Kernelized-Likelihood Ratio Tests for Binary Phase-Shift Keying Signal Detection

Abstract

In this article, kernelized-likelihood ratio tests (LRTs) for binary phase-shift keying (BPSK) signal detection based on the polynomial kernel function are proposed. Specifically, we kernelize the conventional LRT of BPSK signal detection using the so-called kernel trick, such that the inner product of the conventional LRT is replaced with proper polynomial kernel functions allowing for richer feature space to be deployed in the detection. We also derive computationally efficient recursive implementation structures for the proposed methods, resulting overall in six new detectors. With respect to the noise variance uncertainty (NVU), the proposed detectors can be divided into two general classes, namely i) constant false alarm rate (CFAR) and ii) semi-CFAR (S-CFAR) methods. To facilitate efficient operation under NVU, we also propose a new threshold-setting strategy to adjust the level of the proposed S-CFAR detectors. Additionally, we address the well-known energy detector (ED) under NVU and devise a new fixed-level ED formulation while also obtaining closed-form expressions for its false alarm and detection probabilities. Our extensive simulation results show that the proposed S-CFAR detectors outperform the state-of-the-art BPSK signal detectors with 2.4 dB signal-to-noise ratio (SNR) gain under practical worst-case NVU assumptions, while the performance gain is approximately 5.7 dB without NVU. In the case of the proposed CFAR detectors, the corresponding improvement in detection performance is approximately 1.8 dB.