无线信道信息的快速压缩重构研究
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摘要
压缩感知理论是一种新的信息获取方法,能够以远低于耐奎斯特定律的采样速率对稀疏信号进行采样,并精确地进行重构。无线信道的冲激响应通常呈现出稀疏的分簇多径特性。利用此性质并考虑OFDM系统本身的一些特性,如最大相对时延小于循环前缀长度,将压缩感知理论应用到OFDM系统的信道估计中,能够减小导频开销,降低导频图样限制,具有较高的估计精度。
传统的压缩感知理论并未考虑到稀疏信号本身可能具有的结构,块稀疏就是其中的一种,即非零元素成块出现。利用这一特点,可以进一步的降低采样速率,并提高重构精度。然而现有的块稀疏贪婪重构算法,如BOMP,只能够针对块长相同,且非零块间的距离为块长的整数倍这一特例进行很好的重构。因此针对这个问题,文章中提出了一种改进的BOMP算法,它能够适用于更加一般的块稀疏信号,并且获得更好的重构效果。本文还将块稀疏信号重构算法与DPSS基扩展相结合,进行时延多普勒域信道信息的估计。相对于傅里叶基扩展,DPSS基扩展在降低复杂度的同时,克服了能量泄露的问题,并降低了对多普勒频移的敏感度
Compressed sensing (CS) is a new signal acquisition method. It enables signals to be sampled below the Nyquist rate given that the signal is sparse, with an accurate reconstruction. Because of the multipath effect, the channel state information in delay domain has sparsity. When we apply CS theory into channel estimation of OFDM system, the pilots' number decreases, and the accuracy increases.
The traditional CS theory doesn't concern the natural property of the sparse signal, such as block-sparstiy. Applying with this, we can improve the recovery accuracy and promote the efficiency. However, most of the exist reconstruction algrithms, such as BOMP can only get wonderful performance when the lengths of nonzero blocks are the same, and the intervals between them are integral multiple of the length. So, we propose a modified BOMP algorithm for the more general block sparse singals in this paper. And we combine the reconstuction of block-sparsity singal with DPSS basis expand model to estmate the channel state information in time-delay domain. In this way, we can overcome the energy leak of Fourier basisi expand model, and reduce the sensitivity to Doppler shift.
传统的压缩感知理论并未考虑到稀疏信号本身可能具有的结构,块稀疏就是其中的一种,即非零元素成块出现。利用这一特点,可以进一步的降低采样速率,并提高重构精度。然而现有的块稀疏贪婪重构算法,如BOMP,只能够针对块长相同,且非零块间的距离为块长的整数倍这一特例进行很好的重构。因此针对这个问题,文章中提出了一种改进的BOMP算法,它能够适用于更加一般的块稀疏信号,并且获得更好的重构效果。本文还将块稀疏信号重构算法与DPSS基扩展相结合,进行时延多普勒域信道信息的估计。相对于傅里叶基扩展,DPSS基扩展在降低复杂度的同时,克服了能量泄露的问题,并降低了对多普勒频移的敏感度
Compressed sensing (CS) is a new signal acquisition method. It enables signals to be sampled below the Nyquist rate given that the signal is sparse, with an accurate reconstruction. Because of the multipath effect, the channel state information in delay domain has sparsity. When we apply CS theory into channel estimation of OFDM system, the pilots' number decreases, and the accuracy increases.
The traditional CS theory doesn't concern the natural property of the sparse signal, such as block-sparstiy. Applying with this, we can improve the recovery accuracy and promote the efficiency. However, most of the exist reconstruction algrithms, such as BOMP can only get wonderful performance when the lengths of nonzero blocks are the same, and the intervals between them are integral multiple of the length. So, we propose a modified BOMP algorithm for the more general block sparse singals in this paper. And we combine the reconstuction of block-sparsity singal with DPSS basis expand model to estmate the channel state information in time-delay domain. In this way, we can overcome the energy leak of Fourier basisi expand model, and reduce the sensitivity to Doppler shift.
引文
[1]杨大成,《移动传播环境》,机械工业出版社,2003,pp38.
[2]啜钢,王文博,常永宇等,《移动通信原理与系统》,2005,pp26.
[3]M.Narandzie, C.Sehneider, R.Thoma, "Comparison of SCM, SCME and WINNER channel model", Proc. Of the 65st IEEE Veh. Teehnol. Conf. (VTC07), Dublin, Ireland, pp.413-417.
