Optimal Energy Allocation Scheme in Distributed Estimation for Wireless Sensor Networks over Rayleigh Fading Channels

We focus on the issue of energy and bandwidth limitations in Wireless Sensor Networks (WSN). To tackle this issue, we propose the optimal energy allocation scheme and the optimal number of quantization bits by using alternating optimization method. Firstly, we determine the optimal energy allocation scheme which minimizes the reconstruction error on fusion center by keeping the number of quantization bits per sensor fixed. Secondly, we determine the optimal number of quantization bits per sensor such that the energy allocation scheme achieves the minimum reconstruction error. To find the optimal energy allocation scheme and the optimal number of quantization bits jointly, we propose an iterative algorithm. The results show that the proposed algorithms do not only achieve better results than equal energy allocation scheme but also produce reconstruction error close to that of un-quantized estimation. This paper also investigates the effects of sensor noise observation and propagation losses on the design of optimal energy allocation scheme. The optimal energy allocation scheme suggests the allocation of more energy to sensors with small variance noise of sensor observation.