Signal, Image and Video Processing

, Volume 9, Supplement 1, pp 25–39 | Cite as

Compressive sensing applied to radar systems: an overview

  • Muhammad Abdul HadiEmail author
  • Saleh Alshebeili
  • Khalid Jamil
  • Fathi E. Abd El-Samie
Original Paper


Modern radar systems tend to utilize high bandwidth, which requires high sampling rate, and in many cases, these systems involve phased array configurations with a large number of transmit–receive elements. In contrast, the ultimate goal of a radar system is often to estimate only a limited number of target parameters. Thus, there is a pursuit to find better means to perform the radar signal acquisition as well as processing with much reduced amount of data and power requirement. Recently, there has been a great interest to consider compressive sensing (CS) for radar system design; CS is a novel technique which offers the framework for sparse signal detection and estimation for optimized data handling. In radars, CS enables the achievement of better range-Doppler resolution in comparison with the traditional techniques. However, CS requires the selection of suitable (sparse) signal model, the design of measurement system as well as the implementation of appropriate signal recovery method. This work attempts to present an overview of these CS aspects, particularly when CS is applied in monostatic pulse-Doppler and MIMO type of radars. Some of the associated challenges, e.g., grid mismatch and detector design issues, are also discussed.


Compressive sensing Radar Convex optimization  Sparsity 



The authors would like to acknowledge the support of KACST—Technology Innovation Center in RF and Photonics for the e-Society (RFTONICS), Riyadh, Saudi Arabia.


  1. 1.
    Richards, M.A., Scheer, J., Holm, W.A.: Principles of Modern Radar: Basic Principles. SciTech Pub., New York (2010)Google Scholar
  2. 2.
    Skolnik, M.I.: Introduction to Radar. McGraw-Hill, New York (2002)Google Scholar
  3. 3.
    Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)zbMATHCrossRefGoogle Scholar
  4. 4.
    Candes, E., Romberg, J.: Sparsity and incoherence in compressive sampling. Inverse Probl. 23, 969 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Herman, M., Strohmer, T.: High-resolution radar via compressed sensing. IEEE Trans. Signal Process. 57(6), 2275–2284 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Candès, E., Wakin, M.: An introduction to compressive sampling. IEEE Signal Process. Mag. 25(2), 21–30 (2008)CrossRefGoogle Scholar
  8. 8.
    Baraniuk, R.: Compressive sensing [lecture notes]. IEEE Signal Process. Mag. 24(4), 118–121 (2007)CrossRefGoogle Scholar
  9. 9.
    Eldar, Y.C., Kutyniok, G.: Compressed Sensing: Theory and Applications. Cambridge University Press, Cambridge (2012)CrossRefGoogle Scholar
  10. 10.
    Baraniuk, R., Davenport, M., DeVore, R., Wakin, M.: A simple proof of the restricted isometry property for random matrices. Constr. Approx. 28(3), 253–263 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Needell, D., Tropp, J.A.: Cosamp: Iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Needell, D., Vershynin, R.: Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE J. Sel. Top. Signal. Process. 4(2), 310–316 (2010)CrossRefGoogle Scholar
  14. 14.
    Ji, S., Xue, Y., Carin, L.: Bayesian compressive sensing. IEEE Trans. Signal Process. 56(6), 2346–2356 (2008)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Pope, G.: Compressive Sensing: A Summary of Reconstruction Algorithms. Master’s thesis, ETH, Swiss Federal Institute of Technology Zurich, Department of Computer Science (2009)Google Scholar
  16. 16.
    Chen, S., Donoho, D., Saunders, M.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)Google Scholar
  17. 17.
    Petropulu, A.P., Yu, Y., Huang, J.: On exploring sparsity in widely separated mimo radar. In: 45th Asilomar Conference on Signals, Systems and Computers IEEE, pp. 1496–1500 (2011)Google Scholar
  18. 18.
    Yap, H.L., Pribic, R.: False alarms in multi-target radar detection within a sparsity framework. In: International Radar Conference IEEE, pp. 1–6 (2014)Google Scholar
  19. 19.
    Baransky, E., Itzhak, G., Shmuel, I., Wagner, N., Shoshan, E., Eldar, Y.: A sub-nyquist radar prototype: hardware and algorithms. IEEE Trans. Aerosp. Electron. Syst. 2, 809–822 (2014)CrossRefGoogle Scholar
  20. 20.
