A study of hyperplane-based vector quantization for distributed estimation

We consider the problem of distributed estimation of a vector parameter in wireless sensor networks (WSNs). Due to stringent power and bandwidth constraints, vector quantization is performed at each sensor to convert its local noisy vector observation into one bit of information. The one bit quantized data is then sent to the fusion center (FC), where a final estimate of the vector parameter is formed. The vector quantization problem is studied in such a distributed estimation context. Specifically, our study focuses on a class of hyperplane-based vector quantizers which linearly convert the observation vector into a scalar by using a compression vector and then carry out a scalar quantization. Under the framework of the Cramér-Rao bound (CRB) analysis, we study the choice of the quantization thresholds and the design of the compression vectors.