Distributed Estimation in a Power Constrained Sensor Network

This paper derives the optimum non-uniform quantization scheme for a distributed estimation problem based on noisy observations in a wireless sensor network. The optimal quantization scheme minimizes the mean squared estimation error subjected simultaneously to both a total system power as well as individual node power constraints. According to the derived optimal scheme, sensors with poor signal-to-noise ratios (SNR) refrain from transmitting their observations. The rest of the sensors transmit their quantized observations. The number of quantized bits depends on the SNR and the maximum power constraint at each node. The numerical results show that compared to a uniform power allocation scheme, the proposed scheme achieves significantly smaller Mean Squared Error (MSE) for the same average power consumption.