Abstract
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.
Similar content being viewed by others
References
Richards, M.A., Scheer, J., Holm, W.A.: Principles of Modern Radar: Basic Principles. SciTech Pub., New York (2010)
Skolnik, M.I.: Introduction to Radar. McGraw-Hill, New York (2002)
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)
Candes, E., Romberg, J.: Sparsity and incoherence in compressive sampling. Inverse Probl. 23, 969 (2007)
Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
Herman, M., Strohmer, T.: High-resolution radar via compressed sensing. IEEE Trans. Signal Process. 57(6), 2275–2284 (2009)
Candès, E., Wakin, M.: An introduction to compressive sampling. IEEE Signal Process. Mag. 25(2), 21–30 (2008)
Baraniuk, R.: Compressive sensing [lecture notes]. IEEE Signal Process. Mag. 24(4), 118–121 (2007)
Eldar, Y.C., Kutyniok, G.: Compressed Sensing: Theory and Applications. Cambridge University Press, Cambridge (2012)
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)
Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)
Needell, D., Tropp, J.A.: Cosamp: Iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)
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)
Ji, S., Xue, Y., Carin, L.: Bayesian compressive sensing. IEEE Trans. Signal Process. 56(6), 2346–2356 (2008)
Pope, G.: Compressive Sensing: A Summary of Reconstruction Algorithms. Master’s thesis, ETH, Swiss Federal Institute of Technology Zurich, Department of Computer Science (2009)
Chen, S., Donoho, D., Saunders, M.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)
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)
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)
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)
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)
Godrich, H., Haimovich, A., Blum, R.: Target localization accuracy gain in mimo radar-based systems. IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010)
Dai, W., Milenkovic, O.: Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans. Inf. Theory 55(5), 2230–2249 (2009)
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)
Blumensath, T., Davies, M.E.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009)
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)
Donoho, D.L., Maleki, A., Montanari, A.: Message-passing algorithms for compressed sensing. Proc. Natl. Acad. Sci. 106(45), 18 914–18 919 (2009)
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)
Ji, S., Dunson, D., Carin, L.: Multitask compressive sensing. IEEE Trans. Signal Process. 57(1), 92–106 (2009)
Schniter, P., Potter, L.C., Ziniel, J.: Fast bayesian matching pursuit. In: Information Theory and Applications Workshop IEEE, pp. 326–333 (2008)
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)
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)
Bar-Ilan, O., Eldar, Y.C.: Sub-nyquist radar via doppler focusing. IEEE Trans. Signal Process. 62, 1796–1811 (2012)
Potter, L., Ertin, E., Parker, J., Cetin, M.: Sparsity and compressed sensing in radar imaging. Proc. IEEE 98(6), 1006–1020 (2010)
Grant, M., Boyd. S.: Cvx: Matlab Software for Disciplined Convex Programming, version 2.0 beta. (2013, September) [Online]. Available: http://cvxr.com/cvx
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)
Ender, J.: On compressive sensing applied to radar. Signal Process. 90(5), 1402–1414 (2010)
Pfander, G.E., Rauhut, H.: Sparsity in time–frequency representations. J. Fourier Anal. Appl. 16(2), 233–260 (2010)
Gröchenig, K.: Foundations of Time–Frequency Analysis. Springer, New York (2001)
Baraniuk, R., Steeghs, P.: Compressive radar imaging. In: IEEE Radar Conference, pp. 128–133 (2007)
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)
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)
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)
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)
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)
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)
Zegov, L., Pribic, R., Leus, G.: Optimal waveforms for compressive sensing radar. In: 21st IEEE European Signal Processing Conference (EUSIPCO), pp. 1–5 (2013)
Chi, Y., Calderbank, R., Pezeshki, A.: Golay complementary waveforms for sparse delay-doppler radar imaging. In: 3rd IEEE-CAMSAP, pp. 177–180 (2009)
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)
Wehner, D.R.: High Resolution Radar, vol. 1. Artech House Inc., Norwood (1987)
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)
