Applications of Compressed Sensing in Communications Networks

This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the surprising fact that to recover a signal that is sparse in certain representations, one can sample at the rate far below the Nyquist rate. Since its inception in 2006, CS attracted much interest in the research community and found wide-ranging applications from astronomy, biology, communications, image and video processing, medicine, to radar. CS also found successful applications in communications networks. CS was applied in the detection and estimation of wireless signals, source coding, multi-access channels, data collection in sensor networks, and network monitoring, etc. In many cases, CS was shown to bring performance gains on the order of 10X. We believe this is just the beginning of CS applications in communications networks, and the future will see even more fruitful applications of CS in our field.

[1]  Deanna Needell,et al.  Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit , 2007, Found. Comput. Math..

[2]  R. DeVore,et al.  Nonlinear approximation , 1998, Acta Numerica.

[3]  D. Donoho,et al.  Sparse nonnegative solution of underdetermined linear equations by linear programming. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[4]  S. Muthukrishnan,et al.  Data streams: algorithms and applications , 2005, SODA '03.

[5]  David L. Donoho,et al.  Sparse Solution Of Underdetermined Linear Equations By Stagewise Orthogonal Matching Pursuit , 2006 .

[6]  J. Tropp,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, Commun. ACM.

[7]  Mike E. Davies,et al.  Gradient Pursuits , 2008, IEEE Transactions on Signal Processing.

[8]  R. Vershynin,et al.  One sketch for all: fast algorithms for compressed sensing , 2007, STOC '07.

[9]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[10]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[11]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[12]  I. Daubechies,et al.  Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints , 2007, 0706.4297.

[13]  Sundeep Rangan,et al.  On-Off Random Access Channels: A Compressed Sensing Framework , 2009, ArXiv.

[14]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[15]  Yonina C. Eldar,et al.  Xampling: Analog to digital at sub-Nyquist rates , 2009, IET Circuits Devices Syst..

[16]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[17]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[18]  Andrea Montanari,et al.  Matrix completion from a few entries , 2009, 2009 IEEE International Symposium on Information Theory.

[19]  Sungwon Lee EE-Systems.  Compressed Sensing and Routing in Multi-Hop Networks , 2007 .

[20]  R. Nowak,et al.  Compressed Sensing for Networked Data , 2008, IEEE Signal Processing Magazine.

[21]  Deanna Needell,et al.  Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit , 2007, IEEE Journal of Selected Topics in Signal Processing.

[22]  Yan Zhou,et al.  Experimental Study of MIMO Channel Statistics and Capacity via Virtual Channel Representation , 2006 .

[23]  E.J. Candes.  Compressive Sampling , 2022 .

[24]  Paul Barford,et al.  BasisDetect: a model-based network event detection framework , 2010, IMC '10.

[25]  Mark A. Iwen,et al.  Combinatorial Sublinear-Time Fourier Algorithms , 2010, Found. Comput. Math..

[26]  Mark A. Davenport,et al.  Random Observations on Random Observations: Sparse Signal Acquisition and Processing , 2010 .

[27]  Robert D. Nowak,et al.  Compressed Channel Sensing: A New Approach to Estimating Sparse Multipath Channels , 2010, Proceedings of the IEEE.

[28]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[29]  Yonina C. Eldar,et al.  Structured Compressed Sensing: From Theory to Applications , 2011, IEEE Transactions on Signal Processing.

[30]  Konstantina Papagiannaki,et al.  Structural analysis of network traffic flows , 2004, SIGMETRICS '04/Performance '04.

[31]  Yonina C. Eldar.  Generalized SURE for Exponential Families: Applications to Regularization , 2008, IEEE Transactions on Signal Processing.

[32]  Piotr Indyk,et al.  Sparse Recovery Using Sparse Matrices , 2010, Proceedings of the IEEE.

[33]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[34]  Gene H. Golub,et al.  Matrix computations , 1983 .

[35]  Brian M. Sadler,et al.  Mixed-signal parallel compressed sensing and reception for cognitive radio , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[36]  Massimo Fornasier,et al.  Compressive Sensing , 2015, Handbook of Mathematical Methods in Imaging.

[37]  S. Kirolos,et al.  Analog-to-Information Conversion via Random Demodulation , 2006, 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software.

[38]  Georgios B. Giannakis,et al.  Compressed Sensing for Wideband Cognitive Radios , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[39]  J. Haupt,et al.  Compressive wireless sensing , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[40]  Shengli Zhou,et al.  Sparse channel estimation for multicarrier underwater acoustic communication: From subspace methods to compressed sensing , 2009, OCEANS 2009-EUROPE.

