基于Gerschgorin理论稀疏度估计的宽带频谱感知算法

doi:10.11772/j.issn.1001-9081.2016.01.0087

计算机应用 ›› 2016, Vol. 36 ›› Issue (1): 87-90.DOI: 10.11772/j.issn.1001-9081.2016.01.0087

基于Gerschgorin理论稀疏度估计的宽带频谱感知算法

赵知劲^1,2, 陈京来¹

1. 杭州电子科技大学通信工程学院, 杭州 310018;
2. 中国电子科技集团第36研究所通信系统信息控制技术国家级重点实验室, 浙江嘉兴 314001

收稿日期:2015-06-23 修回日期:2015-09-13 出版日期:2016-01-10 发布日期:2016-01-09
通讯作者: 陈京来(1992-),男,浙江温岭人,硕士研究生,主要研究方向:认知无线电
作者简介:赵知劲(1959-),女,浙江宁波人,教授,博士,主要研究方向:认知无线电、通信信号处理、自适应信号处理。

Wide-band spectrum sensing algorithm using sparsity estimation based on Gerschgorin theorem

ZHAO Zhijin^1,2, CHEN Jinglai¹

1. School of Telecommunication Engineering, Hangzhou Dianzi University, Hangzhou Zhejiang 310018, China;
2. State Key Laboratory of Information Control Technology in Communication System, No.36 Research Institute, China Electronic Technology Corporation, Jiaxing Zhejiang 314001, China

Received:2015-06-23 Revised:2015-09-13 Online:2016-01-10 Published:2016-01-09

摘要/Abstract

摘要： 针对在低信噪比(SNR)情况下稀疏度欠估计和高信噪比情况下稀疏度过估计的问题,提出了一种基于Gerschgorin理论稀疏度估计的宽带频谱感知算法。首先,该算法利用Gerschgorin理论分离信号圆盘与噪声圆盘得到稀疏度估计值;然后,利用正交匹配追踪(OMP)算法得到频谱支撑集;最后,完成宽带频谱感知。仿真结果表明,所提算法、AIC-OMP算法和MDL-OMP算法频谱感知的检测概率达到95%信噪比分别需要4.6 dB、8.5 dB和9.7 dB;所提算法频谱感知的虚警概率在信噪比大于13 dB时趋近于0,明显低于BPD-OMP和GDRI-OMP算法的虚警概率,因此,所提算法对于压缩感知(CS)的信号稀疏度估计兼顾了低信噪比和高信噪比时的稀疏度估计性能,频谱感知性能优于AIC-OMP算法、MDL-OMP算法、BPD-OMP算法和GDRI-OMP算法。

关键词: 宽带频谱感知, 压缩感知, 稀疏度, Gerschgorin理论, 正交匹配追踪算法

Abstract: To solve the problems of under-estimation of sparsity at low Signal-to-Noise Ratio (SNR) and over-estimation of sparsity at high SNR, a wide-band spectrum sensing algorithm using sparsity estimation based on Gerschgorin theorem was proposed. Firstly, Gerschgorin theorem was used to separate the signal disk and noise disk in order to estimate the sparsity. Then, the spectrum support set was obtained by using Orthogonal Matching Pursuit (OMP) algorithm. Finally, the wide-band spectrum sensing was accomplished. The simulation results show that, the SNR of the proposed algorithm, AIC-OMP (Akaike Information Criterion-Orthogonal Matching Pursuit) algorithm and MDL-OMP (Minimum Description Length-Orthogonal Matching Pursuit) algorithm need 4.6 dB, 8.5 dB and 9.7 dB respectively while their detection probability reaching to 95%; the false alarm probability of the proposed algorithm tends to 0 when the SNR is higher than 13 dB, which is far lower than that of BPD-OMP (Bayesian Predictive Density-Orthogonal Matching Pursuit) algorithm and GDRI-OMP (Gerschgorin Disk Radii Iteration-Orthogonal Matching Pursuit) algorithm. Therefore, the proposed algorithm takes account of sparsity estimation performances under both low SNR and high SNR, and the spectrum sensing performance of the proposed algorithm is better than that of AIC-OMP algorithm, MDL-OMP algorithm, BPD-OMP algorithm and GDRI-OMP algorithm.

