The existing range-Doppler algorithms for SAR imaging are affected by a fast-time Doppler effect so they cannot be directly applied to FMCW SAR. Moreover, range migration is more evident in squint mode. To reveal the influence of the continuous motion of FMCW SAR in the squint mode on the echo signal and optimize the imaging process, an improved range-Doppler algorithm is based on squint FMCW SAR imaging is proposed in this paper. Firstly, the imaging geometry model and echo signal model of FMCW SAR are analyzed and deduced. The problem of Doppler center offset under squint mode is eliminated by linearly correcting the echo signal. By dealing with the range migration in the frequency domain, the processing process can be simplified. Finally, the effectiveness and feasibility of the algorithm are verified by simulation. The results are as follows: (1) The image quality is improved by correcting the linear motion in squint mode. (2) The peak sidelobe ratio (PSLR) and the integral sidelobe ratio (ISLR) of the imaging index of the improved algorithm are close to the theoretical values. Therefore, the improved range-Doppler algorithm can effectively perform high-efficiency imaging in the case of squint.

The airborne platform for earth observation and imaging system, based on Synthetic Aperture Radar (SAR), is widely used in search and rescue, regional monitoring, disaster monitoring, and control, small unmanned aerial vehicles (UAV) ground reconnaissance and other aspects [

Due to the pulse width of the FMCW reaches the millisecond level, the position change of the radar in the period of the transmitting pulse cannot be neglected, so that the working mode suitable for the pulse-type SAR “stop-and-stop” is no longer applicable, and the load, cost, and power consumption are limited on the micro-platform. Therefore, it is necessary to improve the processing efficiency and reduce the amount of calculation under the premise of ensuring image quality.

Based on this, the researchers have conducted much research on the imaging processing methods applicable to FMCW SAR [

Thus, an echo signal model is derived by analyzing the imaging geometry of FMCW SAR in squint mode. In order to efficiently process the influence of intra-pulse instantaneous slant range on imaging and optimize the range-Doppler algorithm step, which will provide a reference for high efficiency and high-quality imaging of FMCW SAR in squint mode, the characteristics of demodulation signal, the influence of instantaneous slant range on imaging quality and the effect of matching filtering on computational efficiency are analyzed.

Researchers have done a lot of research on imaging algorithms applicable to FMCW SAR. Tebaldini et al. [

The above research results are mainly aimed at the imaging geometry and signal echo characteristics of FMCW SAR in positive and side view mode, but few studies on the imaging of FMCW SAR in the squint mode, especially the correlation research of high-efficiency real-time imaging. In this paper, the first established geometric model of FMCW SAR in squint mode and the instantaneous slant range on echo signals is analyzed. Then the echo signal model in squint mode is derived from analyzing the Doppler characteristics of echo signals and the computational complexity of range migration in the frequency domain, which provides a theoretical basis for the optimization of algorithm flow.

The rest of the article is organized as follows. In the third section, the geometric model in strip mode is established, and the signal echo model and detailed algorithm flow are derived. In the fourth section, the algorithm is analyzed and compared with the classical algorithm. Simulation experiments verify the effectiveness of the algorithm. The final section summarizes the paper and gives relevant conclusions.

In this section, FMCW SAR operating in squint mode is analyzed. Taking the squint geometry model in the strip mode as an example, the geometric model of the radar imaging and its geometric oblique plane with the imaging target are shown in

In

According to the analysis, since FMCW SAR has been moving at a uniform speed during the transmission of signals during the whole radar working period, the instantaneous slant range between the aircraft and the target to be measured is not only related to the slow time ta, but also to the fast time tr and the slant angle. Whose expression is as

The instantaneous slant range

where

Describing the echo range variation in radar imaging scene is related to

where

This section derives the signal echo model based on the imaging geometry model in Section 3.1. Let the transmitted signal be the LFM signal and the amplitude of the transmitted signal be constant. The mathematical expression of the transmitted signal is

where fc is the signal center frequency,

After the radar receives the reflection of the signal, the delay signal is:

