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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Synthetic wideband waveforms (SWW) combine a stepped frequency CW waveform and a chirp signal waveform to achieve high range resolution without requiring a large bandwidth or the consequent very high sampling rate. If an efficient algorithm like the range-Doppler algorithm (RDA) is used to acquire the SAR images for synthetic wideband signals, errors occur due to approximations, so the images may not show the best possible result. This paper proposes a modified subpulse SAR processing algorithm for synthetic wideband signals which is based on RDA. An experiment with an automobile-based SAR system showed that the proposed algorithm is quite accurate with a considerable improvement in resolution and quality of the obtained SAR image.

Synthetic aperture radar (SAR) can produce high resolution two-dimensional imagery of the ground surface. The improvement in resolution is normally achieved by increasing the bandwidth, so a highresolution SAR usually transmits a wideband chirp signal. To increase the range resolution beyond the theoretical value of

The range migration algorithm (RMA) can properly focus a SAR signal without approximations. Alternative methods to avoid this computationally demanding algorithm are the range-Doppler algorithm (RDA) and the chirp scaling algorithm (CSA). The approximations used in RDA and CSA are well-known [

The received signals from narrow subpulses can be combined to form a single pulse with a wide synthetic bandwidth, as if one pulse had been received [

The processing steps necessary to synthesize a wideband pulse from the received narrowband subpulses are: 1) upsampling; 2) frequency shift; 3) phase correction; 4) time shift; and 5) merging of the corrected subpulses.

Because the narrowband subpulses are naturally sampled at a lower rate than the desired wideband signal, they must be upsampled using zero padding in the frequency domain before combining. Then, because all upsampled narrowband pulses are at baseband, they must be shifted to the proper spectrum positions in the frequency domain. A frequency shift of _{Δ} in frequency domain can be achieved by multiplying the phase term exp (2π_{Δ}t) in the time domain. Also, the phase of the wideband pulse must be continuous at the narrowband pulse boundaries, and a phase correction term must be added to each subpulse. Finally, before combining the individual pulses, they must be shifted in the time domain; the resultant final data is the superposition of the corrected subpulses in the range direction.

SAR images for a synthetic wideband waveform can be obtained using a conventional RDA: range compression is performed by a convolution with a single wideband reference signal in the range direction, and then RCMC is performed in the range-Doppler domain (

Our proposed procedure (

A conventional SAR processor performs range compression with a matched filtering: a range FFT is performed and multiplied with a matched filter response, then a range IFFT is performed to complete the range compression. Range compression for a synthetic wideband signal is not much different from that of the conventional single chirp signal. Because all received narrowband pulses are at baseband, the range compression is performed by matched filtering using the same reference signal (_{r}_{base}

_{p}_{bw}_{Cn}_{η}

The resulting PSLR is -13dB when the envelope of the spectrum is approximately rectangular. This level of PSLR in the range direction is usually considered to be too high, and a smoothing window can be applied to the matched filter response in the frequency domain. However, the proposed algorithm (

First, the entire window is split into _{r}_{rc}_{PWn}_{m}_{PWn}

After the range compression with partial windowing, RCMC is performed by range interpolation in the range-Doppler domain. The signal after the azimuth FFT, _{1}_{η}

Also, _{rd}

The amount of RCM, Δ_{rd}

This amount of RCM is range dependent. Because one of the dimensions is range time, the RDA can compensate for the range dependency of Δ_{rd}_{rd}_{rd}_{2} can be represented as

The azimuth compression (_{Cn}_{az}_{ac}_{a}_{m}_{az}

Finally, the azimuth compressed data for each subpulse are simply stitched together. They must be upsampled first using zero padding in the frequency domain before combining (Section 2). Because all upsampled narrowband pulses are at baseband, they must be shifted to proper spectrum positions in the frequency domain. The quadratic phases caused by chirp rate and carrier frequency are completely removed by range and azimuth matched filtering of each subpulse, so no additional phase correction is necessary. However, if relative motion occurs between the antenna and the target, the phase correction in [

