# Efficient sliding spotlight SAR raw signal simulation of extended scenes

- Wei Xu
^{1}Email author, - Pingping Huang
^{2}and - Yunkai Deng
^{1}

**2011**:52

**DOI: **10.1186/1687-6180-2011-52

© Xu et al; licensee Springer. 2011

**Received: **8 December 2010

**Accepted: **5 September 2011

**Published: **5 September 2011

## Abstract

Sliding spotlight mode is a novel synthetic aperture radar (SAR) imaging scheme with an achieved azimuth resolution better than stripmap mode and ground coverage larger than spotlight configuration. However, its raw signal simulation of extended scenes may not be efficiently implemented in the two-dimensional (2D) Fourier transformed domain. This article presents a novel sliding spotlight raw signal simulation approach from the wide-beam SAR imaging modes. This approach can generate sliding spotlight raw signal not only from raw data evaluated by the simulators, but also from real data in the stripmap/spotlight mode. In order to obtain the desired raw data from conventional stripmap/spotlight mode, the azimuth time-varying filtering, which is implemented by de-rotation and low-pass filtering, is adopted. As raw signal of extended scenes in the stripmap/spotlight mode can efficiently be evaluated in the 2D Fourier domain, the proposed approach provides an efficient sliding spotlight SAR simulator of extended scenes. Simulation results validate this efficient simulator.

### Keywords

synthetic aperture radar (SAR) sliding spotlight SAR raw data simulator extended scenes## 1. Introduction

The spotlight synthetic aperture radar (SAR) mode can improve azimuth resolution by increasing the synthetic aperture time, and its azimuth beam is steered during the whole acquisition time. The major drawback of such configuration is that azimuth beam pointing always at the same area limits the extension of the illuminated area in azimuth. The sliding spotlight mode allows a comprise between azimuth resolution and azimuth extension of imaged scene [1–3], and it can be described as using a virtual rotation center which is further away from the radar than the imaging scene [4].

A SAR raw data simulator is an important tool for testing system parameters, imaging algorithms, and mission planning. SAR raw data can precisely be generated target by target in the two-dimensional (2D) time domain [5]. However, to the raw data simulation of extended scenes, this approach is of low efficiency. In order to improve the efficiency of raw data simulator, a series of simulators for different imaging modes are proposed in the 2D Fourier domain [5–9]. Unfortunately, different from the stripmap and the pure spotlight modes, the raw data of extended imaged scenes in the sliding spotlight mode may not efficiently be evaluated in the 2D Fourier transformed domain [10]. The 1D range Fourier domain approach for the sliding spotlight mode is proposed in [10], but it is still less efficient, compared with the 2D Fourier domain simulators.

This article presents a novel sliding spotlight SAR raw data generation approach from the wide-beam imaging modes. Azimuth varying band-pass filter (BPF) could be adopted for extracting the desired signals from the raw data in the wide-beam imaging modes and set others to zero. This filter should just accommodate the Doppler centroid varying rate and be independent of the slant range, and it can efficiently be implemented by de-rotation operation and BPF. This article is organized as follows: Section 2 reviews the acquisition geometry of the sliding spotlight mode and analyzes its special echo characteristics in azimuth. Section 3 is focused on presenting the proposed raw data generation approach of extended scenes for the sliding spotlight mode. Simulation results are given to validate the proposed raw data generation approach in Section 4. Finally, some useful conclusions are reported.

## 2. Sliding spotlight mode implementation

The stripmap and spotlight modes are the two well-known SAR operating schemes. In the stripmap mode, antenna azimuth beam points along a fixed direction with respect to the flight path, while azimuth beam is steered during the whole acquisition interval in the spotlight mode. In this section, both acquisitions geometries and echo characteristics in the sliding spotlight mode are compared with conventional stripmap and spotlight modes.

*v*denotes the effective velocity of the sensor on the imaging plane,

*T*is the duration of the whole acquisition time,

*L*

_{s}and

*L*

_{ss}are the effective azimuth extension of the imaged area in the stripmap mode and sliding spotlight mode, respectively. Assuming that azimuth beam angular interval is

*θ*

_{0}in the sliding spotlight configuration and

*θ*

_{1}in the stripmap mode, their effective azimuth extensions of imaged area are approximatively expressed as follows:

*R*

_{c}is the slant range from the sensor to the imaged area center. If we choose part of azimuth beam interval to imitate azimuth beam steering in the sliding spotlight mode as shown in Figure 1, then the equivalent azimuth beam rotation rate is as follows:

*L*

_{spot}and

*L*

_{ss}are the effective azimuth extension of imaged area in the spotlight mode and sliding spotlight mode, respectively, and they are expressed as follows

*θ*

_{2}is the azimuth beam angular interval in the spotlight mode. Thereafter, the equivalent azimuth beam rotation rate in Figure 2 can be obtained as follows

*λ*is the wavelength. In Figure 3,

*k*

_{a}is the target Doppler rate,

*T*

_{s},

*T*

_{ss}, and

*T*

_{spot}are the effective azimuth output extensions of the stripmap mode, the equivalent sliding spotlight mode, and the pure spotlight mode, respectively. In the figure,

