An Optimization-Based Approach to One-Bit Quantization

In many industrial fields, one-bit signals play an important role, such as improving the operational efficiency in a wide range of applications. This paper introduces a mapping function $\mathcal{F}(\cdot)$ that converts real-valued discrete-time signals into two-level discrete-time one-bit signals, i.e., one-bit signals. By introducing an error function, we can evaluate the quality of the mapping and can introduce different optimization strategies to minimize the error. Mathematical analysis and numerical simulations demonstrate that the optimization approach leads to specific characteristics of the quantization. The well-known Sigma-Delta modulator, for example, turns out to be a special case of the introduced optimization. The new approach has the potential to introduce new ways of one-bit quantization, which can be tailored to specific applications.