[4]D L. Donoho, "Compressed sensing", IEEE Trans. Info. Theory, vol.52, no.4, 2006:pp.1289-1306.
[5]J. A. Tropp, "Greed is Good:Algorithmic Results for Sparse Approximation,' Univ. Texas at Austin, ICES Rep.03-04, Feb.2003.
[6]J. A. Tropp and A. C. Gilbert. "Signal recovery from random measurements via orthogonal matching pursuit".IEEE Trans. Info. Theory,53(12):4655-4666,2007.
[7]王文博,郑侃,《宽带无线通信OFDM技术》,第二版,人民邮电出版社,2007.
[8]李树涛,魏丹,“压缩传感综述”,自动化学报,2008.
[9]Baraniuk R, " Compressive sensing ", IEEE Signal Processing Magazine,2007, 24(4):118-121.
[10]3GPP TR 25.996 V8.8.0, Spatial channel model for Multiple Input MultipleOutput (MIMO) simulations.(Release 8),2009-12
[11]Needell D, Tropp J A. CoSaMP:Iterative signal recovery from incomplete and inaccurate samples. ACM Technical Report 2008-01, California Institute of Technology. Pasadena, July 2008.
[12]Jeffrey D. Blanchard, Coralia Cartis, and Jared Tanner, "Decay Properties of Restricted Isometry Constants," IEEE Signal Processing Letter, Vol.16, No.7, July 2009.
[13]Needell D, Vershynin R.,"Greedy signal recovery and uncertainty principles," In: Proceedings of the SPIE. Bellingham, WA:SPIE,2008.
[14]S. Mallat and Z. Zhang, "Matching pursuit in a time-frequency dictionary", IEEE Trans. Signal Proc.,41 (1993), pp.3397-3415.
[15]S. S. Chen. D. L. Donoho, and M. A. Saunders."Atomic decomposition by basis pursuit". SI AM J. Sci. Comput.,20:33-61.1999.
|16]S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
[17]Georg Taubock, Franz Hlawatsch, Holger Rauhut, "Compressive estimation of doubly selective channels in multicarrier systems:Leakage effects and sparsity-enhancing processing," IEEE Journal of Selected Topics in Signal Processing, April.2010.
[18]A. Nemirovski A. Ben Tal, Lectures on Modern Convex Optimization. Analysis, Algorithms and Engineering Applications, SIAM,2001.
[19]Candes E, Tao T., "Decoding by linear programming",.IEEE Transactions on Information Theory,2005,51(12):4203-4215.
[20]A. Sayeed, "A virtual representation for time- and frequencyselective correlated MIMO channels,"in Proc. ICASSP 2003.
[21]R. G Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Trans. Inf. Theory, vol.56, no.4, pp.1982-2001, 2010.
[22]Kwon and Hwanjoon, "On the benefits of the block-sparsity structure in sparse signal recovery", ICASSP, pp.3685-3688, March 2012.
[23]Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol.55, no.11,pp.5302-5316,2009.
[24]Marco F. Duarte and Yonina C. Eldar, "Structured compressed sensing from theory to applications ", IEEE Trans. Sig. Proc., vol. 59,no.9,pp4053-4085,Sept.2011.
[25]M. Stojnic, F. Parvaresh, and B. Hassibi, "On the reconstruction of block-sparse signals with an optimal number of measurements," IEEE Trans. Signal Process., vol.57, no.8, pp.3075-3085, May 2010.
[26]Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol.55, no.11, pp.5302-5316, Nov.2009.
[27]Y. C. Eldar, P. Kuppinger, and H. Bolcskei, "Block-sparse signals:Uncertainty relations and efficient recovery," IEEE Trans. Signal Process.,vol.58, no.6, pp. 3042-3054,2010.
[28]M. Stojnic, F. Parvaresh, and B. Hassibi. On the reconstruction of block-sparse signals with an optimal number of measurements. IEEE Trans.on Signal Processing, August 2009.
[29]M. Stojnic.l2/l1-optimization in block-sparse compressed sensing and its strong thresholds. IEEE Journal of Selected Topics in Signal Processing,2009.
[30]M. Stojnic. Strong thresholds for l2/l1-optimization in block-sparse compressed sensing. ICASSP, International Conference on Acoustics, Signal and Speech Processing, April 2009.
[31]E. J. Candes and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies?", IEEE Trans.on Information Theory,vol.52, pp. 5406-5452,2006.
[32]M. A. Davenport and M. B.Wakin, "Analysis of orthogonal matching pursuit using the restricted isometry property," IEEE Trans. Inf. Theory, vol.56, pp. 1982-2001,2010.
