Pearson Correlation Fusion Sensing Method for Noncircular Signals
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摘要: 针对传统圆信号频谱感知方案无法精确识别非圆信号的问题，该文提出一种皮尔逊相关系数驱动的融合感知方法。该方法通过实值复合表示形式捕捉非圆信号的二阶统计信息，并据此构建实值相干矩阵以获取接收天线间的皮尔逊相关强度。随后采用线性数据融合方法对不同天线间的皮尔逊相关系数进行加权叠加，并以偏因径系数为性能测度建立理论最优权重及其样本估计值，最终设计出无需依赖信道先验参数的非参量感知技术。通过分析平方皮尔逊相关系数和检验统计量的二阶特性及统计分布，建立虚警概率、感知阈值等关键指标的理论计算解析式。实验结果表明，所提方案相较于其他对比算法，在接收机工作特性(ROC)曲线、感知概率、偏因径系数和曲线下面积(AUC)等性能测度下均表现更优，尤其是在低信噪比环境中，其性能优势更为显著。Abstract:
Objective With the rapid growth of wireless device and communication service, the scarcity of spectrum resources has become increasingly prominent. Spectrum sensing, as a fundamental functionality of cognitive radio, is a promising technology to achieve the dynamic spectrum allocation strategy, thereby enhancing the efficiency of spectrum utilization and resolving the issue of spectrum shortage. However, traditional spectrum sensing methods that are devised by assuming the circular signals, cannot be applied to the detection of noncircular signals. On the other hand, some detectors tailed for the noncircular signals perform poorly in the sample-starving or low signal-to-noise ratio (SNR) regime. To address these drawbacks, this research offers a weighted Pearson correlation coefficient based nonparametric spectrum sensing scheme by applying the linear weighting fusion strategy to the real-valued composite sample coherence matrix (SCM) that can comprehensively capture the statistical characteristics of noncircular signals. Theoretical derivations and simulation results show the superiority of proposed method over other state-of-the-art detectors, especially in the conditions of low SNR or small sample. Methods The WPCC detector constructs the real composite vector of observations and calculates the real-valued composite SCM. It extracts the statistical manners of noncircular signals from the Pearson correlation coefficients (PCCs) determined by the real-valued composite SCM. The deflection coefficient based optimal fusion weights are theoretically presented after deriving the first two product moments of the sample PCCs. By replacing the population PCCs with the corresponding sample values, the data-aided fusion weights that require no prior knowledge of sensing channels are proposed. These weights are then linearly summarized with the square of sample PCCs to construct the test statistic of WPCC, thereby fully leveraging the spatial diversity of the sensing antennas. The final global decision can thus be made by comparing the WPCC statistic to the sensing threshold that can be theoretically determined by the specified false alarm probability. Specifically speaking, A WPCC value below the sensing threshold indicates the null hypothesis of idle frequency band, while a WPCC value above the sensing threshold suggests the alternative hypothesis that the frequency band is occupied by the PUs. Results and Discussions Simulation experiments evaluate the sensing performance of nonparametric weighted Pearson correlation coefficient based method (Algorithm 1) with respect to the performance measures of sensing probability, deflection coefficient, receiver operating characteristic curve and area under the curve, along with comparison to other noncircular signals based competitors, including NCLMPIT, NCAGM, NCHDM and NCJT. The numerical results show that our proposed method outperforms other considered detectors in various simulation conditions. In particularly, the WPCC detector that possesses the highest curve of sensing probability exhibits the locally optimal performance at a low false alarm probability of 0.05 ( Fig.2 ) and 0.01 (Fig. 3(a) ) as well as 0.005(Fig. 3(b) ) with a sample size no more than 100. In addition, the proposed method performs much better than other detectors in different number of antennas (Fig. 4 ), different uniformity of noise powers (Fig. 5 ) and different intensity of coherence coefficients (Fig. 6 ). The applicability of WPCC method to circular signals can be seen by showing its high sensing probability for QPSK and 16PSK signals (Fig.7 ). The superior overall performance of our detector is also revealed because its curves of deflection coefficient and ROC are much higher than other detectors (Figs. 8 -9 ). The largest AUC values of proposed method quantitatively demonstrate its overall optimality among all considered schemes (Table 1 ). These simulations highlight the strong robustness of our propose algorithm against the low SNR or small samples.Conclusions Starting with the NCLMPIT algorithm that integrates the real-valued composite covariance of noncircular signals and the framework of locally most power invariant test, this research addresses a class of Pearson correlation fusion sensing method for noncircular signals by combining the sample Pearson correlation coefficient based optimal fusion weights with the linear weighting summation technique. The first two product moments of squared Pearson correlation coefficients and the statistical properties as well as asymptotic distribution of our proposed test statistic are theoretically derived, armed with which the analytical expressions with respect to the false alarm probability and sensing threshold are further established. The proposed method can not only make full use of the second-order statistical information of noncircular signals, but also significantly enhance the strongly correlated data, while effectively suppressing the weakly correlated data and noise interference. Numerical simulations show that in comparison with the existing noncircular signal based detectors, the WPCC based sensing scheme exhibits significant performance advantages in the aspect of sensing probability, deflection coefficient, ROC curve and AUC. -
Key words:
- Spectrum sensing /
- Noncircular signals /
- Pearson correlation coefficient /
- Data fusion
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1 面向非圆信号的皮尔逊相关融合感知
输入：观测样本$\{z_i\}_{i=1}^N $和虚警概率$P_f $ 输出：$\mathcal{H}_0 $或$\mathcal{H}_1 $ 1. 基于式(2)构造增广向量$\tilde{z}_i $，并基于式(4)计算复合样本协方差
矩阵$S $2.通过式(6)计算样本皮尔逊相关系数$\widehat{C}_{mn} $ 3. 基于式(54)计算基于样本皮尔逊相关系数的最优融合权重
$\widehat{W}_{mn}^o $4. 构建加权皮尔逊相关系数统计量： $\Lambda_{\text{WPCC}} = \displaystyle\sum\limits_{m=1}^{2M-1} \displaystyle\sum\limits_{n=m+1}^{2M} \widehat{W}_{mn}^o \widehat{C}_{mn}^2 $ 5. 基于给定的虚警概率，计算感知阈值$\eta_{\text{WPCC}} $ $\eta_{\text{WPCC}} = \sqrt{\dfrac{2(N-1)}{N^2(N+2)} \displaystyle\sum\limits_{n>m}^{2M} \left( W_{mn}^o \right)^2} \, Q^{-1}(1-P_f) + \dfrac{1}{N} \displaystyle\sum\limits_{n>m}^{2M} \widehat{W}_{mn}^o $ 6. 若$\Lambda_{\text{WPCC}} \gt \eta_{\text{WPCC}} $，输出$\mathcal{H}_1 $，否则输出$\mathcal{H}_0 $ 
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