Key words: wide-band spectrum sensing, Compressed Sensing (CS), sparsity, Gerschgorin theorem, Orthogonal Matching Pursuit (OMP) algorithm

中图分类号:

TP393.04

赵知劲, 陈京来. 基于Gerschgorin理论稀疏度估计的宽带频谱感知算法[J]. 计算机应用, 2016, 36(1): 87-90.

ZHAO Zhijin, CHEN Jinglai. Wide-band spectrum sensing algorithm using sparsity estimation based on Gerschgorin theorem[J]. Journal of Computer Applications, 2016, 36(1): 87-90.

参考文献

[1] SUN H, NALLANATHAN A, WANG C, et al. Wideband spectrum sensing for cognitive radio networks: a survey [J]. IEEE wireless communications, 2013, 20(2): 74-81.
[2] DONOHO D L. Compressed sensing [J]. IEEE transactions on information theory, 2006, 52(4): 1289-1306.
[3] ZHI T, GIANNAKIS G B. Compressed sensing for wideband cognitive radios [C]// Proceedings of the 2007 IEEE International Conference on Acoustics, Speech and Signal Processing. Piscataway, NJ: IEEE, 2007: 1357-1360.
[4] MISHALI M, ELDAR Y C. From theory to practice: sub-Nyquist sampling of sparse wideband analog signals [J]. IEEE journal of selected topics in signal processing, 2010, 4(2): 375-391.
[5] ZHANG Z, LI H, YANG D, et al. Space-time Bayesian compressed spectrum sensing for wideband cognitive radio networks [C]// Proceedings of the 2010 IEEE Symposium on New Frontiers in Dynamic Spectrum. Piscataway, NJ: IEEE, 2010: 1-11.
[6] 赵知劲,张鹏,王海泉,等.基于OMP算法的宽带频谱感知[J].信号处理,2012,28(5):723-728.(ZHAO Z J, ZHANG P, WANG H Q, et al. Wideband spectrum sensing based on OMP algorithm [J]. Signal processing, 2012, 28(5): 723-728.)
[7] 赵知劲,胡伟康.基于贝叶斯预测密度的弱匹配追踪频谱检测[J].计算机应用研究,2015,32(7):2119-2122.(ZHAO Z J, HU W K. Spectrum detection algorithm using weak matching pursuit based on Bayesian predictive densities [J]. Application research of computers, 2015, 32(7): 2119-2122.)
[8] 张平平,伍俊良,胡兴凯,等.Gerschgorin圆盘的分离[J].西南师范大学学报(自然科学版),2011,36(3):1-3.(ZHANG P P, WU J L, HU X K, et al. On the separation of Gerschgorin circular discs [J]. Journal of Southwest China normal university (natural science edition), 2011, 36(3): 1-3.)
[9] WU H, YANG J, CHEN F. Source number estimators using transformed Gerschgorin radii [J]. IEEE transactions on signal processing, 1995, 43(6): 1325-1333.
[10] 董姝敏,梁国龙.一种改进的盖尔圆源数目估计方法[J].哈尔滨工程大学学报,2013,34(4):440-444.(DONG S M, LIANG G L. A modified Gerschgorin disks estimation method for source number estimation [J]. Journal of Harbin engineering university, 2013, 34(4): 440-444.)
[11] 申滨,王舒,黄琼,等.基于Gerschgorin圆盘理论的认知无线电宽带频谱感知[J].通信学报,2014,35(4):1-10.(SHEN B, WANG S, HUANG Q, et al. Gerschgorin disk theorem based spectrum sensing for wideband cognitive radio [J]. Journal on communications, 2014, 35(4): 1-10.)
[12] RASHIDI M, HAGHIGHI K, OWRANG A, et al. A wideband spectrum sensing method for cognitive radio using sub-Nyquist sampling [C]// Proceedings of the 2011 IEEE Digital Signal Processing Workshop and IEEE Signal Processing Education Workshop. Piscataway, NJ: IEEE, 2011: 30-35.
[13] CAI T T, LIE W. Orthogonal matching pursuit for sparse signal recovery with noise [J]. IEEE transactions on information theory, 2011, 57(7): 4680-4688.
[14] MISHALI M, ELDAR Y C. Reduce and boost: recovering arbitrary sets of jointly sparse vectors [J]. IEEE transactions on signal processing, 2008, 56(10): 4692-4702.

