Why Can One-Bit Quantization Work? A Mathematical Theory Analysis

With the increase of demand in the flexibility and rapidity in different industry areas, unmanned systems are implemented under various circumstances for the convenience they bring. However, the mobility restricts the system size and power consumption. In this case, much attention has been attracted by one-bit quantization for its simplification in signal acquiring and processing. Whereas, most of existing literature focus on how to reap information from one-bit data. Much less work explains the reason why the information can be achieved from the coarsely quantized data. In this paper, the process of one-bit quantization is analytically analyzed in detailed in a mathematical angle of view, where the quantization noise resulting from the nonlinear effect is analyzed. Specifically, the one-bit quantized data is decomposed mathematically, and the components are analyzed to show the existence of the requisite signal in the quantized signal. This offers a theoretical explanation of the effectiveness of one-bit quantization.