[33]O. Edfors, M. Sandell, and P. O.Borjesson, "OFDM channel estimation by singular value decomposition,"IEEE Trans. Comm., vol.46, pp.931-939, July 1998.
[34]P. Fertl and G. Matz, "Efficient OFDM channel estimation in mobile environments based on irregular sampling," in Proc. Asilomar Conf. Signals, Systems, Computers, (Pacific Grove, CA), pp.1777-1781, Oct.-Nov.2006.
[35]P. Fertl and G. Matz, "Efficient OFDM channel estimation in mobile environments based on irregular sampling," in Proc. Asilomar Conf. Signals, Systems, Computers, (Pacific Grove, CA), pp.1777-1781, Oct.-Nov.2006.
[36]A. M. Sayeed,A. Sendonaris, and B. Aazhang, "Multiuser detection in fast-fading multipath environment," IEEE J. Select. Areas, vol.16, no.9, pp.1691-1701, December 1998.
[37]D. B. Percival and A. T. Walden, Spectral Analysis for Physical Applications. Cambridge University Press,1963.
[38]J. G. Proakis and D. G. Manolakis, Digital Signal Processing,3rd ed. Prentice-Hall.1996.
[39]Zemen. T.; Mecklenbrauker, C.F. "Time-Variant Channel Equalization via Discrete Prolate Spheroidal Sequences", Conference Record of the Thirty-Seventh Asilomar Conference on,2003. Page(s):1288-1292 Vol.2
[40]D. Slepian. Prolate spheroidal wave functions, Fourier analysis, and uncertainty. V:The discrete case. Bell Systems Tech. J.,57(5):1371-1430.1978.
[41]D. Slepian. Some comments on Fourier analysis, uncertainty, and modeling. SIAM Rev.,25(3):379-393.1983.
|42]D. Slepian and H. Pollak. Prolate spheroidal wave functions, Fourier analysis, and uncertainty. I. Bell Systems Tech. J.,40(1):43-64.1961.
[2]啜钢,王文博,常永宇等,《移动通信原理与系统》,2005,pp26.
[3]M.Narandzie, C.Sehneider, R.Thoma, "Comparison of SCM, SCME and WINNER channel model", Proc. Of the 65st IEEE Veh. Teehnol. Conf. (VTC07), Dublin, Ireland, pp.413-417.
[4]D L. Donoho, "Compressed sensing", IEEE Trans. Info. Theory, vol.52, no.4, 2006:pp.1289-1306.
[5]J. A. Tropp, "Greed is Good:Algorithmic Results for Sparse Approximation,' Univ. Texas at Austin, ICES Rep.03-04, Feb.2003.
[6]J. A. Tropp and A. C. Gilbert. "Signal recovery from random measurements via orthogonal matching pursuit".IEEE Trans. Info. Theory,53(12):4655-4666,2007.
[7]王文博,郑侃,《宽带无线通信OFDM技术》,第二版,人民邮电出版社,2007.
[8]李树涛,魏丹,“压缩传感综述”,自动化学报,2008.
[9]Baraniuk R, " Compressive sensing ", IEEE Signal Processing Magazine,2007, 24(4):118-121.
[10]3GPP TR 25.996 V8.8.0, Spatial channel model for Multiple Input MultipleOutput (MIMO) simulations.(Release 8),2009-12
[11]Needell D, Tropp J A. CoSaMP:Iterative signal recovery from incomplete and inaccurate samples. ACM Technical Report 2008-01, California Institute of Technology. Pasadena, July 2008.
[12]Jeffrey D. Blanchard, Coralia Cartis, and Jared Tanner, "Decay Properties of Restricted Isometry Constants," IEEE Signal Processing Letter, Vol.16, No.7, July 2009.
[13]Needell D, Vershynin R.,"Greedy signal recovery and uncertainty principles," In: Proceedings of the SPIE. Bellingham, WA:SPIE,2008.
[14]S. Mallat and Z. Zhang, "Matching pursuit in a time-frequency dictionary", IEEE Trans. Signal Proc.,41 (1993), pp.3397-3415.
[15]S. S. Chen. D. L. Donoho, and M. A. Saunders."Atomic decomposition by basis pursuit". SI AM J. Sci. Comput.,20:33-61.1999.
|16]S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
[17]Georg Taubock, Franz Hlawatsch, Holger Rauhut, "Compressive estimation of doubly selective channels in multicarrier systems:Leakage effects and sparsity-enhancing processing," IEEE Journal of Selected Topics in Signal Processing, April.2010.
