Spectrum Sensing Based on Graph Fourier Transform Using Laplacian Matrix and Vertex Probability Vector

Quantization-based graph transform (QGT) provides a unique perspective on spectrum sensing in cognitive radio networks. Conventional QGT-based spectrum sensing algorithms leverage the topological characteristics of the graph derived from observed signals. However, they often exhibit poor performance in scenarios with low signal-to-noise ratios, strong interference, and severely fading channels because they do not effectively incorporate the statistical feature of the signal. To address this issue, we propose a spectrum sensing algorithm based on graph Fourier transform (GFT) to combine both the topological and statistical features of the signal effectively. First, the summation of the block maxima and minima (B2M) of the power spectrum is transformed into a simple graph using QGT. Then, the vertex probability vector of the B2M is defined as the graph signal, and the eigenmatrix is created by collecting the eigenvectors of the graph Laplacian matrix. The GFT of the graph signal is obtained by multiplying the graph signal by the inverse of the eigenmatrix. The weighted energy of the GFT (WEG) is selected as the test statistic for detecting the presence of a primary users signal. The effectiveness of the proposed algorithm under diverse conditions is demonstrated through computer simulations, which validate its superior performance compared with the existing convolutional neural network (CNN)-free detectors.