[41]  Matthew Roughan,et al.  Simplifying the synthesis of internet traffic matrices , 2005, CCRV.

[42]  Catherine Rosenberg,et al.  Does Compressed Sensing Improve the Throughput of Wireless Sensor Networks? , 2010, 2010 IEEE International Conference on Communications.

[43]  Wei Wang,et al.  Distributed Sparse Random Projections for Refinable Approximation , 2007, 2007 6th International Symposium on Information Processing in Sensor Networks.

[44]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[45]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[46]  Michele Zorzi,et al.  On the interplay between routing and signal representation for Compressive Sensing in wireless sensor networks , 2009, 2009 Information Theory and Applications Workshop.

[47]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[48]  Robert D. Nowak,et al.  Toeplitz Compressed Sensing Matrices With Applications to Sparse Channel Estimation , 2010, IEEE Transactions on Information Theory.

[49]  Marios Hadjieleftheriou,et al.  Finding the frequent items in streams of data , 2009, CACM.

[50]  R. Coifman,et al.  Diffusion Wavelets , 2004 .

[51]  Zhi Tian,et al.  Compressed Wideband Sensing in Cooperative Cognitive Radio Networks , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[52]  Franz Hlawatsch,et al.  A compressed sensing technique for OFDM channel estimation in mobile environments: Exploiting channel sparsity for reducing pilots , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[53]  G.R. Arce,et al.  Ultra-Wideband Compressed Sensing: Channel Estimation , 2007, IEEE Journal of Selected Topics in Signal Processing.

[54]  Richard G. Baraniuk,et al.  Theory and Implementation of an Analog-to-Information Converter using Random Demodulation , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[55]  Andrea Montanari,et al.  Matrix Completion from Noisy Entries , 2009, J. Mach. Learn. Res..

[56]  Mike E. Davies,et al.  Iterative Hard Thresholding for Compressed Sensing , 2008, ArXiv.

[57]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[58]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[59]  Walter Willinger,et al.  Spatio-temporal compressive sensing and internet traffic matrices , 2009, SIGCOMM '09.

[60]  Mani B. Srivastava,et al.  Compressive Oversampling for Robust Data Transmission in Sensor Networks , 2010, 2010 Proceedings IEEE INFOCOM.

[61]  Shiqian Ma,et al.  Fixed point and Bregman iterative methods for matrix rank minimization , 2009, Math. Program..

[62]  Jun Sun,et al.  Compressive data gathering for large-scale wireless sensor networks , 2009, MobiCom '09.

[63]  Michael G. Rabbat,et al.  Compressed network monitoring for ip and all-optical networks , 2007, IMC '07.

[64]  Akbar M. Sayeed,et al.  Deconstructing multiantenna fading channels , 2002, IEEE Trans. Signal Process..

[65]  Guangming Shi,et al.  UWB Echo Signal Detection With Ultra-Low Rate Sampling Based on Compressed Sensing , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[66]  M. Rabbat,et al.  Decentralized compression and predistribution via randomized gossiping , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[67]  Akbar M. Sayeed,et al.  A virtual representation for time- and frequency-selective correlated MIMO channels , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[68]  Justin Romberg,et al.  Practical Signal Recovery from Random Projections , 2005 .

[69]  R.G. Baraniuk,et al.  Universal distributed sensing via random projections , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[70]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[71]  Xuefeng Yin,et al.  Cluster Characteristics in a MIMO Indoor Propagation Environment , 2007, IEEE Transactions on Wireless Communications.

[72]  Dima Grigoriev,et al.  Complexity of Quantifier Elimination in the Theory of Algebraically Closed Fields , 1984, MFCS.

[73]  Ronald L. Graham,et al.  The Mathematics of Paul Erdős II , 1997 .

[74]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[75]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[76]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[77]  Mohammad Hamed Firooz,et al.  Network Tomography via Compressed Sensing , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[78]  Yonina C. Eldar,et al.  Rank Awareness in Joint Sparse Recovery , 2010, IEEE Transactions on Information Theory.

[79]  Yonina C. Eldar,et al.  Introduction to Compressed Sensing , 2022 .

[80]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[81]  Emmanuel J. Candès,et al.  The Power of Convex Relaxation: Near-Optimal Matrix Completion , 2009, IEEE Transactions on Information Theory.

[82]  R. DeVore,et al.  Compressed sensing and best k-term approximation , 2008 .

[83]  Thomas Strohmer,et al.  GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION , 2003, math/0301135.

[84]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[85]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[86]  Antonio Ortega,et al.  Spatially-Localized Compressed Sensing and Routing in Multi-hop Sensor Networks , 2009, GSN.