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Existing spectrum sensing systems are commonly designed based on the famous Nyquist theorem. With the rapid development of radio frequency technology, the corresponding sampling frequency is so high that many problems may be brought about, such as the increasing hardware complexity, large volume of measurements and difficulties to meet the real time requirement etc. To tackle these problems caused by high sampling frequency, a novel scheme, adaptive modulated wideband converter, is proposed. By exploiting the band width of the narrow bands, the total sampling frequency is proved to be as low as four times of the sum of the narrow bands. There is a trade-off between the sampling complexity and the total sampling frequency for different choices of the repeating frequency of the random function. Sufficient conditions are derived to guarantee exact signal recovery from sub-Nyquist measurements. Conditions of full row rank of the equivalent unknown matrix are also explored to guarantee that the multiple signal classification can be adopted to implement the signal reconstruction. The simulations verify the analysis. This novel scheme can be used to implement front-end spectrum analysis for absorbing materials and detect the active channels in cognitive radio.
[1] Bao S, Luo C R, Zhao X P 2011 Acta Phys. Sin. 60 1 (in Chinese) [保石, 罗春荣, 赵晓鹏 2011 物理学报 60 1]
[2] Chen Q, Jiang J J, Bie S W, Wang P, Liu P, Xu X X 2011 Acta Phys. Sin. 60 7 (in Chinese) [陈谦, 江建军, 别少伟, 王鹏, 刘鹏, 徐欣欣 2011 物理学报 60 7]
[3] Li J, Wen G J, Huang Y J, Wang P, Sun Y H 2013 Acta Phys. Sin. 62 8 (in Chinese) [李建, 文光俊, 黄勇军, 王平, 孙元华 2013 物理学报 62 8]
[4] Sun B, Jiang J J 2013 Acta Phys. Sin. 60 11 (in Chinese) [孙彪, 江建军 2011 物理学报 60 11]
[5] Liu Y, Peng Q C, Shao H Z, Peng Q H, Wang L 2013 Acta Phys. Sin. 62 7 (in Chinese) [刘允, 彭启琮, 邵怀宗, 彭启航, 王玲 2013 物理学报 62 7]
[6] Zheng S L, Yang X N 2013 Acta Phys. Sin. 62 7 (in Chinese) [郑仕链, 杨小牛 2013 物理学报 62 7]
[7] Zu Y X, Zhou J 2012 Chin. Phys. B 21 1
[8] Zu Y X, Zhou J, Zeng C C 2010 Chin. Phys. B 19 11
[9] Bao D, Vito L, Rapuano S 2013 IEEE Trans. Instrum. Meas. 62 7
[10] Tropp J A, Laska J N, Duarte M F, Romberg J K, Baraniuk R G 2010 IEEE Trans. Inf. Theory 56 1
[11] Eldar Y C, Michaeli T 2009 IEEE Signal Process. Mag. 26 3
[12] Dominguez-Jimenez M E, Gonzalez-Prelcic N, Vazquez-Vilar G, Lopez-Valcarce R 2012 Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing Kyoto, Japan, March 25–30, 2012
[13] Romberg J 2009 SIAM Journal on Imaging Sciences 2 4
[14] Tropp J A, Wakin M B, Duarte M F, Baron D, Baraniuk R G 2006 Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing Toulouse, France, May 14–19, 2006
[15] Mishali M, Eldar Y C 2010 IEEE J. Sel. Topics Signal Process. 4 2
[16] Mishali M, Eldar Y C 2011 IEEE Signal Process. Mag. 28 4
[17] Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 2
[18] Tropp J A, Gilbert A C, Strauss M J 2006 Signal Processing 86 3
[19] Eldar Y C, Rauhut H 2010 IEEE Trans. Inf. Theory 56 1
[20] Mishali M, Eldar Y C 2008 IEEE Signal Process. 56 10
[21] Schmidt R 1986 IEEE Trans. Antennas Propag. 34 3
[22] Feng P, Bresler Y 1996 Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing Atlanta, USA, May 7–10, 1996
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[1] Bao S, Luo C R, Zhao X P 2011 Acta Phys. Sin. 60 1 (in Chinese) [保石, 罗春荣, 赵晓鹏 2011 物理学报 60 1]
[2] Chen Q, Jiang J J, Bie S W, Wang P, Liu P, Xu X X 2011 Acta Phys. Sin. 60 7 (in Chinese) [陈谦, 江建军, 别少伟, 王鹏, 刘鹏, 徐欣欣 2011 物理学报 60 7]
[3] Li J, Wen G J, Huang Y J, Wang P, Sun Y H 2013 Acta Phys. Sin. 62 8 (in Chinese) [李建, 文光俊, 黄勇军, 王平, 孙元华 2013 物理学报 62 8]
[4] Sun B, Jiang J J 2013 Acta Phys. Sin. 60 11 (in Chinese) [孙彪, 江建军 2011 物理学报 60 11]
[5] Liu Y, Peng Q C, Shao H Z, Peng Q H, Wang L 2013 Acta Phys. Sin. 62 7 (in Chinese) [刘允, 彭启琮, 邵怀宗, 彭启航, 王玲 2013 物理学报 62 7]
[6] Zheng S L, Yang X N 2013 Acta Phys. Sin. 62 7 (in Chinese) [郑仕链, 杨小牛 2013 物理学报 62 7]
[7] Zu Y X, Zhou J 2012 Chin. Phys. B 21 1
[8] Zu Y X, Zhou J, Zeng C C 2010 Chin. Phys. B 19 11
[9] Bao D, Vito L, Rapuano S 2013 IEEE Trans. Instrum. Meas. 62 7
[10] Tropp J A, Laska J N, Duarte M F, Romberg J K, Baraniuk R G 2010 IEEE Trans. Inf. Theory 56 1
[11] Eldar Y C, Michaeli T 2009 IEEE Signal Process. Mag. 26 3
[12] Dominguez-Jimenez M E, Gonzalez-Prelcic N, Vazquez-Vilar G, Lopez-Valcarce R 2012 Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing Kyoto, Japan, March 25–30, 2012
[13] Romberg J 2009 SIAM Journal on Imaging Sciences 2 4
[14] Tropp J A, Wakin M B, Duarte M F, Baron D, Baraniuk R G 2006 Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing Toulouse, France, May 14–19, 2006
[15] Mishali M, Eldar Y C 2010 IEEE J. Sel. Topics Signal Process. 4 2
[16] Mishali M, Eldar Y C 2011 IEEE Signal Process. Mag. 28 4
[17] Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 2
[18] Tropp J A, Gilbert A C, Strauss M J 2006 Signal Processing 86 3
[19] Eldar Y C, Rauhut H 2010 IEEE Trans. Inf. Theory 56 1
[20] Mishali M, Eldar Y C 2008 IEEE Signal Process. 56 10
[21] Schmidt R 1986 IEEE Trans. Antennas Propag. 34 3
[22] Feng P, Bresler Y 1996 Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing Atlanta, USA, May 7–10, 1996
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