# Adaptive Antenna Pattern Notching of Interference in Synthetic Aperture Radar Data Using Digital Beamforming

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## Abstract

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## 1. Introduction

## 2. Theoretical Background

#### 2.1. Minimum Variance Distortionless Beamformer

#### 2.2. Interference-Noise-Covariance Estimation

#### 2.3. The Angular Extension of SAR Signals

#### 2.4. The Impact of Range Compression on the Angular Signal Extension

## 3. Proposed RFI Mitigation Algorithms Using DBF

#### 3.1. DBF in Elevation

#### 3.1.1. Pulse-Wise MVDR

#### 3.1.2. Segment-Wise Frequency MVDR

#### 3.1.3. Range-Dependent Time MVDR

#### 3.1.4. Range-Dependent Frequency MVDR

#### 3.1.5. On the Utilization of Range-Frequency Sublooks

#### 3.1.6. Pulsed-RFI MVDR

#### 3.2. DBF in Azimuth

#### 3.2.1. Doppler-Dependent MVDR

#### 3.2.2. Doppler-Dependent Frequency MVDR

#### 3.3. Two-Dimensional DBF

#### 3.4. Summary

## 4. Simulations for DBF in Elevation

#### 4.1. Simulation Steps and Parameters

#### 4.2. Error Model

#### 4.3. Simulated Interference Scenarios

#### 4.3.1. Scenario A

#### 4.3.2. Scenario B

#### 4.3.3. Scenario C

#### 4.3.4. Scenario D

#### 4.4. Simulation Results

#### 4.4.1. Scenario A

#### 4.4.2. Scenario B

#### 4.4.3. Scenario C

#### 4.4.4. Scenario D

## 5. Experimental Results

#### 5.1. EcoSAR System Description

#### 5.2. Dataset Description

#### 5.3. Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Illustration of the travelling pulse extension in red. Returns from all targets within the red zone arrive at the radar simultaneously. (

**b**) Capon spatial spectrum (power from AoA) versus range sample for raw SAR signal. The radar is receiving energy from a wide span of AoAs at each range because of the pulse extension. (

**c**) Capon spatial spectrum versus range sample for range-compressed SAR signal. The energy is compressed to the instantaneous range. (

**d**) Instantaneous frequency of near and far range target within the receive window for a transmit pulse that is modulated with a linear frequency. The signals are simulated under the simulation conditions of Table 1 (Section 2.3).

**Figure 2.**(

**a**) The beamwidth in azimuth allows the SAR to record the Doppler chirp caused by the relative motion between radar and target (red mark). (

**b**) Two-dimensional ground extent. The Doppler frequency is directly related to the azimuth AoA.

**Figure 3.**Angular signal extent in elevation for SAR systems operating with a 20 microsecond chirp at H = 3 km (airborne, orange), at H = 600 km (spaceborne. The green line represents the airborne system after range compression.

**Figure 4.**The estimation of the interference noise covariance (INC) matrix in the presence of the SAR signal is achieved by integrating the angular spectrum over the angular area $\overline{\mathsf{\Theta}}$. The instantaneous SAR signal occupies the angular area $\mathsf{\Theta}$.

**Figure 5.**Pulse-Wise Minimum Variance Distortionless Response (MVDR) RFI mitigation with DBF. A mitigation of $N-1$ interferers per pulse is possible.

**Figure 6.**Segment-Wise Frequency MVDR RFI mitigation with Digital Beamforming (DBF). A mitigation of $N-1$ interferers per frequency bin is possible.

**Figure 7.**After range compression, the pulse extent (PE) in each range line is reduced to the resolution of the Impulse Response Function (IRF).

**Figure 8.**Range-Dependent Time MVDR RFI mitigation with DBF. A mitigation of $N-1$ interferers per range line u is possible.

**Figure 9.**Range Dependent Frequency MVDR RFI mitigation with DBF. A mitigation of $N-1$ interferers per range window and frequency bin is possible. Range window is centered around range sample u.

**Figure 10.**A Pulsed-RFI MVDR mitigation with DBF. A mitigation of $N-1$ interferers per window is possible.

**Figure 11.**(

**a**) At each time instance, the radar is receiving returns from the entire synthetic aperture. (

**b**) In the range-Doppler domain, the AoA in azimuth is correlated with the Doppler frequency. This can be utilized to reduce the blindspot because the instantaneous Doppler angle is different in each Doppler bin.

