基于特征值的动态信道化子带频谱检测改进算法

Dynamic channelization subband spectrum sensing based on eigenvalue

为对子带信号进行正确的频谱检测来判断子带中是否存在信号,继而判断信道数量及位置,提出了2种改进的基于特征值的动态信道化频谱检测算法。根据Wishart随机矩阵的最小特征值具有Tracy-Widom分布的特性,采用最小特征值的极限分布函数确定检测门限。以各个子信道采样协方差矩阵的平均特征值的2种不同形式与最小特征值的比值作为检验统计量,根据最大特征值与平均特征值的关系推导出相应的表达式,并用最大特征值的渐近值进行代替,根据虚警概率的定义推导出检测门限。继而根据检验统计量与检测门限的关系判断信号是否存在,完成频谱检测。仿真结果验证了提出的2种改进方法在低信噪比、低采样点等情况下与已有方法相比,能够获得更高的检测概率,提高了频谱检测的性能,且算法不需要任何有关信号和噪声的先验信息,对信号具有较强的适应性,易于实现频谱的盲检测。

A key problem to be solved is the estimation of the number and position of channels occupied by subband signals in dynamic digital channelization.Proper spectrum sensing of subband signals is the key to judge whether there are signals in subband,and then the number and position of channels.In order to solve this problem,two improved dynamic channelization spectrum sensing algorithms are proposed in this paper based on eigenvalue.According to the fact that the minimum eigenvalue of the Wishart random matrix has the characteristics of the Tracy-Widom distribution,the detection threshold is determined by the limit distribution function of the minimum eigenvalue.The ratio of the average eigenvalue in two different forms and the minimum eigenvalue of sampling covariance matrix of each subchannel is used as test statistics.The corresponding expression is deduced according to the relationship between the maximum and average eigenvalue.The maximum eigenvalue is replaced with the asymptotic value of it,detection threshold is deduced according to the definition of false-alarm probability.Then,whether signal exists is judged according to the relationship between test statistics and detection threshold,and spectrum sensing is completed.The simulation results verify that the proposed two new methods can obtain higher detection probability and improve the performance of spectrum sensing in the case of low SNR and low sampling points.Moreover,the algorithm does not need any priori information about signal and noise.The algorithm has strong adaptability to signal and is easy to realize the blind detection of frequency spectrum.