    Gogineni, S., Nehorai, A.: Sparsity-based mimo noise radar for multiple target estimation. In: IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 33–36 (2012)Google Scholar
  21. 21.
    Godrich, H., Haimovich, A., Blum, R.: Target localization accuracy gain in mimo radar-based systems. IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Dai, W., Milenkovic, O.: Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans. Inf. Theory 55(5), 2230–2249 (2009)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Huang, T., Liu, Y., Meng, H., Wang, X.: Cognitive random stepped frequency radar with sparse recovery. IEEE Trans. Aerosp. Electron. Syst. 50, 858–870 (2014)CrossRefGoogle Scholar
  24. 24.
    Blumensath, T., Davies, M.E.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  25. 25.
    Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)zbMATHCrossRefGoogle Scholar
  26. 26.
    Donoho, D.L., Maleki, A., Montanari, A.: Message-passing algorithms for compressed sensing. Proc. Natl. Acad. Sci. 106(45), 18 914–18 919 (2009)CrossRefGoogle Scholar
  27. 27.
    Anitori, L., Maleki, A., Otten, M., Baraniuk, R.G., Hoogeboom, P.: Design and analysis of compressed sensing radar detectors. IEEE Trans. Signal Process. 61(4), 813–827 (2013)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Ji, S., Dunson, D., Carin, L.: Multitask compressive sensing. IEEE Trans. Signal Process. 57(1), 92–106 (2009)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Schniter, P., Potter, L.C., Ziniel, J.: Fast bayesian matching pursuit. In: Information Theory and Applications Workshop IEEE, pp. 326–333 (2008)Google Scholar
  30. 30.
    Shen, F., Zhao, G., Shi, G., Jin, D.: Compressed sensing based ultra-wideband radar system. In: IEEE CIE International Conference on Radar, vol. 2, pp. 1850–1853 (2011)Google Scholar
  31. 31.
    Bellasi, D.E., Bettini, L., Benkeser, C., Burger, T., Huang, Q., Studer, C.: Vlsi design of a monolithic compressive-sensing wideband analog-to-information converter. IEEE J. Emerg. Sel. Top. Circuits Syst. 3(4), 552–565 (2013)CrossRefGoogle Scholar
  32. 32.
    Bar-Ilan, O., Eldar, Y.C.: Sub-nyquist radar via doppler focusing. IEEE Trans. Signal Process. 62, 1796–1811 (2012)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Potter, L., Ertin, E., Parker, J., Cetin, M.: Sparsity and compressed sensing in radar imaging. Proc. IEEE 98(6), 1006–1020 (2010)CrossRefGoogle Scholar
  34. 34.
    Grant, M., Boyd. S.: Cvx: Matlab Software for Disciplined Convex Programming, version 2.0 beta. (2013, September) [Online]. Available:
  35. 35.
    Teke, O., Gurbuz, A.C., Arikan, O.: A robust compressive sensing based technique for reconstruction of sparse radar scenes. Digit. Signal Process. 27, 23–32 (2014)CrossRefGoogle Scholar
  36. 36.
    Ender, J.: On compressive sensing applied to radar. Signal Process. 90(5), 1402–1414 (2010)zbMATHCrossRefGoogle Scholar
  37. 37.
    Pfander, G.E., Rauhut, H.: Sparsity in time–frequency representations. J. Fourier Anal. Appl. 16(2), 233–260 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  38. 38.
    Gröchenig, K.: Foundations of Time–Frequency Analysis. Springer, New York (2001)zbMATHCrossRefGoogle Scholar
  39. 39.
    Baraniuk, R., Steeghs, P.: Compressive radar imaging. In: IEEE Radar Conference, pp. 128–133 (2007)Google Scholar
  40. 40.
    Shi, G., Lin, J., Chen, X., Qi, F., Liu, D., Zhang, L.: Uwb echo signal detection with ultra-low rate sampling based on compressed sensing. IEEE Trans. Circuits Syst. II Express Briefs 55(4), 379–383 (2008)CrossRefGoogle Scholar
  41. 41.
    Ertin, E., Potter, L., Moses, R.: Sparse target recovery performance of multi-frequency chirp waveforms. In: 19th European Signal Processing Conference (EUSIPCO), pp. 446–450 (2011)Google Scholar
  42. 42.