**Figure 12.**Doppler-Dependent MVDR RFI mitigation with DBF. A mitigation of $M-1$ interferers per Doppler bin is possible.

**Figure 13.**Doppler-Dependent Frequency MVDR RFI mitigation with DBF. A mitigation of $M-1$ interferers per window is possible.

**Figure 14.**The pulse and Doppler extent of an ideal point target projected onto the ground (yellow). Two-dimensional DBF is capable of separating the extent to small patches (red box) in the range-compressed Doppler domain. This reduces the blindspot of the INC estimation.

**Figure 15.**Two-dimensional MVDR RFI mitigation with DBF. A mitigation of $(N-1)(M-1)$ interferers per window is possible.

**Figure 16.**Simulation chain for the performance evaluation of the RFI mitigation. The simulated SAR and RFI data are range compressed individually. The range-compressed SAR data is then beamformed with SCORE to create the ideal reference data. Contaminated data is produced by summing the range-compressed SAR and RFI data. The contaminated data is then corrected using the algorithms. In the end, the algorithm output is divided by the reference data to produce the residual error image.

**Figure 17.**(

**a**) Additive error model: SAR signal (black vector) imposed with additive RFI (blue-dashed vector). A phase change of the interferer (red) causes the measured signal to be within the green-dashed circle. The resulting gain error depends on both RFI amplitude and phase. The resulting phase error depends on amplitude and phase as well. (

**b**) Multiplicative error model: SAR signal (black vector) that is affected by multiplicative gain error (blue-dashed vector) and multiplicative phase error (red). The resulting gain error depends on the multiplicative gain, the resulting phase error on the multiplicative phase.

**Figure 18.**Scenario A: A single interferer is located outside the swath at −20°. It is transmitting a signal at 40 MHz in baseband.

**Figure 19.**Scenario B: Two interferers are present. The first interferer is outside the swath at −20° with baseband frequency 40 MHz. The second interferer is inside the swath at 40° with baseband frequency 25 MHz.

**Figure 20.**Scenario C: 11 interferers are present and outside of the swath. Locations range from −50° to 0° in 5° intervals. Transmitting frequencies range from −60 MHz to 25 MHz in baseband with 5 MHz spacing.

**Figure 21.**Scenario D: 11 interferers are present. They are located inside and outside of the swath. Locations range from −50° to 50° in 10° intervals. Transmitting frequencies range from −60 MHz to 25 MHz in baseband with 5 MHz spacing.

**Figure 22.**Capon spatial spectrum estimate of range-compressed range line with instantaneous SAR signal coming from 54° and RFI source at −20°.

**Figure 23.**The phase standard deviation of the residual error image of scenario A for different RFI-Noise-Ratios versus the incidence angle of the instantaneous SAR signal. The SNR is 37.36 dB. (

**a**) No RFI mitigation for N = 8, (

**b**) After RD-Frequency MVDR beamforming for N = 8, (

**c**) No RFI mitigation for N = 32, (

**d**) After RD-Frequency MVDR beamforming for N = 32.

**Figure 24.**The 3 sigma phase standard deviation error of the residual error image of Scenario A versus RFI-Noise-Ratio. The plots are shown for SNR = 0 dB (solid lines) and SNR = 37.36 dB (dashed lines). (

**a**) N = 2, (

**b**) N = 4, (

**c**) N = 8, (

**d**) N = 16.

**Figure 25.**The 3 sigma error increase of the residual error image of scenario A at a RFI-Noise-Ratio of 40 dB vs. the antenna array length. The plots are shown for SNR = 0 dB (solid lines) and SNR = 37.36 dB (dashed lines). (

**a**) Phase offset, (

**b**) Gain offset.

**Figure 26.**The phase standard deviation of the residual error image of scenario B for different RFI-Noise-Ratios versus the incidence angle of the instantaneous SAR signal. The SNR is 37.36 dB. (

**a**) No RFI mitigation for N = 8, (

**b**) After RD-Frequency MVDR beamforming for N = 8, (

**c**) No RFI mitigation for N = 32, (

**d**) After RD-Frequency MVDR beamforming for N = 32.

**Figure 27.**The phase standard deviation increase of the residual error image for scenario B at a RFI-Noise-Ratio of 40 dB. (