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)
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)
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)
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)
Gurbuz, A., Cevher, V., Mcclellan, J.: Bearing estimation via spatial sparsity using compressive sensing. IEEE Trans. Aerosp. Electron. Syst. 48(2), 1358–1369 (2012)
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)
Lyubomir Zegovy, G.L., Pribic, Radmila: optimal waveforms for compressive sensing radar. In: 21st European Signal Processing Conference(EUSIPCO) (2013)
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)
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)
Sarkas, I.: Step Frequency Radar using Compressed Sensing. Department of Mathematics of the University of Toronto. Tech, Rep. (2010)
Gandhi, P.P., Kassam, S.A.: Analysis of cfar processors in homogeneous background. IEEE Trans. Aerosp. Electron. Syst. 24(4), 427–445 (1988)
Anitori, L., Otten, M., Hoogeboom, P.: Detection performance of compressive sensing applied to radar. In: IEEE Radar Conference, pp. 200–205 (2011)
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)
Li, J., Stoica, P.: Mimo radar with colocated antennas. IEEE Signal Process. Mag. 24(5), 106–114 (2007)
Haimovich, A., Blum, R., Cimini, L.: Mimo radar with widely separated antennas. IEEE Signal Process. Mag. 25(1), 116–129 (2008)
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)
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)
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)
Strohmer, T., Wang, H.: Accurate imaging of moving targets via random sensor arrays and kerdock codes. Inverse Probl. 29(8), 085001 (2013)
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)
Yu, T., Gong, Z., De, B.: Joint sparse modeling for target parameter estimation in distributed mimo radar. IET International Radar Conference (2013)
Chen, C., Vaidyanathan, P.: Compressed sensing in mimo radar. In: 42nd IEEE Asilomar Conference on Signals, Systems and Computers, pp. 41–44 (2008)
Strohmer, T., Friedlander, B.: Analysis of sparse mimo radar. Appl. Comput. Harmon. Anal. 37(3), 361–388 (2014)
Friedlander, B.: Waveform design for mimo radars. IEEE Trans. Aerosp. Electron. Syst. 43(3), 1227–1238 (2007)
Gogineni, S., Nehorai, A.: Target estimation using sparse modeling for distributed mimo radar. IEEE Trans. Signal Process. 59(11), 5315–5325 (2011)
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)
Stoica, P., Li, J., Xue, M.: Transmit codes and receive filters for radar. IEEE Signal Process. Mag. 25(6), 94–109 (2008)
Hyder, M., Mahata, K.: An improved smoothed l0 approximation algorithm for sparse representation. IEEE Trans. Signal Process. 58(4), 2194–2205 (2010)
Tian, Z., Blasch, E.: Compressed sensing for mimo radar: a stochastic perspective. In: IEEE Statistical Signal Processing Workshop (SSP), pp. 548–551 (2012)
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)
Yu, Y., Petropulu, A., Poor, H.: Mimo radar using compressive sampling. IEEE J. Sel. Top. Signal Process. 4(1), 146–163 (2010)
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)
Minner, M.: On-grid mimo radar via compressive sensing. In: 2nd International Workshop on Compressed Sensing applied to Radar (CoSeRa), Bonn (2013)
Gogineni, S., Nehorai, A.: Adaptive waveform design for colocated mimo radar using sparse modeling. In: 4th IEEE-CAMSAP, pp. 13–16 (2011)
Fannjiang, A., Tseng, H.-C.: Compressive radar with off-grid targets: a perturbation approach. Inverse Probl. 29(5), 054008 (2013)
Chi, Y., Scharf, L., Pezeshki, A., Calderbank, A.: Sensitivity to basis mismatch in compressed sensing. IEEE Trans. Signal Process. 59(5), 2182–2195 (2011)
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)
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)
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)
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)
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)
Zhang, B., Hong, W., Wu, Y.: Sparse microwave imaging: principles and applications. Sci. China Inf. Sci. 55(8), 1722–1754 (2012)
Massa, A., Rocca, P., Oliveri, G.: Compressive sensing in electromagnetics-a review. IEEE Antennas Propag. Mag. 57(1), 224–238 (2015)
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hadi, M.A., Alshebeili, S., Jamil, K. et al. Compressive sensing applied to radar systems: an overview. SIViP 9 (Suppl 1), 25–39 (2015). https://doi.org/10.1007/s11760-015-0824-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-015-0824-y