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According to the limitations of single channel Frequency Modulation Continuous Wave (FMCW) Synthetic Aperture Radar (SAR), Digital Beamforming (DBF) technology is introduced to improve system performance. Combined with multiple receive apertures, DBF FMCW SAR can obtain high resolution in low pulse repetition frequency, which can increase the processing gain and decrease the sampling frequency. The received signal model of DBF FMCW SAR is derived. The continuous antenna motion which is the main characteristic of FMCW SAR received signal is taken into account in the whole signal processing. The detailed imaging diagram of DBF FMCW SAR is given. A reference system is also demonstrated in the paper by comparing with a single channel FMCW SAR. The validity of the presented diagram is demonstrated with a point target simulation results.

The combination of Frequency Modulated Continuous Wave (FMCW) technology and Synthetic Aperture Radar (SAR) paves a way to light-weight, cost-effective, high-resolution active microwave remote sensing instrument. This system is suitable for small platforms such as Unmanned Aerial Vehicles (UAV). In the last years, several FMCW SAR systems have been constructed and have been successfully used in ice measurement [

However, these systems are currently applied in the short range and narrow swath case. According to the single channel FMCW SAR radar equation [

In pulsed SAR systems, wide unambiguous swath coverage and high azimuth resolution are also contradicting requirements. Several proposals, such as multiple beam SAR system operating in a squinted imaging geometry [

The HRWS SAR concept relies on separated transmit and receive antennas, which is also the characteristic of FMCW SAR systems. So the HRWS concept may be a suitable solution for improving the system performance of FMCW SAR. Now, multichannel FMCW SAR is becoming a hot area of miniature SAR research. And many research institutions have announced their research projects on multichannel FMCW SAR [

According to the imaging algorithm of pulsed DBF SAR, the basic steps are firstly the azimuth reconstruction and then single channel imaging. However, the multichannel azimuth reconstruction algorithm [

The remaining sections are organized as follows. Compared with single channel FMCW SAR, the performance improvement of DBF FMCW SAR is given in Section

The noise equivalent sigma zero (NESZ) is a quantity directly related to SAR imaging performance, which is defined as the target Radar Cross Section (RCS) when the SNR of the image is equal to one [

From (

Illustration of multiple receive apertures.

The DBF in azimuth is applied to suppress the azimuth ambiguity. This does not increase the antenna gain. In elevation, the channels are coherently combined. Performed by the SCan-On-REceive (SCORE) technique, the DBF in elevation can obtain full array gain over a wide area. Thus, under the same resolution and swath width, the maximum receive antenna gain of the DBF system is

The DBF technique increases the antenna gain by

Range processing of FMCW SAR is analog with pulsed SAR. They are all based on pulse compressing using matched filter. Theoretically, range processing gain is about the following:

In order to maintain the low-power and lightweight characteristics of FMCW SAR, the sampling frequency should be chosen as lowly as possible. According to the Nyquist theorem, the lowest sampling frequency for FMCW SAR is

The DBF FMCW SAR operates with a low PRF to increase the swath width. To decrease the PRF, the significant and challenging processing is the azimuth ambiguity suppression. In the next section, we focus on the multichannel signal reconstruction in azimuth.

Let the transmitted signal of FMCW SAR be written in complex form as follows:

The received signal is a delayed version of the transmitted one. The

Dechirp on receive is often used in FMCW SAR. In order to further decrease the sampling frequency, and then to decrease the data in range dimension, the radar demodulates the received signal by mixing it with a replica of the transmitted waveform delayed by a time

The intermediate frequency signal that results from mixing (

Using Taylor series, the round-trip range

Different from pulsed SAR,

After substituting (

In (

As mentioned above, the main characteristic of FMCW SAR is the continuous antenna motion. The range cell migration (RCM) introduced by the continuous antenna motion may result in reconstruction mismatch. Even worse, the extraphase term introduced by the continuous antenna motion may degrade the quality of the focus image.

Multichannel azimuth reconstruction algorithm [

where

Using basic matrix theory, the system matrix

In the SAR case, the range history is not a line but spans several range cells, which results in mismatch between the signal and the reconstruction. In FMCW SAR, the additional mismatch introduced by the continuous antenna motion is

Figure

System parameters.

