Byzantine Attack Identification using Graph Signal Processing in Cooperative Spectrum Sensing

Graph signal processing (GSP) paradigm generalizes the existing one-dimensional signal processing concept and focuses on multi-dimensional signals residing on a structure that can be represented by a graph. Researches have been conducted by signal processing society to extend the existing signal processing concepts originally introduced for one- or two-dimensional signals into GSP framework. This paper first considers a double star graph to explore the important ideas about low-frequency and high-frequency graph signals and its projection into basis functions using the graph Fourier transform (GFT). Next, we consider a cognitive radio (CR) network where a frequency band licensed to the so-called primary user (PU) can be borrowed by the so-called rental users (RUs), who do not own license for using the frequency band, when the PU is inactive. The graph signals decomposition using GFT is exploited for the identification of the so-called Byzantine attack in the CR network, where malicious RUs (MRUs) attempt to falsify the spectrum sensing information, which is used to detect the PU activity in its own licensed frequency band, and mislead the remaining benign RUs to make a wrong conclusion about the existence of the PU in its band. The numerical study shows that our proposed GSP-based Byzantine attack identification shows a good performance especially when the collected number of discrete samples of the received PU signals is sufficiently large and when the MRU has a lot of neighbors in the corresponding graph model.