    Whitelonis, N., Ling, H.: Radar signature analysis using a joint time–frequency distribution based on compressed sensing. IEEE Trans. Antennas Propag. 62(2), 755–763 (2014)CrossRefGoogle Scholar
  43. 43.
    Smith, G., Diethe, T., Hussain, Z., Shawe-Taylor, J., Hardoon, D.: Compressed sampling for pulse doppler radar. In: IEEE Radar Conference, pp. 887–892 (2010)Google Scholar
  44. 44.
    Rilling, G., Davies, M., Mulgrew, B.: Compressed sensing based compression of sar raw data. In: SPARS’09-Signal Processing with Adaptive Sparse Structured Representations (2009)Google Scholar
  45. 45.
    Song, X., Zhou, S., Willett, P.: The role of the ambiguity function in compressed sensing radar. In: 35th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2758–2761 (2010)Google Scholar
  46. 46.
    Zegov, L., Pribic, R., Leus, G.: Optimal waveforms for compressive sensing radar. In: 21st IEEE European Signal Processing Conference (EUSIPCO), pp. 1–5 (2013)Google Scholar
  47. 47.
    Chi, Y., Calderbank, R., Pezeshki, A.: Golay complementary waveforms for sparse delay-doppler radar imaging. In: 3rd IEEE-CAMSAP, pp. 177–180 (2009)Google Scholar
  48. 48.
    Stoica, P., He, H., Li, J.: New algorithms for designing unimodular sequences with good correlation properties. IEEE Trans. Signal Process. 57(4), 1415–1425 (2009)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Wehner, D.R.: High Resolution Radar, vol. 1. Artech House Inc., Norwood (1987)Google Scholar
  50. 50.
    Shah, S., Yu, Y., Petropulu, A.: Step-frequency radar with compressive sampling (sfr-cs). In: 35th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1686–1689 (2010)Google Scholar
  51. 51.
    Xu, L., Liang, Q.: Compressive sensing in radar sensor networks using pulse compression waveforms. In: IEE ICC Ad-hoc and sensor Networking Symposium IEEE, pp. 794–798 (2012)Google Scholar
  52. 52.
    Zhiping, Y., Hao, X., Weidong, C.: A new hybrid-frequency radar system based on compressed sensing theory. In: International Conference on Microwave and Millimeter Wave Technology (ICMMT) IEEE, pp. 1731–1734 (2010)Google Scholar
  53. 53.
    Huang, T., Liu, Y., Meng, H., Wang, X.: Randomized step frequency radar with adaptive compressed sensing. In: IEEE Radar Conference IEEE, pp. 411–414 (2011)Google Scholar
  54. 54.
    Anitori, L., Hoogeboom, P., LeChevalier, F., Otten, M.: Compressive sensing for high resolution profiles with enhanced doppler performance. In: 9th IEEE European Radar Conference (EuRAD), pp. 107–110 (2012)Google Scholar
  55. 55.
    Gurbuz, A., Cevher, V., Mcclellan, J.: Bearing estimation via spatial sparsity using compressive sensing. IEEE Trans. Aerosp. Electron. Syst. 48(2), 1358–1369 (2012)CrossRefGoogle Scholar
  56. 56.
    Wei, W., Yipeng, D., Xin, X., Wenpeng, W., Qunying, Z., Guangyou, F.: The applying of compressed sensing in m-sequence uwb radar. In: First IEEE IC-IMCCC, pp. 708–711 (2011)Google Scholar
  57. 57.
    Lyubomir Zegovy, G.L., Pribic, Radmila: optimal waveforms for compressive sensing radar. In: 21st European Signal Processing Conference(EUSIPCO) (2013)Google Scholar
  58. 58.
    Krichene, H., Pekala, M., Sharp, M., Lauritzen, K., Lucarelli, D., Wang, I.: Compressive sensing and stretch processing. In: IEEE Radar Conference, pp. 362–367 (2011)Google Scholar
  59. 59.
    Kyriakides, I.: Ambiguity functions of compressively sensed and processed radar waveforms. In: 36th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4256–4259 (2011)Google Scholar
  60. 60.
    Sarkas, I.: Step Frequency Radar using Compressed Sensing. Department of Mathematics of the University of Toronto. Tech, Rep. (2010)Google Scholar
  61. 61.
