RFI Detection for Multichannel HRWS SAR System Based on Spatial Cross Correlation

Yanyang Liu, Xiangdong Li, Junli Chen, Mingliang Tao

Abstract: Multichannel high-resolution and wide-swath (HRWS) imaging is an advanced digital beamforming technique for future synthetic aperture radar (SAR) systems.However, radio frequency interference (RFI) is a critical concern for HRWS SAR missions, which distorts measurements and produces image artifacts.In this paper, the spatial cross-correlation coefficients of multichannel HRWS SAR signals are investigated for RFI detection.It is found when the two channels are correlated, RFI-polluted areas present lower coherence values than non-polluted areas in the same scenarios, which makes previous methods fail.Further, this paper studies the case of two fully decorrelated channels to maximize the coherence difference among RFI and target echoes, and RFI detection is realized by exploiting the anomaly value of coherence.Experimental results of real airborne multichannel SAR data demonstrate that the RFI can be detected successfully.

Keywords: synthetic aperture radar (SAR); high-resolution wide-swath (HRWS); radio frequency interference (RFI); interference detection and mitigation; coherence

1 Introduction

Spaceborne synthetic aperture radar (SAR)plays an important role in disaster emergency response, environmental monitoring as well as reconnaissance, and security-related applications.Meanwhile, with the advancement of radio networks and systems, radio frequency interference(RFI) has become a major issue in SAR imaging,especially in low-frequency bands like P and L bands.It poses significant obstacles to raw data collection, image formation, and subsequent interpretation processing [1].

In the past years, most of the SAR systems have been single channels and deal with RFI issues via various signal processing techniques[2-5].Modern spaceborne SAR systems exploit the multichannel in azimuth to overcome the minimum-antenna-area constraint to obtain large swath width and high azimuth resolution, which is referred to as the high-resolution and wideswath (HRWS) SAR system.It emits a signal with pulse repetition frequency (PRF) less than the Doppler bandwidth, while the digital beam forming (DBF) technique is adopted to reconstruct the unambiguous spectrum in the Doppler bandwidth using the multichannel received echo [6].

Investigations for RFI detection and mitigation techniques in multichannel HRWS SAR systems are emerging.Rosenberg pioneered the research on hot-clutter interference via optimal slow and fast-time space-time adaptive processing (STAP) [7].Huang et al.proposed a narrowband RFI mitigation scheme for HRWS SAR systems by employing an image-domain sparse regularization and solving the low-rank recovery problems [8].

As the RFI and SAR signals originate from different spatial directions, it is applicable to orient antenna pattern nulls towards sources of RFI for mitigation using the adaptive DBF technique for the multichannel HRWS SAR [9, 10].However, the DBF method would fail when there is no auxiliary channel.The detection method based on the cross-correlation between two receiving channels is firstly proposed in [11, 12],which assumed that the coherence among different channels with RFI is higher than that without RFI.However, it is found that the coherence among receiving channels would be decreased by the RFI in some scenarios.

Motivated by this, the RFI detection scheme proposed in [11, 12 ] by exploiting the spatial coherence among receiving channels is further studied.The main contributions of this paper lie on:

1) The effect of RFI on the spatial coherence among channels is analyzed.The variation relationship of cross-correlation coefficients with the signal-to-interference ratio (SIR) and the differential interferometric phase are firstly derived and analyzed.

2) A two-step RFI detection and mitigation scheme using fully decorrelated channels is proposed to effectively eliminate the pixels corresponding to the coherence anomalies.The coherence between these two channels would be dominated by the RFI and thus can be detected by exploiting the anomaly value of coherence.

3) The effectiveness of the proposed method is verified with real airborne multichannel SAR data with simulated RFI, which is applicable to existing and future planned two-channel SAR systems.

This paper is organized as follows.Section 2 provides a brief introduction to the multichannel HRWS SAR signal model and derivation of the coherence among receiving channels.Section 3 presents the proposed RFI detection scheme based on spatial cross-correlation in detail.In Section 4, experimental results of simulated multichannel SAR data are provided, and Section 5 concludes this paper.