[1]	沈子懿, 王卫亚, 蒋东华, 荣宪伟. 基于Hopfield混沌神经网络和压缩感知的可视化图像加密算法[J]. 计算机应用, 2021, 41(10): 2893-2899.
[2]	席雅睿, 乔志伟, 温静, 张艳娇, 杨雯晶, 闫慧文. 基于Chambolle-Pock算法框架的高阶TV图像重建算法[J]. 计算机应用, 2020, 40(6): 1793-1798.
[3]	徐志强, 蒋铁钢, 杨立波. 基于随机支撑挑选的广义正交匹配追踪算法[J]. 计算机应用, 2020, 40(4): 1104-1108.
[4]	杨立波, 蒋铁钢, 徐志强. 基于混合梯度的硬阈值追踪算法[J]. 计算机应用, 2020, 40(3): 912-916.
[5]	高彦彦, 李莉, 张晶, 贾英茜. 结合梯度投影稀疏重构和复数小波的图像重构[J]. 计算机应用, 2020, 40(2): 486-490.
[6]	宗春梅, 张月琴, 曹建芳, 赵青杉. 基于深度先验及非局部相似性的压缩感知核磁共振成像[J]. 计算机应用, 2020, 40(10): 3054-3059.
[7]	杜小磊, 陈志刚, 张楠, 许旭. 基于压缩感知和深度小波网络的列车故障识别[J]. 计算机应用, 2019, 39(7): 2175-2180.
[8]	宋子晖, 李卓, 陈昕. 基于压缩感知的移动群智感知任务分发机制[J]. 计算机应用, 2019, 39(1): 15-21.
[9]	刘晓晖, 路利军, 冯前进, 陈武凡. 基于Moreau-包络的近似平滑迭代磁共振图像重建算法[J]. 计算机应用, 2018, 38(7): 2076-2082.
[10]	乔建华, 张雪英. 基于均衡分簇的无线传感器网络压缩数据收集[J]. 计算机应用, 2018, 38(6): 1691-1697.
[11]	金凤, 唐宏, 张进彦, 尹礼欣. 基于压缩感知的大规模MIMO系统导频优化及信道估计算法[J]. 计算机应用, 2018, 38(5): 1447-1452.
[12]	唐虎, 刘紫燕, 刘世美, 冯丽. 基于压缩感知的大规模多输入多输出空间共稀疏信道估计[J]. 计算机应用, 2018, 38(4): 1106-1110.
[13]	肖文, 胡娟. 基于数据集稀疏度的频繁项集挖掘算法性能分析[J]. 计算机应用, 2018, 38(4): 995-1000.
[14]	李周, 崔琛. 基于奇异值分解的压缩感知观测矩阵优化算法[J]. 计算机应用, 2018, 38(2): 568-572.
[15]	杜秀丽, 张薇, 陈波. 基于波浪式矩阵置换的稀疏度均衡分块压缩感知算法[J]. 计算机应用, 2018, 38(12): 3541-3546.

基于Gerschgorin理论稀疏度估计的宽带频谱感知算法

Wide-band spectrum sensing algorithm using sparsity estimation based on Gerschgorin theorem

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics