Asymptotically Optimal One-Bit Quantizer Design for Weak-signal Detection in Generalized Gaussian Noise and Lossy Binary Communication Channel

TL;DR

This paper develops an asymptotically optimal one-bit quantizer design for weak-signal detection in generalized Gaussian noise over binary channels, providing a polynomial-time solution and validating it through numerical experiments.

Contribution

It introduces a novel threshold design approach based on noncentrality parameter maximization for weak-signal detection in generalized Gaussian noise, with proven optimality and efficient algorithms.

Findings

Optimal threshold can be zero in certain cases.

The proposed method achieves asymptotic optimality.

Numerical results confirm theoretical predictions.

Abstract

In this paper, quantizer design for weak-signal detection under arbitrary binary channel in generalized Gaussian noise is studied. Since the performances of the generalized likelihood ratio test (GLRT) and Rao test are asymptotically characterized by the noncentral chi-squared probability density function (PDF), the threshold design problem can be formulated as a noncentrality parameter maximization problem. The theoretical property of the noncentrality parameter with respect to the threshold is investigated, and the optimal threshold is shown to be found in polynomial time with appropriate numerical algorithm and proper initializations. In certain cases, the optimal threshold is proved to be zero. Finally, numerical experiments are conducted to substantiate the theoretical analysis.