Graph-based spectrum sensing algorithm via nonlinear function regulation

To solve the difficulties in threshold selection and poor performance under low signal-to-noise ratio (SNR) conditions in existing spectrum sensing algorithms, a graph-based spectrum sensing algorithm using nonlinear function regulation was proposed. The idea was to add a specific nonlinear transformation between the normalisation and quantization steps of the existing signal-to-graph converter (SGC). If the autocorrelation function of the observed signal selected as the input fed to SGC, the nonlinear function has the ability to adjust the uniformity of its probability distribution, increasing the probability of the observed signal being transformed into a complete graph under the alternative hypothesis, whereas remaining a noncomplete graph under the null hypothesis. Thus transformed the graph-based spectrum sensing into a complete graph-detection problem. Based on the theory of dispersive ordering, a theoretical analysis of the mechanism by which nonlinear transformations affect graph connectivity was conducted. The simulation results showed that the detection performance of the proposed algorithm was superior to that of existing graph-based spectrum sensing algorithms. When SNR was −7 dB, the detection probability of the proposed algorithm exceeded 95%. Moreover, among the existing graph-based spectrum sensing algorithms, the proposed algorithm exhibited the lowest computational complexity apart from the block range-based method.