The final operation needed is simply to sum all spectrum data in the range direction. However, when the frequency step is smaller than the bandwidth of the baseband signal, there is a problem with overlap. Due to the spectral discontinuity, undesired sidelobes and grating-lobes are generated. Also, abrupt phase changes at the boundary between the adjacent spectra can deteriorate the quality of the SAR image can be deteriorated. This problem can be avoided by applying a raised cosine filter for the range spectrum [_{rcf}

To verify the performance of the proposed algorithm, several experiments were conducted using the automobile-based SAR (AutoSAR) system designed by Pohang University of Science and Technology (POSTECH) [

To quantify the range resolution improvement of the proposed algorithms, a simulation was performed for the case of an ideal point scatterer located at a range of 100 m. The parameters of the simulations were chosen to be same as those for the AutoSAR system. The range profiles acquired by three different algorithms near the center of the point scatterer (

Also, quantification of the resolution improvement was performed by measuring the resolution in the SAR images of a trihedral corner reflector located at a range of 100 m, using a single chirp of 200 MHz bandwidth, together with additional profiles using the SWW of 600 MHz bandwidth, one with the conventional algorithm and another with the proposed algorithm.

Both range (

A SAR image (

Region A is in dry field, which was selected to visualize the effect of the range resolution improvement over textured distributed targets. The expanded images of region A, using a single chirp (200 MHz), an SWW (600 MHz) processed with the conventional algorithm, and a synthetic wideband signals (600 MHz) processed with the proposed algorithm, (

Another method of measuring the range resolution improvement is to calculate the resolution of the speckle over a homogeneous area [

Many papers have dealt with synthetic wideband waveforms, but most have emphasized methods to implement SWW or methods to reduce the sidelobes and grating lobes. Also, they tend to use conventional SAR processing algorithms without much attention to the errors, which may not be negligible when a very wide bandwidth is used. This paper proposes a modified RDA procedure in an attempt to improve the quality of SAR images from SWW. Experiments with an automobile-based SAR system showed that the proposed algorithm is quite accurate in processing the synthetic wideband signals, with a resolution improvement of 20 to 30% compared to the conventional SAR processing algorithm. Moreover, if parallel processing is possible, subpulses can be processed independently and merged to obtain a high quality SAR image much more efficiently.

This research was supported by the Ministry of Knowledge Economy, Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Advancement) (IITA-2008-C1090-0801-0037).

The Frequency up-down scheme of the synthetic wideband signals. _{p}_{p}_{C1}, f_{C2}, f_{C3}

SAR processing algorithm: (a) Conventional algorithm; (b) modified RDA.

The partial windowing.

Simulation and experimental results for a point target. (a) Range profiles using simulation, (b) mainlobe comparison of simulated data, (c) measured range profiles, (d) measured azimuth profiles

SAR image of a rural area obtained by AutoSAR [

An expanded image of region A. Single chirp 200 MHz (top), SWW (600 MHz) with conventional algorithm (center), SWW (600 MHz) with proposed algorithm (bottom). The size of each imaged area is 70 m × 20 m.

The specification of AutoSAR

| |
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Pulse period, _{p} |
10 |

Pulse width, _{p} |
4 |

Carrier frequencies, _{Cn} |
9.45, 9.65, 9.85 GHz |

RF Bandwidth | up to 600 MHz |

Baseband Bandwidth | 200 MHz |

Sampling frequency | 500 MHz |

Beamwidth (range, azimuthal) | 10°, 5° |

Azimuth sampling interval | 3 cm |

The summary of the range resolution measured by several cases.

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Single chirp (200 MHz) | 66.5 | 71.2 | 69.0 | 68.4 |

Conventional algorithm (600 MHz) | 22.2 | 30.8 | 30.4 | 31.5 |

Proposed algorithm (600 MHz) | 22.2 | 24.5 | 24.3 | 22.4 |