Energy efficient quantization of correlated noisy observations of a sensor

Quantization is an essential component of digital communication and storage systems thanks to the finite capacity of communication channels, and available storage and computational resources. To this end, this paper studies the problem of quantization of spatially correlated noisy observations of a sensor. We developed a mathematical formulation to quantize the observations without imposing any statistical structure on the associated quantization noise. The proposed quantization scheme is based on an MMSE estimation rule and assumes uniform quantization scheme. We developed exact formulation of the estimation distortion and a simplified approximation of the distortion function. Subsequently, we proposed a solution to determine the quantization step-size and the number of quantization levels under the constraints of given channel capacity and total power expended in the sensor node. The effectiveness of the quantization scheme is illustrated with simulation examples.