One-Bit Quantizer Design for Distributed Estimation under the Minimax Criterion

In this paper, we study one-bit quantizer design for distributed estimation under the minimax criterion for wireless sensor network (WSN) applications. Identical local quantizers are generally difficult to design because of the dependence on the unknown parameter under estimation. Nonidentical local quantizers are more robust in that sense. However, its design generally involves multi-dimensional optimization, which is computationally complex and the complexity increases with the number of sensors in the WSN. By studying the optimal nonidentical quantizers of M sensors, two quantizer structures are proposed. One is the sinusoid function, i.e., the quantization thresholds at M sensors follow a sinusoid function. The other is the more general raised cosine function, which requires two-dimensional optimization. The Nelder-Mead optimization method is adopted, which is simplex-based search directly using objective function values. Simulation results show that the quantizers with proposed structures outperform the intuitive uniform quantizer design. The raised cosine structure achieves near optimal performance.