SCIENCE CHINA Information Sciences, Volume 60, Issue 10: 102307(2017) https://doi.org/10.1007/s11432-016-9003-9

Circulate shifted OFDM chirp waveform diversity design with digital beamforming for MIMO SAR

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  • ReceivedNov 29, 2016
  • AcceptedDec 29, 2016
  • PublishedJun 20, 2017


Waveform diversity design has always been the key to multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) systems, and it is known that synthetic integral side lobe ratio (SISLR) is a more optimal indicator than the integral side lobe ratio (ISLR) to evaluate the orthogonality between different MIMO SAR waveforms. This paper presents proof that it is difficult to obtain the SISLR of an existing waveform such that it is sufficiently low to achieve high SNR for SAR imaging. Thus, it is necessary to find a way to separate these MIMO SAR waveforms in other domains, for example, a spatial domain by digital beamforming (DBF). Learning from Krieger's idea of short-term shift-orthogonal waveforms and using joint time-frequency transforms (Gabor transform) to prove that for most existing SAR waveforms cyclic shift is a good operation with which to generate short-term shift-orthogonal waveforms. This paper presents the designs of four circulate shifted OFDM chirp waveforms, which have a much lower SISLR and retain all the advantages of the classical chirp waveform such as a large time-bandwidth product, constant amplitude, implementation simplicity, and good Doppler tolerance.


This work was supported in part by National Natural Science Foundation of China (Grant No. 61331015). The authors would like to thank the anonymous reviewers for their valuable comments, time, and suggestions to improve the quality of this paper.


[1] Krieger G. MIMO-SAR: Opportunities and Pitfalls. IEEE Trans Geosci Remote Sens, 2014, 52: 2628-2645 CrossRef ADS Google Scholar

[2] Zou B, Dong Z, Liang D N. Design and performance analysis of orthogonal coding signal in MIMO-SAR. Sci China Inf Sci, 2011, 54: 1723-1737 CrossRef Google Scholar

[3] Zhenfang Li , Zheng Bao , Hongyang Wang . Performance improvement for constellation SAR using signal processing techniques. IEEE Trans Aerosp Electron Syst, 2006, 42: 436-452 CrossRef ADS Google Scholar

[4] Wang J, Liang X D, Chen L Y. MIMO SAR system using digital implemented OFDM waveforms. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium, Munich, 2012. 7428--7431. Google Scholar

[5] Freeman A, Krieger G, Rosen P, et al. SweepSAR: Beam-forming on receive using a reflector-phased array feed combination for spaceborne SAR. In: Proceedings of IEEE Radar Conference, Pasadena, 2009. 1--9. Google Scholar

[6] Wang J, Chen L Y, Liang X D. Implementation of the OFDM Chirp Waveform on MIMO SAR Systems. IEEE Trans Geosci Remote Sens, 2015, 53: 5218-5228 CrossRef ADS Google Scholar

[7] Kim J H, Younis M, Moreira A. Spaceborne MIMO Synthetic Aperture Radar for Multimodal Operation. IEEE Trans Geosci Remote Sens, 2015, 53: 2453-2466 CrossRef ADS Google Scholar

[8] Krieger G, Gebert N, Moreira A. Multidimensional Waveform Encoding: A New Digital Beamforming Technique for Synthetic Aperture Radar Remote Sensing. IEEE Trans Geosci Remote Sens, 2008, 46: 31-46 CrossRef ADS Google Scholar

[9] Krieger G, Gebert N, Moreira A. High resolution synthetic aperture side view radar system used by means of digital beamforming (in German). German Patent, DE502007007062. Google Scholar

[10] Krieger G, Gebert N, Moreira A. Digital beamforming techniques for spaceborne radar remote sensing. In: Proceedings of European Conference on Synthetic Aperture Radar (EUSAR), Dresden, 2006. Google Scholar

[11] Krieger G, Moreira A. Potentials of digital beamforming in bi- and multistatic SAR. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium, Toulouse, 2006. 527--529. Google Scholar

[12] Born M, Wolf E. Principles of Optics. 7th ed. Cambridge: Cambridge University Press, 1999. Google Scholar

[13] Papoulis A. Signal Analysis. New York: McGraw-Hill, 1977. Google Scholar

[14] Skolnik M I. Radar Handbook. 3rd ed. New York: McGraw-Hill, 2008. Google Scholar

