The multiple-input-multiple-output (MIMO) synthetic aperture radar (SAR) system with a linear antenna array can obtain 3D resolution. In practice, it suffers from both the translational motion errors and the rotational motion errors. Conventional single-channel motion compensation methods could be used to compensate the motion errors channel by channel. However, this method might not be accurate enough for all the channels. What is more, the single-channel compensation may break the coherence among channels, which would cause defocusing and false targets. In this paper, both the translational motion errors and the rotational motion errors are discussed, and a joint multichannel motion compensation method is proposed for MIMO SAR 3D imaging. It is demonstrated through simulations that the proposed method exceeds the conventional methods in accuracy. And the final MIMO SAR 3D imaging simulation confirms the validity of the proposed algorithm.

Conventional single-channel synthetic aperture radar (SAR) uses wideband signal and synthetic apertures to obtain high range resolution and high azimuth resolution, respectively. But it could not resolve along height due to the lack of baseline in the elevation direction. The imaging results are the projection from the scene in 3D to the range-azimuth plane. To resolve along height, the multiple-input-multiple-output (MIMO) SAR system [

The MIMO SAR system has two main advantages: (1) the degrees of freedom can be greatly increased by the concept of virtual array provided by the multiple antennas [

The paper is organized as follows. In Section

The MIMO SAR utilizes an across-track array to gain the third dimension resolution. The transmitter and receiver antennas are usually distributed nonuniformly along the linear across-track array. Assume a MIMO SAR platform flies at the altitude of

The ideal geometry of MIMO SAR 3D imaging.

Ignoring two-way antenna characteristics and propagation attenuation, after demodulation and range compression, the echo signal transmitted by the

As described in [

In practice, due to the presence of atmospheric turbulence that produces sensor track deviations from an ideal straight track, motion errors need to be accurately compensated. There have been numerous good methods dealing with the translational motion errors but ignoring the rotational motion errors [

Before the introduction of our method, we first discuss the core element that causes the defocusing of SAR images, that is, the range migration error.

As shown in Figure _{,} respectively. Then, the real position of the APC can be denoted as

The geometry of MIMO SAR 3D imaging with translational motion errors.

The geometry of MIMO SAR 3D imaging with rotational motion errors.

The slant range from

To compensate the motion errors, the conventional method is used to estimate and compensate the motion errors for each channel. However, the inevitable estimating errors of each channel may cause the incoherence among channels which would cause defocusing and false targets. Combining the linear properties of the across-track array, in this section we present a new method which can compensate both the translational motion errors and the rotational motion errors and preserve the coherence among different channels at the same time.

To avoid the incoherence after motion error compensation, the motion error estimating and compensating need to be jointed among channels. From (

The range error alters the Doppler rate and finally defocuses the image. Hence, to estimate the motion error, let us first analyze the true Doppler rates. As expressed in (

In (

From (

Suppose there are

This method combines all the estimating results of each channel to obtain the linear coefficient and then derives each Doppler rate. Comparing to the conventional SC-MOCO method, this method has three advantages: (1) the estimating accuracy is dramatically improved; (2) the influence from occasional bad estimating values can be suppressed; and (3) the multichannels maintain coherence after motion estimation. This will be demonstrated in Section

In order to prove that the proposed method is of higher precision than the conventional method, a MIMO SAR system with a linear MIMO array is simulated. The key simulation parameters are listed in Table

Simulation parameters.

Wavelength | 0.0313 m |

Bandwidth | 150 MHz |

Pulse duration | 2 |

PRF | 180 Hz |

Antenna width | 2 m |

Flying height | 6 km |

Flying speed | 150 m/s |

Incidence angle | 60^{°} |

Baseline length | 8 m |

The simulated rotational motion errors and the translational motion errors.

After range compression and migration correction, the echo data are processed separately by the proposed JMC-MOCO method and the conventional SC-MOCO method.

For the center APC, the Doppler rate estimation errors (defined as

Comparison of the center APC Doppler rate estimation accuracy between the proposed method and the conventional method.

Comparison between the estimated value and the theoretical value of (a)

Now we apply our method to simulated MIMO SAR 3D imaging and compare the imaging results with the conventional method. In the simulation, a complex 3D model containing 5 tall “buildings” is constructed with 1020 points. The structure of the model is illustrated in Figure

Point targets layout.

After MOCO with the conventional method and the proposed JMC-MOCO method, the 3D imaging results are shown in Figures

The imaging results with (a) the SC-MOCO method and (b) the proposed JMC-MOCO method.

The magnified imaging results with (a) the SC-MOCO method and (b) the proposed JMC-MOCO method.

This paper proposed a JMC-MOCO method to estimate and compensate both the translational motion errors and the rotational motion errors for the MIMO SAR 3D imaging. Instead of estimating and compensating motion errors channel by channel, the proposed MOCO method utilizes the linear properties of the linear MIMO array, combining all the channel data to improve the accuracy of motion error estimation. It is demonstrated through 3D scenario imaging simulation that this new method can significantly improve the image quality.

The authors declare that there is no conflict of interests regarding the publication of this paper.