[18]A. Nemirovski A. Ben Tal, Lectures on Modern Convex Optimization. Analysis, Algorithms and Engineering Applications, SIAM,2001.
[19]Candes E, Tao T., "Decoding by linear programming",.IEEE Transactions on Information Theory,2005,51(12):4203-4215.
[20]A. Sayeed, "A virtual representation for time- and frequencyselective correlated MIMO channels,"in Proc. ICASSP 2003.
[21]R. G Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Trans. Inf. Theory, vol.56, no.4, pp.1982-2001, 2010.
[22]Kwon and Hwanjoon, "On the benefits of the block-sparsity structure in sparse signal recovery", ICASSP, pp.3685-3688, March 2012.
[23]Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol.55, no.11,pp.5302-5316,2009.
[24]Marco F. Duarte and Yonina C. Eldar, "Structured compressed sensing from theory to applications ", IEEE Trans. Sig. Proc., vol. 59,no.9,pp4053-4085,Sept.2011.
[25]M. Stojnic, F. Parvaresh, and B. Hassibi, "On the reconstruction of block-sparse signals with an optimal number of measurements," IEEE Trans. Signal Process., vol.57, no.8, pp.3075-3085, May 2010.
[26]Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol.55, no.11, pp.5302-5316, Nov.2009.
[27]Y. C. Eldar, P. Kuppinger, and H. Bolcskei, "Block-sparse signals:Uncertainty relations and efficient recovery," IEEE Trans. Signal Process.,vol.58, no.6, pp. 3042-3054,2010.
[28]M. Stojnic, F. Parvaresh, and B. Hassibi. On the reconstruction of block-sparse signals with an optimal number of measurements. IEEE Trans.on Signal Processing, August 2009.
[29]M. Stojnic.l2/l1-optimization in block-sparse compressed sensing and its strong thresholds. IEEE Journal of Selected Topics in Signal Processing,2009.
[30]M. Stojnic. Strong thresholds for l2/l1-optimization in block-sparse compressed sensing. ICASSP, International Conference on Acoustics, Signal and Speech Processing, April 2009.
[31]E. J. Candes and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies?", IEEE Trans.on Information Theory,vol.52, pp. 5406-5452,2006.
[32]M. A. Davenport and M. B.Wakin, "Analysis of orthogonal matching pursuit using the restricted isometry property," IEEE Trans. Inf. Theory, vol.56, pp. 1982-2001,2010.
[33]O. Edfors, M. Sandell, and P. O.Borjesson, "OFDM channel estimation by singular value decomposition,"IEEE Trans. Comm., vol.46, pp.931-939, July 1998.
[34]P. Fertl and G. Matz, "Efficient OFDM channel estimation in mobile environments based on irregular sampling," in Proc. Asilomar Conf. Signals, Systems, Computers, (Pacific Grove, CA), pp.1777-1781, Oct.-Nov.2006.
[35]P. Fertl and G. Matz, "Efficient OFDM channel estimation in mobile environments based on irregular sampling," in Proc. Asilomar Conf. Signals, Systems, Computers, (Pacific Grove, CA), pp.1777-1781, Oct.-Nov.2006.
[36]A. M. Sayeed,A. Sendonaris, and B. Aazhang, "Multiuser detection in fast-fading multipath environment," IEEE J. Select. Areas, vol.16, no.9, pp.1691-1701, December 1998.
[37]D. B. Percival and A. T. Walden, Spectral Analysis for Physical Applications. Cambridge University Press,1963.
[38]J. G. Proakis and D. G. Manolakis, Digital Signal Processing,3rd ed. Prentice-Hall.1996.
[39]Zemen. T.; Mecklenbrauker, C.F. "Time-Variant Channel Equalization via Discrete Prolate Spheroidal Sequences", Conference Record of the Thirty-Seventh Asilomar Conference on,2003. Page(s):1288-1292 Vol.2
[40]D. Slepian. Prolate spheroidal wave functions, Fourier analysis, and uncertainty. V:The discrete case. Bell Systems Tech. J.,57(5):1371-1430.1978.
[41]D. Slepian. Some comments on Fourier analysis, uncertainty, and modeling. SIAM Rev.,25(3):379-393.1983.
|42]D. Slepian and H. Pollak. Prolate spheroidal wave functions, Fourier analysis, and uncertainty. I. Bell Systems Tech. J.,40(1):43-64.1961.
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