[15] Key E L, Fowle E N, Haggarty R D. A method of designing signals of large time-bandwidth product. IRE Int Conv Record, 1961, 146--154. Google Scholar

[16] Curlander J C, McDonough R N. Synthetic Aperture Radar: Systems and Signal Processing. New York: Wiley, 1991. Google Scholar

[17] Wen-Qin Wang . MIMO SAR Chirp Modulation Diversity Waveform Design. IEEE Geosci Remote Sens Lett, 2014, 11: 1644-1648 CrossRef ADS Google Scholar

[18] Wang W Q. MIMO SAR OFDM Chirp Waveform Diversity Design With Random Matrix Modulation. IEEE Trans Geosci Remote Sens, 2015, 53: 1615-1625 CrossRef ADS Google Scholar

[19] Tianxian Zhang , Xiang-Gen Xia . OFDM Synthetic Aperture Radar Imaging With Sufficient Cyclic Prefix. IEEE Trans Geosci Remote Sens, 2015, 53: 394-404 CrossRef ADS Google Scholar

[20] Gabor D. Theory of communication. J IEE (London), 1946, 93: 429--457. Google Scholar

[21] Chen V C, Ling H. Time-frequency Transforms for Radar Imaging and Signal Analysis. Norwood: Artech House, 2002. Google Scholar

[22] Sen S. PAPR-Constrained Pareto-Optimal Waveform Design for OFDM-STAP Radar. IEEE Trans Geosci Remote Sens, 2014, 52: 3658-3669 CrossRef ADS Google Scholar

[23] Kauffman K, Raquet J, Morton Y. Real-Time UWB-OFDM Radar-Based Navigation in Unknown Terrain. IEEE Trans Aerosp Electron Syst, 2013, 49: 1453-1466 CrossRef ADS Google Scholar

  • Figure 1

    (Color online) Schematic diagram of SISLR.

  • Figure 2

    (Color online) Frequency spectrum of typical MIMO SAR waveform.

  • Figure 3

    Time-frequency diagram of circulate shifted OFDM chirp waveform set.

  • Figure 4

    (Color online) Comparative autocorrelation and cross-correlation of the four waveforms. (a) Waveforms 1 and 2; (b) waveforms 1 and 3; (c) waveforms 1 and 4; (d) waveforms 2 and 3; (e) waveforms 2 and 4; (f) waveforms 3 and 4.

  • Figure 5

    (Color online) Ambiguity functions and their zero-Doppler and zero-delay “cuts”. (a)–(c) Waveforms 1; (d)–(f) waveforms 2; (g)–(i) waveforms 3; (j)–(l) waveforms 4.

  • Figure 6

    (Color online) Point-target simulations for the proposed waveforms. (a) Simulation result of waveform 1; protectłinebreak(b) range profiles of the simulation results shown in (a).

  • Table 1   ${E_{{C_{p,q}}}}/{E_A}$ and ${\gamma _w}$ with different $\beta$
    Parameter Unit Values
    $\beta$ 0 2.25603.5135 4.66155.7635 6.8655 7.9675
    ${\gamma _w}$ 1 1.1492 1.2960 1.43391.5582 1.6757 1.7887
    ${E_{{C_{p,q}}}}/{E_A}$ dB 0 $-$0.2799 $-$0.7633 $-$1.2102 $-$1.5893$-$1.9191 $-$2.2082
  • Table 2   Simulation system parameters
    Parameter Value Unit
    Carrier frequency ($f_c$) $10$ GHz
    Platform velocity ($v_s$) $100$ m/s
    Platform altitude ($H$) $15$ km
    Antenna length in range ($D_{\rm range}$) $1$ m
    Central slant range ($R_c$) $30$ km
    Equivalent PRF (PRF) $500$ Hz
    OFDM chirp waveform duration ($T_p$)$40$ $\mu$s
    OFDM chirp waveform bandwidth ($B$)$500$ MHz
  • Table 3   SISLR of the circulate shifted OFDM chirp waveform set and shifted chirp waveforms
    Waveform SISLR (dB) SISLR (dB) with tapering window
    Circulate shifted OFDM chirp waveforms $-$17.11 $-$18.37
    Shifted chirp waveforms $-$16.84 $-$17.36

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