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.

中文翻译：

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通过非线性函数调节的基于图的频谱感知算法

针对现有频谱感知算法阈值选取困难、低信噪比条件下性能较差的问题，提出一种基于图的非线性函数调节频谱感知算法。这个想法是在现有信号图转换器 (SGC) 的归一化和量化步骤之间添加特定的非线性变换。如果选择观测信号的自相关函数作为 SGC 的输入，则非线性函数能够调整其概率分布的均匀性，从而增加在备择假设下将观测信号转化为完整图的概率，而在零假设下仍然是一个不完整的图。从而将基于图的频谱感知转化为完整的图检测问题。基于色散排序理论，对非线性变换影响图连通性的机制进行了理论分析。仿真结果表明，该算法的检测性能优于现有的基于图的频谱感知算法。当SNR为-7 dB时，该算法的检测概率超过95%。此外，在现有的基于图的频谱感知算法中，除了基于块范围的方法之外，所提出的算法表现出最低的计算复杂度。