**a**) Error plotted versus incidence angle for N = 16 and for SNR = 0 dB (pale lines) and SNR = 37.36 dB (saturated lines), (

**b**) Error plotted versus incidence angle for N = 64 and for SNR = 0 dB (pale lines) and SNR = 37.36 dB (saturated lines), (

**c**) The percentage of the recovered SAR swath that is within the phase std. dev. limits of 20°, (

**d**) The percentage of the recovered SAR swath that is within the phase offset limits of 5°, (

**e**) The percentage of the recovered SAR swath that is within the absolute gain limits of 0.5 dB.

**Figure 28.**The phase standard deviation of the residual error image of scenario C for different RFI-Noise-Ratios versus the incidence angle of the instantaneous SAR signal. The SNR is 37.36 dB. (

**a**) No RFI mitigation for N = 8, (

**b**) After RD-Frequency MVDR beamforming for N = 8, (

**c**) No RFI mitigation for N = 32, (

**d**) After RD-Frequency MVDR beamforming for N = 32.

**Figure 29.**The 3 sigma phase standard deviation error of the residual error image of scenario C versus RFI-Noise-Ratio. The plots are shown for SNR = 0 dB (solid lines) and SNR = 37.36 dB (dashed lines). (

**a**) N = 2, (

**b**) N = 4, (

**c**) N = 8, (

**d**) N = 16.

**Figure 30.**The 3 sigma error increaser of the residual error image of Scenario C at a RFI-Noise-Ratio of 40 dB vs. the antenna array length. The plots are shown for SNR = 0 dB (solid lines) and SNR = 37.36 dB (dashed lines). (

**a**) Phase offset, (

**b**) Amplitude offset.

**Figure 31.**The phase standard deviation of the residual error image of scenario D for different RFI-Noise-Ratios versus the incidence angle of the instantaneous SAR signal. The SNR is 37.36 dB. (

**a**) No RFI mitigation for N = 8, (

**b**) After RD-Frequency MVDR beamforming for N = 8, (

**c**) No RFI mitigation for N = 32, (

**d**) After RD-Frequency MVDR beamforming for N = 32.

**Figure 32.**The phase standard deviation increase of the residual error image for scenario D at a RFI-Noise-Ratio of 40 dB. (

**a**) Error plotted versus incidence angle for N = 16 and for SNR = 0 dB (pale lines) and SNR = 37.36 dB (saturated lines), (

**b**) Error plotted versus incidence angle for N = 64 and for SNR = 0 dB (pale lines) and SNR = 37.36 dB (saturated lines), (

**c**) The percentage of the recovered SAR swath that is within the phase std. dev. limits of 20°, (

**d**) The percentage of the recovered SAR swath that is within the phase offset limits of 5°, (

**e**) The percentage of the recovered SAR swath that is within the absolute gain limits of 0.5 dB.

**Figure 33.**EcoSAR antenna mounted on a wing of the P3 airplane during the 2014 flight campaign (

**left**) and illustration of antenna positions on each wing (

**right**).

**Figure 34.**Flight lines of the collected EcoSAR data in Costa Rica in March 2014. Green and red boxes represent the image swaths on left and right respectively (

**left**). Geocoded EcoSAR HH image of Osa_T1 analysed in this section. Data was acquired on both sides of the flight track simultaneously (

**right**).

**Figure 35.**Averaged range-frequency spectrum of the available EcoSAR scene for the HH (blue) and VH (orange) image: (

**a**) Entire recorded spectrum with cut-off chirp due to too short receive window; (

**b**) Spectrum after hamming window is applied to keep common spectrum only.

**Figure 36.**Coherence Histograms for uncorrected, manually notched, RD-Time MVDR filtered and RD-Frequency MVDR filtered image for (

**a**) HH interferogram of left side, (

**b**) HH interferogram of right side, (

**c**) VH interferogram of left side, (

**d**) VH interferogram of right side. The normalized pixel count values reported on the left axis indicate the ratio of the number of pixels with the given coherence value to the total number of pixels.

**Figure 37.**Top to bottom: Intensity of focused SAR image, HH coherence with Scan-On-Receive and HH coherence with adaptive RD-Time MVDR for ambiguity and RFI suppression. Periodic coherence losses due to interference are visible in the uncorrected image and in the manually notched image. Red boxes mark areas of most evident coherence improvement after notching ambiguities from the other side. After the RFI mitigation, the periodic coherence losses disappear.

