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Time delay estimation (TDE) is a hot research topic in wireless location technology. Compressed sensing (CS) theory has been widely applied to image reconstruction and direction of arrival estimation since it was proposed in 2004. The sparse model can be constructed in time domain for estimating the time delay by using the CS theory. The measurement matrix plays a crucial role in the processing of signal reconstruction which is the core problem of CS theory. Therefore the research in the measurement matrix has becomes a hotspot in recent years. The existing measurement matrix is mainly divided into two categories, i.e., random measurement matrix and deterministic measurement matrix. The performance of random measurement matrix has bottlenecks. Firstly, because of the redundant measurement matrix data, the generation and storage of the random number put forward a high requirement for hardware. Secondly the random matrix can only satisfy the restricted isometry property in a statistical sense. The research of the deterministic measurement matrix is of great value under this background. The parity check matrix of low density parity check (LDPC) code has good performance in CS theory. However, the method of randomly selecting non-zero element position has a certain probability to generate a measurement matrix with a short loop structure during generating LDPC code measurement matrix. The robustness of the reconstruction performance decreases with the increase of iteration times. A novel quasi-cyclic CS algorithm based on progressive edge-growth is constructed to estimate the time delay. The purpose of this article is to deal with the need to store a large number of data in existing measurement matrix during time delay, by using the CS theory. The algorithm presented here can achieve TDE in a high precision. First, the theoretical bridge between CS and the maximum likelihood decoding is established. And the design criterion of measurement matrix based on the LDPC code is derived. The sparse measurement matrix with quasi-cyclic structure is constructed by introducing the idea of progressive edge-growth. Finally, the orthogonal matching pursuit algorithm is used to estimate the time delay. Furthermore, the computational complexity of the algorithm and the data storage of the measurement matrix are analyzed theoretically. Simulations show that the correct reconstruction probability of the proposed approach is higher than those of the Gauss random matrix and random LDPC matrix under the same dimension. Compared with the random LDPC matrix, the proposed method can improve performance at the expense of less complexity under the condition of the same data storage.
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[6] Leng X D, Ba B, Lu Z Y, Wang D M 2016 Acta Phys. Sin. 65 210701 (in Chinese) [冷雪冬, 巴斌, 逯志宇, 王大鸣 2016 65 210701]
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[9] DeVore R A 2007 J. Complexity 23 918
[10] Xia P F, Zhou S L, Giannakis G B 2005 IEEE Trans. Inform. Theory 51 1900
[11] Dimakis A G, Smarandache R, Vontobel P O 2012 IEEE Trans. Inform. Theory 58 3093
[12] Xia S T, Liu X J, Jiang Y 2015 IEEE Trans. Signal Process. 63 1017
[13] Mohades A, Tadaion A A 2016 IET Signal Process 10 168
[14] Elad M 2008 IEEE Trans. Signal Process. 55 5695
[15] Hochba D S 1997 ACM Sigact News 28 40
[16] Tillmann A M, Pfetsch M E 2014 IEEE Trans. Inform. Theory 60 1248
[17] Gao Y, Peng J G, Yue S G, Zhao Y 2015 J. Function Spaces 205 579853
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[19] Dang K, Ma L H, Tian Y, Zhang H W, Ru L, Li X B 2015 J. Xidian Univ. 42 186 (in Chinese) [党骙, 马林华, 田雨, 张海威, 茹乐, 李小蓓 2015 西安电子科技大学学报(自然科学版) 42 186]
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[1] Zhang Q F, Huang J G, Xie Y Q 1995 Acta Acust. 20 211 (in Chinese) [张群飞, 黄建国, 谢一清 1995 声学学报 20 211]
[2] Li J 2011 Electron. Meas. Technol. 34 73 (in Chinese) [李剑 2011 电子测量技术 34 73]
[3] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[4] Ning F L, He B J, Wei J 2013 Acta Phys. Sin. 62 174212 (in Chinese) [宁方立, 何碧静, 韦娟 2013 62 174212]
[5] Shen Z B, Dong C X, Huang L, Zhao G Q 2014 J. Electron. Inform. Technol. 36 2935 (in Chinese) [沈志博, 董春曦, 黄龙, 赵国庆 2014 电子与信息学报 36 2935]
[6] Leng X D, Ba B, Lu Z Y, Wang D M 2016 Acta Phys. Sin. 65 210701 (in Chinese) [冷雪冬, 巴斌, 逯志宇, 王大鸣 2016 65 210701]
[7] Wang Q, Li J, Shen Y 2013 Acta Electron. Sin. 41 2041 (in Chinese) [王强, 李佳, 沈毅 2013 电子学报 41 2041]
[8] Candes E J, Tao T 2005 IEEE Trans. Inform. Theory 51 4203
[9] DeVore R A 2007 J. Complexity 23 918
[10] Xia P F, Zhou S L, Giannakis G B 2005 IEEE Trans. Inform. Theory 51 1900
[11] Dimakis A G, Smarandache R, Vontobel P O 2012 IEEE Trans. Inform. Theory 58 3093
[12] Xia S T, Liu X J, Jiang Y 2015 IEEE Trans. Signal Process. 63 1017
[13] Mohades A, Tadaion A A 2016 IET Signal Process 10 168
[14] Elad M 2008 IEEE Trans. Signal Process. 55 5695
[15] Hochba D S 1997 ACM Sigact News 28 40
[16] Tillmann A M, Pfetsch M E 2014 IEEE Trans. Inform. Theory 60 1248
[17] Gao Y, Peng J G, Yue S G, Zhao Y 2015 J. Function Spaces 205 579853
[18] Sun J M 2016 Modern Radar 38 46 (in Chinese) [孙晶明 2016 现代雷达 38 46]
[19] Dang K, Ma L H, Tian Y, Zhang H W, Ru L, Li X B 2015 J. Xidian Univ. 42 186 (in Chinese) [党骙, 马林华, 田雨, 张海威, 茹乐, 李小蓓 2015 西安电子科技大学学报(自然科学版) 42 186]
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