Harmonic Parameter Design In The Approximated One-Bit Hermite Law

One-bit quantization allows for signal parameter recovery from one-bit Gaussian data under low power consumption. The parameter recovery can be built on the statistical properties of one-bit data, such as the one-bit Hermite law (OBHL). For computational purposes, the OBHL is extended to the approximated OBHL (AppOBHL) with a truncation parameter and harmonic parameters. This paper designs the harmonic parameters in the AppOBHL by minimizing the approximation error bounds. This optimization is formulated into a minimax problem. With the continuous relaxation of a discrete variable, explicit expressions of two stationary points are derived. These stationary points facilitate a transformed parameter space, additional constraints, and simple expressions for the proposed harmonic parameters. Numerical examples demonstrate the proximity of the proposed design to the optimal solution on a discrete grid. Simulations also show the improved performance of the AppOBHL with the proposed harmonic parameters when the correlation coefficient is close to unity.