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.


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  • 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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