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SCIENTIA SINICA Informationis, Volume 48, Issue 12: 1634-1650(2018) https://doi.org/10.1360/N112018-00033

A sparse estimation algorithm for the radar target range-direction under strong mainlobe jamming conditions

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  • ReceivedFeb 12, 2018
  • AcceptedApr 28, 2018
  • PublishedNov 27, 2018

Abstract

In this paper, a sparse estimation algorithm for the radar target range and direction under strong mainlobe blanket jamming conditions is presented. This algorithm can effectively suppress multiple strong mainlobe blanket jammings (multi-MLJs) and extract the information about target distance and direction. First, the space domain adaptive processing for the received signal in each row (or column) is adopted to suppress multi-MLJs. Second, the sparse Bayesian learning is employed to obtain the information of the target distance and elevation (or azimuth). In addition, the proposed method still has an effective performance under the error condition and the applicable conditions of the new algorithm based on the performance analysis are provided in this paper.


Funded by

国家自然科学基金(61501506,61501505)


References

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  • Figure 1

    Array model

  • Figure 2

    The diagram of the new algorithm

  • Figure 4

    (Color online) The outputs of beamforming

  • Figure 5

    (Color online) The elevation sparse Bayesian estimation (conventional row beamforming). (a) 3D plan;protect łinebreak (b) horizontal projection

  • Figure 6

    (Color online) The outputs with the row adaptive processing

  • Figure 7

    (Color online) The elevation sparse Bayesian estimation (row adaptive processing). (a) 3D plan; (b) horizontal projection

  • Figure 8

    (Color online) The azimuth sparse Bayesian estimation (column adaptive processing). (a) 3D plan; (b) horizontal projection

  • Figure 9

    (Color online) The method of [6]. (a) Adaptive elevation sum beam pattern; (b) adaptive azimuth sum beam pattern; (c) elevation monopulse ratio; (d) azimuth monopulse ratio

  • Figure 10

    (Color online) The outputs of adaptive beamforming

  • Figure 11

    (Color online) The elevation (azimuth) sparse Bayesian estimation. (a) Row adaptive processing; (b) column adaptive processing

  • Figure 12

    (Color online) The elevation (azimuth) sparse Bayesian estimation. (a) Row adaptive processing; (b) column adaptive processing

  • Figure 13

    (Color online) The target parameter estimation. (a) The distance estimation; (b) the elevation estimation

  • Figure 14

    (Color online) The outputs of SINR

  • Figure 15

    (Color online) The target parameter estimation. (a) The distance estimation; (b) the elevation estimation

  • Figure 16

    (Color online) The outputs of SINR

  • 1   Table 1The simulation parameters setting
    Parameter Setting
    The array antenna Consider a rectangular planar array which has 24 columns, and each column
    has 20 elements.
    The element spacing Half a wavelength.
    The beam boresight $\left(~\text{9}0{}^\circ~,30{}^\circ~~\right)$, the former is azimuth, and the latter is elevation.
    The 3 dB beam width $\left(~4.21{}^\circ~,5.05{}^\circ~~\right)$.
    The transmission signal Linear frequency modulation (LFM) signal, with bandwidth $B=5$ MHz,
    pulse width $\tau~=20~\mu$s and sampling rate ${{f}_{s}}=10$ MHz.
    The target One target with 5 dB is located at $\left(~\text{9}0{}^\circ~,30{}^\circ~~\right)$ and the 500-th sampling point.
    The jammings Two mainlobe blanket jammings with 50 dB are located at $\left(~\text{91}.05{}^\circ~,31.26{}^\circ~~\right)$,
    $\left(~88.95{}^\circ~,28.74{}^\circ~~\right)$, which are located at the one quarter of 3 dB beam width.
    Noise White Gaussian noise with 0 dB.
    The observation sample 5.
    number of sparse recovery
  •   

    Algorithm 1

    Inputs: the array received signal ${\boldsymbol~x}\in~{{\mathbb{C}}^{{{N}_{1}}\times~{{N}_{2}}}}$, angle dictionary $\mathbf{\varphi~}\in~{{\mathbb{C}}^{{{N}_{1}}\times~L}}$.

    Outputs: the sparsity coefficient $\mathbf{\omega~}$.

    1. The outputs by the spatial row adaptive processing: ${\boldsymbol~r}(~n~)={\boldsymbol~a}\left(~{{\varphi~}_{0}}~\right)p{{s}_{0}}(~n~)+{{{\boldsymbol~v}}_{r}}(~n~)$;

    2. Selecting $K$ training samples: ${\boldsymbol~r}\in~{{\mathbb{C}}^{{{N}_{1}}\times~K}}$;

    3. Setting initial values: ${{\mathbf{\gamma~}}_{0}}=1$, $\sigma~_{0}^{2}={{10}^{-1}}$;

    4. Calculating the posterior component:

    ${{\boldsymbol D}_{f+1}}={{\mathbf{\Gamma}}_{f}}-{{\mathbf{\Gamma }}_{f}}{{\mathbf{\varphi }}^{\text{H}}}{{\left( \sigma _{f}^{2}{\boldsymbol I}+\mathbf{\varphi }{{\mathbf{\Gamma }}_{f}}{{\mathbf{\varphi }}^{\text{H}}} \right)}^{-1}}\mathbf{\varphi }{{\mathbf{\Gamma }}_{f}}$,

    $\mathbf{\mu}_{f+1}^{\left( k \right)}={{\mathbf{\Gamma }}_{f}}{{\mathbf{\varphi }}^{\text{H}}}{{\left( \sigma _{f}^{2}{\boldsymbol I}+\mathbf{\varphi }{{\mathbf{\Gamma }}_{f}}{{\mathbf{\varphi }}^{\text{H}}} \right)}^{-1}}{{{\boldsymbol r}}^{\left( k \right)}}$;

    5. The iterative updating of $\mathbf{\gamma~}$ and ${{\sigma~}^{2}}$ with the EM algorithm:

    ${{\gamma }_{l,f+1}}=\frac{1}{K}\left\| \mathbf{\mu }_{l,f+1}^{\left( k \right)} \right\|_{2}^{2}+{{{\boldsymbol D}}_{l,f+1}}$,

    $\sigma _{f+1}^{2}=\frac{\frac{1}{K}\left\| {\boldsymbol r}-\mathbf{\varphi }{{\mathbf{\omega }}_{f+1}} \right\|_{2}^{2}+\sigma _{f}^{2}\sum\nolimits_{l=1}^{L}{\big( 1-\frac{{{{\boldsymbol D}}_{l,l}}}{{{\gamma }_{l,f}}} \big)}}{{{N}_{1}}}$ ;

    6. Repeating steps 4 and 5 until satisfying the convergence conditions: ${{{\|~{{\mathbf{\gamma~}}_{f+1}}-{{\mathbf{\gamma~}}_{f}}~\|}_{2}}}/{{{\|~{{\mathbf{\gamma~}}_{f+1}}~\|}_{2}}}\;\le~\delta~$ or ${{\sigma~}^{2}}\le~{{(~{{\sigma~}^{*}}~)}^{2}}$;

    7. The sparse coefficient estimation: $\mathbf{\omega~}\approx~\text{E}(~\mathbf{\omega~}|~{\boldsymbol~r};{{\mathbf{\Gamma~}}^{*}},{{(~{{\sigma~}^{*}}~)}^{2}}~)$;

    8. The target distance and elevation estimation can be obtained by the maximum index of $\mathbf{\omega~}$;

    9. Similarly, the target azimuth can be estimated.

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