一种基于广义Jaccard系数的改进SAMP压缩信号快速恢复算法  

A Fast Recovery Algorithm of Improved SAMP for Compressed Signal Based on Generalized Jaccard Coefficient

作　　者：时天昊 白银山 沈堤[3] 沈志远[1] SHI Tianhao;BAI Yinshan;SHEN Di;SHEN Zhiyuan(College of Civil Aviation,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;Unit 94116 in Air Force,Hotan 848000,Xinjiang,China;Air Traffic Control and Navigation School,Air Force Engineering University,Xi’an 710051,China)

机构地区：[1]南京航空航天大学民航学院,南京211106 [2]94116部队,新疆和田848000 [3]空军工程大学空管领航学院,西安710051

出　　处：《空军工程大学学报》2023年第2期91-97,共7页Journal of Air Force Engineering University

基　　金：国家自然科学基金(U2233208)。

摘　　要：压缩感知算法作为一种信号处理方法,可以解决机场终端区实时频谱监测的问题。基于稀疏度自适应匹配追踪(SAMP)信号重构算法,引入了广义Jaccard系数、t-平均相关系数、变步长思想,提出了JTVSSAMP算法。在算法的原子筛选部分引入广义Jaccard系数可以减少原子混淆导致的精度下降问题,t-平均相关系数的引入可以避免测量矩阵RIP系数的计算,降低了算法的复杂度,变步长思想中的大步长迭代,小步长靠近的步骤使得算法的效率及精度都大大提升。采用一维高斯随机稀疏信号作为测量信号进行仿真,可以有效的模拟机场终端区经过能量检测后的测量信号,经过仿真,JTVS-SAMP在不同的测量数、稀疏度情况下的算法重构成功率的表现明显优于传统压缩感知算法,且与SAMP算法相比,JTVS-SAMP在重构误差和算法时间方面的表现均有显著提升。Compressed sensing algorithm can be utilized for solving the problems of dynamic spectrum detection at the airport terminal area,and determining on the precision and the efficiency of signal recovery.Based on sparsity adaptive matching pursuit(SAMP)signal reconstruction algorithm,this paper introduces generalized Jaccard coefficient,t-average correlation coefficient and variable step size idea,and proposes a JTVS-SAMP algorithm.The generalized Jaccard coefficient in the atomic screening part of the algorithm can reduce the accuracy degradation caused by atomic confusion,the t-average correlation coefficient can avoid calculating the rip coefficient of the measurement matrix,and reducing the complexity of the algorithm.And the large step iteration in the variable step idea and the small step approach step enable the efficiency and accuracy of the algorithm to be greatly improved.Taking the 1-D Gaussian random sparse signal as the measurement signal for simulation,the measured signal after energy detection in the airport terminal area can be effectively simulated.Through the simulation,the performance of JTVSSAMP is better than that of the traditional compressed sensing algorithm in the algorithm reconstruction success rate under different measurement numbers and sparsity.Compared with the SAMP algorithm,JTVS-SAMP performs significantly in the reconstruction error and algorithm time.

关 键 词：压缩感知 信号重构 广义Jaccard系数 变步长 

分 类 号：TN919[电子电信—通信与信息系统]