    Gandhi, P.P., Kassam, S.A.: Analysis of cfar processors in homogeneous background. IEEE Trans. Aerosp. Electron. Syst. 24(4), 427–445 (1988)CrossRefGoogle Scholar
  62. 62.
    Anitori, L., Otten, M., Hoogeboom, P.: Detection performance of compressive sensing applied to radar. In: IEEE Radar Conference, pp. 200–205 (2011)Google Scholar
  63. 63.
    Maleki, A., Anitori, L., Yang, Z., Baraniuk, R.: Asymptotic analysis of complex lasso via complex approximate message passing (camp). IEEE Trans. Inf. Theory 59(7), 4290–4308 (2013)MathSciNetCrossRefGoogle Scholar
  64. 64.
    Li, J., Stoica, P.: Mimo radar with colocated antennas. IEEE Signal Process. Mag. 24(5), 106–114 (2007)CrossRefGoogle Scholar
  65. 65.
    Haimovich, A., Blum, R., Cimini, L.: Mimo radar with widely separated antennas. IEEE Signal Process. Mag. 25(1), 116–129 (2008)CrossRefGoogle Scholar
  66. 66.
    Yu, Y., Petropulu, A., Poor, H.: Compressive sensing for mimo radar. In: 34th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3017–3020 (2009)Google Scholar
  67. 67.
    Zhu, F., Zhang, Q., Lei, Q., Luo, Y.: Reconstruction of moving target’s HRRP using sparse frequency-stepped chirp signal. IEEE Sens. J. 11(10), 2327–2334 (2011)CrossRefGoogle Scholar
  68. 68.
    Zhu, F., Zhang, Q., Xiang, Y., Feng, Y.: Compressive sensing in isar spectrogram data transmission. In: 2nd IEEE Asian-Pacific Conference on Synthetic Aperture Radar (APSAR), pp. 89–92 (2009)Google Scholar
  69. 69.
    Strohmer, T., Wang, H.: Accurate imaging of moving targets via random sensor arrays and kerdock codes. Inverse Probl. 29(8), 085001 (2013)MathSciNetCrossRefGoogle Scholar
  70. 70.
    Hyder, M., Mahata, K.: A joint sparse signal representation perspective for target detection using bistatic mimo radar system. In: 17th IEEE International Conference on Digital Signal Processing (DSP), pp. 1–5 (2011)Google Scholar
  71. 71.
    Yu, T., Gong, Z., De, B.: Joint sparse modeling for target parameter estimation in distributed mimo radar. IET International Radar Conference (2013)Google Scholar
  72. 72.
    Chen, C., Vaidyanathan, P.: Compressed sensing in mimo radar. In: 42nd IEEE Asilomar Conference on Signals, Systems and Computers, pp. 41–44 (2008)Google Scholar
  73. 73.
    Strohmer, T., Friedlander, B.: Analysis of sparse mimo radar. Appl. Comput. Harmon. Anal. 37(3), 361–388 (2014)zbMATHMathSciNetCrossRefGoogle Scholar
  74. 74.
    Friedlander, B.: Waveform design for mimo radars. IEEE Trans. Aerosp. Electron. Syst. 43(3), 1227–1238 (2007)CrossRefGoogle Scholar
  75. 75.
    Gogineni, S., Nehorai, A.: Target estimation using sparse modeling for distributed mimo radar. IEEE Trans. Signal Process. 59(11), 5315–5325 (2011)MathSciNetCrossRefGoogle Scholar
  76. 76.
    Yu, Y., Sun, S., Madan, R.N., Petropulu, A.: Power allocation and waveform design for the compressive sensing based mimo radar. IEEE Trans. Aerosp. Electron. Syst. 50(2), 898–909 (2014)CrossRefGoogle Scholar
  77. 77.
    Stoica, P., Li, J., Xue, M.: Transmit codes and receive filters for radar. IEEE Signal Process. Mag. 25(6), 94–109 (2008)CrossRefGoogle Scholar
  78. 78.
    Hyder, M., Mahata, K.: An improved smoothed l0 approximation algorithm for sparse representation. IEEE Trans. Signal Process. 58(4), 2194–2205 (2010)MathSciNetCrossRefGoogle Scholar
  79. 79.