De chirp of echo signal is processed. Assuming that the reference slant range is Rref, then the reference signal expression is:

where

where A0 is the backscattering coefficient of the imaging point target; the first exponential term is the phase information in the range direction of the target; the second exponential term is the Doppler phase in the azimuthal direction, which can be used for the azimuth direction focusing, and the third exponential term is the Remain Video Phase (RVP), which can be ignored in the imaging process [

Based on the analysis in Section 3.2, it is known that each exponential term in the de-chirp difference frequency signal contains the linear walking component. We need to correct the linear walking component in the echo signal. The corresponding linear walking component correction function is:

where

where

Because the subsequent signal processing ignores the impact on the RVP term, the RVP term is no longer processed during the correction linear walk.

In this section, the process of optimizing range Doppler algorithm is deduced in detail.

where

As shown in

When the signal frequency is converted from fc to

Therefore, at the point fa in the

Then the instantaneous slant range difference in the

Therefore, the frequency of the fast time along the range in the Doppler domain is

The distance Fourier transform is performed on

Since the reference distance is introduced, the reference distance needs to be compensated, and the compensation phase function is

The fourth exponential term in

According to

The correction function of

Multiply this function by the decoupled signal and then perform the azimuthal inverse Fourier transform, so that the azimuthal compression is completed. The scene image at this time is

where Br and Ba are azimuth doppler bandwidth and range doppler bandwidth respectively. The complete flow chart of squint FMCW SAR processing is shown as follows.

In this section, the computational complexity of the improved algorithm in Section 3.3 is analyzed. The computational cost of a N-point FFT or IFFT is 5 NlbN times of floating-point operation (FLOP), while a reset multiplication is 6 times of FLOP without optimization. As can be seen from

In order to verify the effectiveness of the proposed improved algorithm, Matlab software is used to simulate the echo signal. The parameters of FMCW SAR system are shown in

Parameter | Value |
---|---|

Carrier frequency | Ka |

Signal band (MHz) | 500 |

Period (ms) | 1 |

Reference slant (m) | 1000 |

Platform velocity (m/s) | 40 |

Beam width in azimuth (°) | 2.1 |

Down-looking angle (°) | 15 |

Pulse repetition frequency (PRF) | 1000 |

The specific simulation parameters are shown in

Using the data in

The simulation results of the above simulation experiments under the condition of 15 degree squint angle prove that the improved algorithm achieves good simulation results.

Azimuth | Range | |||||
---|---|---|---|---|---|---|

Index | IRW (point) | PSLR (dB) | ISLR (dB) | IRW (point) | PSLR (dB) | ISLR (dB) |

0.566 | –13.5003 | –13.03 | 0.503 | –15.3002 | –17.7613 |

As can be seen from

In order to explore the squint imaging characteristics of FMCW SAR, the relationship between echo signal and instantaneous slant range is analyzed, and the range Doppler algorithm flow is optimized. Starting from the squint geometric model of FMCW SAR, the echo signal model, the Doppler characteristics of the echo signal and the operational efficiency of the algorithm are analyzed by mathematical deduction and analysis. Finally, the following conclusions are drawn:

First, the influence of linear walk in squint mode on FMCW SAR imaging quality cannot be neglected. As the squint angle increases, the azimuth spectrum is no longer centered symmetrical with respect to Doppler.

Second, the range curvature term in range migration is inversely proportional to the squint angle and directly proportional to the range walk.

Third, when range migration is corrected in the frequency domain, the interpolation operation of the algorithm can be replaced by FFT transform and phase multiplication, which can effectively improve the operation efficiency.

By analyzing the geometric model of FMCW SAR imaging and establishing the signal echo model, an improved range Doppler algorithm in squint mode is proposed, which provides an effective and feasible solution to meet the real-time imaging needs of small airborne radar. Due to the lack of measured data, the motion of the aircraft has a certain impact on the imaging. Therefore, in the future research, the combination of the motion compensation of the aircraft and the echo signal model will be revised, and the recognition of the imaging characteristics of FMCW SAR in squint mode will be more accurate.