基于随机共振和非中心F分布的频谱感知算法

为解决频谱感知算法在低信噪比（SNR）时检测概率较低且检测所需采样点数较多的问题，提出了基于随机共振和非中心F分布（SRNF）的频谱感知算法。通过引入直流随机共振噪声，建立了SRNF的系统模型，推导了服从非中心F分布的检验统计量表达式、虚警概率与检测概率以及判决门限表达式，并采用数值法求解最佳的随机共振噪声参数。仿真结果表明，在低信噪比时，所提基于SRNF算法的检测性能优于能量检测（ED）算法和基于F分布的盲频谱感知（BSF）算法，当虚警概率为5%、信噪比为–12 d B、采样点数为200时，所提算法的检测概率是95%，分别比BSF算法和ED算法高34%和67%；当信噪比为–12 dB、检测概率达到95%时，所提算法所需的采样点数是210，比BSF算法节省了340个采样点。此外，噪声不确定度对所提算法的影响小于ED算法。

Spectrum sensing algorithm based on stochastic resonance and non-central F-distribution

To solve the problem that the detection probability of the spectrum sensing algorithm is low and the number of samples required for detection is large at low signal-to-noise ratio (SNR), a spectrum sensing algorithm based on stochastic resonance and non-central F-distribution (SRNF) was proposed.By introducing direct-current stochastic resonance noise, the system model of SRNF was established, and the expression of test statistic, false alarm probability and detection probability, and the expression of decision threshold obeying non-central F-distribution were deduced, and the optimal stochastic resonance noise parameter was solved by numerical method.The simulation results show that the detection performance of the proposed SRNF algorithm is better than that of energy detection (ED) algorithm and blind spectrum sensing based on F-distribution (BSF) algorithm at a low SNR.When the false alarm probability is 5%, the SNR is -12 dB, and the number of samples is 200, the detection probability of the proposed algorithm is 95%, which is 34% and 67% higher than BSF algorithm and ED algorithm, respectively.When the SNR is -12 dB, and the detection probability reaches 95%, the number of samples required by the proposed algorithm is 210, which saves 340 samples compared to the BSF algorithm.Furthermore, the proposed algorithm is less affected by noise uncertainty than ED algorithm.