Spectrum Sensing Algorithm Based on the Euclidean Norm of the Horizontal Visibility Graph for Cognitive Radio

To address the issues of poor detection performance under low signal-to-noise ratios (SNRs) and high computational complexity in existing visibility graph-based spectrum sensing algorithms, this article proposes a novel algorithm based on the Euclidean norm of the horizontal visibility graph (HVG) adjacency matrix. The algorithm begins by computing the block summation of the observed signal's power spectrum. The squared modulus of its autocorrelation function is subsequently calculated, normalised and quantised to form the new sequence, which is then transformed to the HVG and defined as the graph signal. The one-hop graph filter is constructed from the graph signal and the adjacency matrix, and its Euclidean norm serves as the detection statistic. This statistic is compared against a predefined threshold to determine the presence of the primary user signal. To theoretically analyse detection performance, the weak submajorisation order is introduced to evaluate the statistical differences between graph signals under the two hypotheses. Additionally, data exploration demonstrates that the proposed statistic approximately follows a Burr distribution under the null hypothesis, allowing for an approximate analytical expression for the detection threshold is derived. Simulation results show that the proposed algorithm outperforms existing graph-based algorithms at low SNRs while maintaining moderate computational complexity.