    Tian, Z., Blasch, E.: Compressed sensing for mimo radar: a stochastic perspective. In: IEEE Statistical Signal Processing Workshop (SSP), pp. 548–551 (2012)Google Scholar
  80. 80.
    Hadi, M., AlShebeili, S., El-Samie, F., Jamil, K.: Compressive sensing for improved mimo radar performance: a review. In: International Conference on Information and Communication Technology Research (ICTRC), Dubai, UAE, pp. 270–273 (2015)Google Scholar
  81. 81.
    Yu, Y., Petropulu, A., Poor, H.: Mimo radar using compressive sampling. IEEE J. Sel. Top. Signal Process. 4(1), 146–163 (2010)CrossRefGoogle Scholar
  82. 82.
    He, X., Liu, C., Liu, B., Wang, D.: Sparse frequency diverse mimo radar imaging for off-grid target based on adaptive iterative map. Remote Sens. 5(2), 631–647 (2013)CrossRefGoogle Scholar
  83. 83.
    Minner, M.: On-grid mimo radar via compressive sensing. In: 2nd International Workshop on Compressed Sensing applied to Radar (CoSeRa), Bonn (2013)Google Scholar
  84. 84.
    Gogineni, S., Nehorai, A.: Adaptive waveform design for colocated mimo radar using sparse modeling. In: 4th IEEE-CAMSAP, pp. 13–16 (2011)Google Scholar
  85. 85.
    Fannjiang, A., Tseng, H.-C.: Compressive radar with off-grid targets: a perturbation approach. Inverse Probl. 29(5), 054008 (2013)CrossRefGoogle Scholar
  86. 86.
    Chi, Y., Scharf, L., Pezeshki, A., Calderbank, A.: Sensitivity to basis mismatch in compressed sensing. IEEE Trans. Signal Process. 59(5), 2182–2195 (2011)MathSciNetCrossRefGoogle Scholar
  87. 87.
    Chae, D.H., Sadeghi, P., Kennedy, R.A.: Effects of basis-mismatch in compressive sampling of continuous sinusoidal signals. In: 2nd IEEE International Conference on Future Computer and Communication (ICFCC), vol. 2, pp. 739–743 (2010)Google Scholar
  88. 88.
    Yang, Z., Zhang, C., Xie, L.: Robustly stable signal recovery in compressed sensing with structured matrix perturbation. IEEE Trans. Signal Process. 60(9), 4658–4671 (2012)MathSciNetCrossRefGoogle Scholar
  89. 89.
    Ekanadham, C., Tranchina, D., Simoncelli, E.P.: Recovery of sparse translation-invariant signals with continuous basis pursuit. IEEE Trans. Signal Process. 59(10), 4735–4744 (2011)MathSciNetCrossRefGoogle Scholar
  90. 90.
    Zhu, H., Leus, G., Giannakis, G.B.: Sparsity-cognizant total least-squares for perturbed compressive sampling. IEEE Trans. Signal Process. 59(5), 2002–2016 (2011)MathSciNetCrossRefGoogle Scholar
  91. 91.
    Huang, T., Liu, Y., Meng, H., Wang, X.: Adaptive matching pursuit with constrained total least squares. EURASIP J. Adv. Signal Process. 2012(1), 1–12 (2012)CrossRefGoogle Scholar
  92. 92.
    Zhang, B., Hong, W., Wu, Y.: Sparse microwave imaging: principles and applications. Sci. China Inf. Sci. 55(8), 1722–1754 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  93. 93.
    Massa, A., Rocca, P., Oliveri, G.: Compressive sensing in electromagnetics-a review. IEEE Antennas Propag. Mag. 57(1), 224–238 (2015)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Muhammad Abdul Hadi
    • 1
    Email author
  • Saleh Alshebeili
    • 2
    • 3
  • Khalid Jamil
    • 4
  • Fathi E. Abd El-Samie
    • 3
  1. 1.Prince Sultan Advanced Technology Research Institute (PSATRI)King Saud University (KSU)RiyadhSaudi Arabia
  2. 2.Department of Electrical EngineeringKSURiyadhSaudi Arabia
  3. 3.KACST - Technology Innovation Center in RF and Photonics for the e-Society (RFTONICS)RiyadhSaudi Arabia
  4. 4.PSATRIKSURiyadhSaudi Arabia

Personalised recommendations