Graph Signal Processing for Anomaly Detection in Cooperative Power Spectrum Estimation

Classical signal processing generally deals with one-dimensional, such as time-domain, signals. However, many real world signals are multi-dimensional and might be defined on complex and irregular structures modeled as graphs. Hence, time-domain signal processing approaches might not be suitable for signals defined on a graph (also called graph signals), and it is important to develop graph signal processing (GSP) methods from the well-known signal processing theories. Our work first attempts to demonstrate the concept of low and high frequency in graph signals by evaluating the decomposition of signals located on a simple star graph, using the so-called graph Fourier transform (GFT). The graph signals are presented as a linear combination of the eigenvectors of the so-called graph operator matrices, which play a role as basis vectors. We then examine the implementation of GSP in spectrum sensing application for cognitive radio (CR) networks to detect the anomaly in the power spectrum estimate collected by multiple secondary users (SUs) in the CR network. Our work focuses on the anomaly caused by differences in fading statistics at different locations. The simulation study shows a good performance of our approach in the identification of fading statistics anomaly when the number of block of samples is sufficiently large and when the SU experiencing anomaly has a sufficiently large number of neighbors.