*B*

_{f _0},

*B*

_{f _1,}, and

*B*

_{f _2}are the azimuth beam bandwidths in the equivalent sliding spotlight, stripmap, and the spotlight modes, respectively. The overall Doppler bandwidth of the equivalent sliding spotlight mode is as follows

## 3. Raw data generation approach

- (1)Assuming that azimuth extension of the designed extended scene is
*L*_{ss}, azimuth beam interval is*θ*_{2}, and the obtained azimuth resolution is*ρ*_{az}, the equivalent azimuth beam rotation rate is computed as follows:${\omega}_{r}=\frac{v}{{R}_{\mathsf{\text{c}}}}\left(1-\frac{2{\theta}_{0}{\rho}_{\mathsf{\text{az}}}}{\lambda}\right)$(8)

*θ*

_{1}exploited in the stripmap mode and

*θ*

_{2}in the spotlight mode are considered as follows:

- (2)
After computing all the parameters used in the stripmap/spotlight mode SAR raw data generation, we can introduce the efficient 2D frequency domain simulators of extended scenes in the stripmap/spotlight mode to generate raw data [5–9].

- (3)
Extracting desired azimuth signal in the equivalent sliding spotlight mode, and reduce the azimuth sampling frequency with the designed system pulse repetition frequency (PRF).

- (1)De-rotating azimuth data to remove the time-varying Doppler centroid of the desired Doppler spectrums. The de-rotation function is given as follows:$h\left(t\right)=exp\left[-j\pi {k}_{\mathsf{\text{rot}}}{\left(t-{t}_{\mathsf{\text{mid}}}\right)}^{2}\right]$(12)

*t*

_{mid}is the acquisition center time.

- (2)
Fourier transforming (FT) the de-rotated signals in the azimuth direction. It should be noted that up-sampling in azimuth may be required in the spotlight mode to avoid the Doppler spectrum aliasing.

- (3)
Low-pass filtering the azimuth signals, the bandwidth of the low-pass filter is

*B*_{f _0}equivalent to the bandwidth of the reduced azimuth beam interval adopted in the equivalent sliding spotlight mode. Afterward, we should resample the azimuth signals with the designed PRF by decreasing azimuth total samples in the Doppler domain. - (4)
Inverse FT (IFT) the raw data in the azimuth direction and reramping of the azimuth data. The reramping referenced function is just conjugated to (12).

- (1)
FT the raw data in the azimuth direction and low-pass filtering in the Doppler domain with the bandwidth

*B*_{w}which is equivalent to the overall Doppler bandwidth*B*_{ s }in (7). - (2)Deramping the azimuth data in the Doppler domain to shift the azimuth signals, the referenced deramping function is given as follows:$H(f)=\mathrm{exp}\left[j\pi {({f}_{a}-{f}_{\text{sdc}})}^{2}/{k}_{\text{rot}}\right]$(13)

*f*

_{ a }is the Doppler frequency, and

*f*

_{sdc}is the Doppler centroid of the illuminated scene.

- (3)IFT the raw data in the azimuth direction and low-pass filtering the raw data in the azimuth time domain. The duration of the low-pass filter is
*T*_{w}given by:${T}_{w}=\frac{{B}_{d}}{\left|{k}_{a}{k}_{\text{rot}}/({k}_{a}-{k}_{\text{rot}})\right|}$(14)

*k*

_{ a }= -2ν

^{2}/(

*λr*) is the Doppler rate and

*B*

_{d}is the target Doppler bandwidth in the sliding spotlight mode given by

*r*is the slant range. Substituting (15) into (14) yields:

- (4)
FT the deramped signals in the azimuth direction and reramping of raw data by the referenced function which is conjugated to (13).

- (5)
IFT and resampling the raw data in the azimuth direction to obtain the desired sliding spotlight raw data.

Compared with the time domain approach, the Doppler domain approach is less efficient, as it requires two FT operations and two IFT operations while the time domain approach only needs one FT operation and one IFT operation in azimuth, as shown in Figure 4.

## 4. Simulation experiment

System parameters in the simulation

Carrier frequency | 9.65 GHZ |
---|---|

Platform velocity | 200 m/s |

Pulse duration | 1 μs |

Pulse bandwidth | 100 MHz |

Sampling frequency | 120 MHz |

Antenna length in the wide-beam mode | 0.5 m |

Antenna length in the sliding spotlight mode | 2 m |

PRF in the wide-beam mode | 1000 Hz |

PRF in the sliding spotlight mode | 250 Hz |

Slant range | 10 km |

The desired azimuth resolution in the sliding spotlight mode | 0.8 m |

## 5. Conclusion

This article presents a novel approach to generate the sliding spotlight SAR raw data from the wide-beam stripmap/spotlight mode. As both stripmap and spotlight SAR raw data of extended scenes can efficiently be generated in the 2D Fourier transformed domain [5–9], this approach provides an efficient real-time sliding spotlight raw data simulator of extended scenes. From Figure 4, it can be seen that this approach is quite efficient, owning to the fact that only complex multiplications and FFT codes are needed. Furthermore, the equivalent sliding spotlight raw data can also be obtained from real data of the wide-beam imaging modes.

## Declarations

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.