Joint Estimation in Sensor Networks under Energy Constraint

We consider the optimal power scheduling problem for the decentralized estimation of a noise-corrupted deterministic signal in an inhomogeneous sensor network. Sensor observations are first quantized into discrete messages, then transmitted to a fusion center where a final estimate is generated. Supposing that the sensors use a universal decentralized quantization/estimation scheme and an uncoded Quadrature Amplitude Modulated (QAM) transmission strategy, we determine the optimal quantization and transmit power levels at local sensors so as to minimize the total transmit power, while ensuring a given Mean Squared Error (MSE) performance. The proposed power scheduling scheme suggests that the sensors with bad channels or poor observation qualities should decrease their quantization resolutions or simply become inactive in order to save power. For the remaining active sensors, their optimal quantization and transmit power levels are determined jointly by individual channel path losses, local observation noise variance, and the targeted MSE performance. Numerical examples show that in inhomogeneous sensing environment, significant energy savings is possible when compared to the uniform quantization strategy.