Graph-based confidence verification for BPSK signal analysis under low SNRs

•The majorization relationships between the continuous PDFs and their discrete area sampling PDFs are analyzed, which provides a theoretical basis to compare the connectivity of the graphs converted from two different distributed random samples, and the probabilities of the graphs being complete.•A novel graph-based confidence verification algorithm to evaluate the analysis results of BPSK signals is proposed, where the block sum of the correlation spectrum is selected as an input fed to the signal-to-graph converter, and the entropy of the quantized samples’ histogram is utilized as a novel feature to check the graph's completeness, which results in better performance and lower computational cost than the conventional graph-based detector using the second largest eigenvalue of the Laplacian matrix.•Compared with existing algorithms, the proposed algorithm can obtain superior performance under lower SNRs in the presence of transmission impairments including channel fading, timing offset, Doppler frequency shift, and phase noise. Confidence verification for intercepted signal analysis has important military applications where a priori knowledge of the signal or transmission channel is insufficient or absent. However, existing methods do not perform well under low signal-to-noise ratios (SNRs). In this study, we propose a graph-based verification algorithm for binary phase shift keying (BPSK) signal analysis. The correlation spectrum between the original observed signal and reference signal can be divided into blocks of equal size and the summation of each block (called the block summation (BS) spectrum) obtained. Then, the BS spectrum samples are transformed into a specific simple undirected graph using the signal-to-graph convertor. Accordingly, the verification issue can be simplified to determining whether the graph is fully-connected. The majorization relationships between the probability density functions of the BS and the original correlation spectra are evaluated. This is used to compare the connectivity of the graphs generated from those two types of samples, as well as their probabilities of being complete graphs. Simulation results confirm the superior performance of the proposed algorithm over previous confidence verification algorithms for low SNRs and in the presence of transmission impairments, as well as a lower computational complexity when compared with the conventional graph-based algorithm.