Parameter | Multi-Channel System | Single Channel System |
---|---|---|

RF center frequency | 15 GHz | 15 GHz |

Band Width | 1.5 GHz | 1.5 GHz |

Operational Altitude | 5000 m | 5000 m |

Operational Velocity | 70 m/s | 70 m/s |

Swath Width | 7 km | 7 km |

Resolution | 0.1 m × 0.1 m | 0.1 m × 0.1 m |

Radar Losses | 2 dB | 2 dB |

Incidence Angle | 5–70° | 5–70° |

Number of Receive Apertures | 2 | 1 |

Transmitted Power | 5 W | 5 W |

Transmit Antenna Gain | 19.5 dB | 19.5 dB |

Receive Antenna Gain | 19.5 dB | 19.5 dB |

PRF | 350 Hz | 700 Hz |

Range Processing Gain | 66.3 dB | 63.3 dB |

Sampling Frequency | 16 MHz | 32 MHz |

RCM introduced by the continuous antenna motion.

The first part of signal processing for DBF FMCW SAR is the azimuth ambiguity suppression. All the recorded subaperture signals whose azimuth frequencies are aliasing become an equivalent single channel signal without azimuth ambiguity. To focus the signal, the second part of the diagram is the classic single channel SAR imaging.

In the first part, multichannel azimuth reconstruction algorithm [

The entire signal processing block diagram of DBF FMCW SAR is shown in Figure

Signal processing block diagram for DBF FMCW SAR.

Apply Azimuth Fast Fourier Transform (FFT) to the received signal of each channel. Then, the Doppler domain signal

Design the azimuth reconstruction filter

Multiply each channel signal to the corresponding reconstruction filter. At this time, the signal becomes

Add each channel signal after passing the corresponding reconstruction filter. Then, we can obtain the equivalent single channel signal

where

Multiplying the signal

Multiplying the signal with the Doppler frequency correction factor, we have the following:

In actual implementation, Steps

After an equivalent transform, (

The correction is applied in 2D frequency domain. It is to eliminate the last exponential term in (

The RVP correction factor is expressed as

Multiply

Secondary range compression: multiply the signal with the secondary range compression factor

Bulk range shift: multiply the signal with the bulk range shift factor

In actual implementation, Step

Apply FFT to

The 2D focused image of DBF FMCW SAR is obtained after azimuth matched filtering [

The parameters of an example FMCW SAR system using dual channels combined with DBF are listed in Table

To achieve the required resolution in azimuth, the Doppler bandwidth must be greater than 700 Hz. The transmit antenna length in azimuth should be less than 0.2 m. According to the swath width, the transmit antenna length in elevation can be chosen to be 2.9 cm, which corresponds to 40° beamwidth. The transmit antenna gain is 19.5 dB with the antenna efficiency 0.5.

The receive antenna is the same with the transmit antenna for single channel FMCW SAR. In the two-channel system, the receive antennas are placed in azimuth. The receive antenna gain is still the same. However the overall receive antenna length in azimuth reaches 0.4 m.

According to the Nyquist theorem, the PRF of classic FMCW SAR should be greater than the Doppler bandwidth. However, the PRF of DBF FMCW SAR can be chosen to be 700/2 Hz using two receive channels. To ensure a slant range resolution of 0.1 m, a chirp bandwidth of 1.5 GHz is necessary. The range processing gain 66.3 dB is obtained for DBF FMCW SAR. Nevertheless, that value of single channel FMCW SAR is only 63.3 dB. The sampling frequency of DBF FMCW SAR and single channel system are 16 MHz and 32 MHz, respectively. All the parameters are listed in Table

The target raw data are simulated using the two-channel system parameters listed in Table

The azimuth reconstruction is shown in Figure

The azimuth aliasing spectrum before reconstruction filters (a) and the aliasing-removal spectrum after reconstruction filters (b).

Contour plots of impulse response function of a point target without azimuth reconstruction (a), without Doppler frequency correction (b), and with azimuth reconstruction and Doppler frequency correction (c).

Using the parameters of the two-channel example system, the signal processing presented in Section

Using the parameters in Table

NESZ versus cross track range for DBF (solid) and single channel FMCW SAR (dotted).

A multichannel receive antenna FMCW SAR system combined with DBF is introduced. DBF FMCW SAR overcomes the limitation of high PRF caused by high azimuth resolution. It has higher receive antenna gain and range processing gain than single channel system. The received signal of DBF FMCW SAR is modeled. The impact of continuous antenna motion which is the main characteristic of FMCW SAR is negligible in multichannel azimuth reconstruction for DBF FMCW SAR, but it must be considered in the process during RCM correction. The whole signal processing diagram is given. Simulated point target experiments have been performed to verify the processing diagram successfully. Future works will include performance analysis thoroughly, moving target indication, and the miniaturization of the system.

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

This work was supported by the National Natural Science Foundation of China (nos. 41301397).