**Table 1.**Parameters used for the simulation of the Synthetic Aperture Radar (SAR) and Radio Frequency Interference (RFI) data.

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

Elevation Channels | 2 to 64 |

Channel Spacing | 0.5$\lambda $ |

Sample Frequency | 290 MHz |

Center Frequency | 435 MHz |

Pulse Bandwidth | 120 MHz |

Pulse Duration | 20 $\mathsf{\mu}$s |

Near Range Angle | 21° |

Far Range Angle | 60° |

Platform Altitude | 3.2 km |

Number of Pulses | 500 |

Backscatter Amplitude | Normal distribution with zero mean |

Backscatter Phase | Uniform distribution from 0° to 360° |

SNR | 0 dB, 37.63 dB |

RFI Type | Continuous Wave |

Algorithm | DBF Type | Placing of up to N-1 Nulls Per | RFI Type | Advantage | Disadvantage |
---|---|---|---|---|---|

Pulse-Wise | Elevation | per pulse | Both | Fast, for scenes without expected in-swath interference | Blind in-swath |

Segment-Wise Frequency | Elevation | per frequency bin | Continuous | Fast, for scenes without expected in-swath interference | Blind in-swath |

Range-Dependent Time | Elevation | per range line | Continuous | Recovers part of swath despite in-swath interference | Processing time |

Range-Dependent Frequency | Elevation | per range window and frequency bin | Continuous | Recovers part of swath despite in-swath interference. Beneficial for smaller antenna arrays. | Increased processing time |

Pulsed-RFI | Elevation | per range window | Pulsed | Suitable for pulsed RFI Scenarios. Recovers in-swath interference | Not detecting weak CW interference |

Doppler Dependent | Azimuth | per Doppler frequency bin | Continuous | Fast, for scenes without expected in-swath interference | Blind in-swath |

Doppler Dependent Frequency | Azimuth | per range-Doppler window | Both | Suitable for CW and pulsed in-swath interference | Processing time |

2D | Both | per range-Doppler window | Both | Capable of placing most notches and can recover largest swath percentage | Increased processing time |

**Table 3.**EcoSAR system parameters: Operational range (middle) and parameters of analyzed dataset (right).

Capability | Dataset | |
---|---|---|

Center Frequency | 435 MHz | 479 MHz |

Bandwidth | up to 120 MHz (H) up to 200 MHz (V) | 20 MHz |

Pulse Length | 1 $\mathsf{\mu}$s to 50 $\mathsf{\mu}$s | 2.5 $\mathsf{\mu}$s (H) 1.5 $\mathsf{\mu}$s (V) |

PRF | 100 Hz to 10 kHz | 500 Hz |

Range Resolution | 0.75 m | 7.5 m |

Azimuth Resolution | 0.5 m | 0.675 m |

Array Power | 40 Watts | 40 Watts |

Flight Altitude | 3.7 km | |

Platform Velocity | 136 m/s | |

Physical Baseline | 25 m | |

Antenna elements | 8 per antenna | |

Antenna element spacing | 0.29 cm (0.46$\lambda $) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Bollian, T.; Osmanoglu, B.; Rincon, R.; Lee, S.-K.; Fatoyinbo, T.
Adaptive Antenna Pattern Notching of Interference in Synthetic Aperture Radar Data Using Digital Beamforming. *Remote Sens.* **2019**, *11*, 1346.
https://doi.org/10.3390/rs11111346

**AMA Style**

Bollian T, Osmanoglu B, Rincon R, Lee S-K, Fatoyinbo T.
Adaptive Antenna Pattern Notching of Interference in Synthetic Aperture Radar Data Using Digital Beamforming. *Remote Sensing*. 2019; 11(11):1346.
https://doi.org/10.3390/rs11111346

**Chicago/Turabian Style**

Bollian, Tobias, Batuhan Osmanoglu, Rafael Rincon, Seung-Kuk Lee, and Temilola Fatoyinbo.
2019. "Adaptive Antenna Pattern Notching of Interference in Synthetic Aperture Radar Data Using Digital Beamforming" *Remote Sensing* 11, no. 11: 1346.
https://doi.org/10.3390/rs11111346