeneous sensor networks, which is also based on the equivalent 1-bit MSE function, and the upper bound of the estimation MSE of the proposed algorithm is addressed. Furthermore, a theoretical nonachievable lower bound of the estimation MSE under the total bit rate constraint is stated and it is shown that our proposed algorithm is quasi-optimal within a factor 2.2872 of the theoretical lower bound. Simulation results also show that significant reduction in estimation MSE is achieved by our proposed algorithm when compared with other uniform methods