2 Theory and Problem Formulation

2.1 Signal Model of Multichannel HRWS SAR Signal

The geometry of the multichannel HRWS SAR system is shown in Fig.1, where the origin of the coordinate frame is located at the phase center of the reference channel at azimuth timeη=0.The spaceborne SAR flies along theX-axis with velocity ofvs.Z-axis points up away from the Earth’s center, andY-axis points to the left, composing the orthogonal right-handed frame.Here, a multichannel HRWS SAR system withMchannels separated bydin azimuth is investigated.

Fig.1 Illustration of acquisition geometry for a multichannel HRWS SAR

To achieve high-resolution imaging in azimuth, a broad transmission beam is created by all antennas, and a wideband signal is employed, while all channels receive the echoes simultaneously [6].This makes it easier to be interfered by other terrestrial radio systems like ground-based radars.In the presence of RFI, the SAR echo received by them- th channel in azimuth-time and range-frequency domain can be expressed as

whereηdenotes the azimuth time,fdenotes the range frequency.sm,xmandnmrepresent the useful signal, interference, and system noise,respectively.

The RFI received by them-th channel can be expressed as the time-delayed copy received by the first channel

whereθRFIrepresents the arrival angle of RFI,crepresents the speed of light.

To improve the anti-jamming capability, it is applicable to orient antenna pattern nulls towards sources of RFI to mitigate the RFI in the Doppler frequency domain using the adaptive DBF technique for the multichannel HRWS SAR with auxiliary channels.Here, the auxiliary channel refers to the condition that PRF satisfies the following relation

where PRF is the pulse repetition frequency, andBais the Doppler bandwidth.

2.2 Effect of RFI on the Spatial Coherence between Channels

The spatial coherence between the SAR signals received by the first channel and them-th channel can be expressed as

with

where SIRmand SINRmrepresent the signal-tointerference ratio and signal-to-interference and noise ratio, respectively.

Assume the receiving channels have equal SIR and SINR, and thus Eq.(11) can be simplified as

According to the above mathematical derivations, the interferometric coherence among channels would be affected by the RFI.In [11, 12],the correlation coefficient for neighboring receivers is examined.It is found that the RFI-polluted parts have a correlation coefficient larger than 0.8 while non-polluted parts have a value below 0.6.However, the effect of RFI on coherence is much more complicated, and it is rather difficult to detect the RFI when the useful signals are highly correlated, as shown in the analysis above.

Fig.2 illustrates the variation of cross-correlation coefficients varying with the SIR and the differential interferometric phase between the useful signal and RFI (ϕs1,sm-ϕx1,xm) under three particular cases, in whichγs1,smequals 0.6,0.25 and 0 under signal to noise ratio (SNR)=10 dB, respectively.The coherence between two receiving channels without RFI is calculated as 0.545, 0.23, and 0 for these three cases, respectively.

1) Case 1:γs1,sm=0.6

The coherenceγ1,mwith RFI is higher than that without RFI in most situations, whileγ1,mis lower in some situations that concentrate the distribution at the right-top corner in Fig.2 (a).These areas are with higher SIR and the majority of the phase difference (ϕs1,sm-ϕx1,xm) are larger than 90°.This increases the difficulty of setting an appropriate threshold to detect and mitigate the RFI.

2) Case 2:γs1,sm=0.25

3) Case 3:γs1,sm=0

As shown in Fig.2(c), the coherenceγ1,mwill be determined only by the SIR and higher than zero when RFI exists.

Fig.2 Variation of cross-correlation coefficients with different SIR and differential interferometric phases: (a)γs1,sm =0.6 ; (b) γs1,sm =0.25 ; (c)γs1,sm =0

From the simulation analysis above, it is shown that the RFI-polluted parts may have a lower correlation coefficient compared with the non-polluted parts in some cases.Therefore, the underlying assumption of the proposed scheme is the existence of two fully decorrelated channels,which can be determined by using Eq.(8).

3 Detection Scheme

In practice, the coherence estimateγˆ1,mis obtained by averaging the samples

whereNis the number of samples,k0is the initial azimuth bin to estimate the coherence.The probability density function of the coherence magnitude estimator can be expressed as a function of the absolute value of the true coherence and the number of independent samples as [14]

whereγis the coherence between channales,Lis the multilook number,pFqis the generalized hypergeometric function.To detect the RFI, the estimated coherence is compared with a critical value under a confidence level of (1-α).TakeL=50 and (1-α)= 99.5% for example, and the detection threshold of the useful signal coherence is 0.32.

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Fig.3 Flowchart of the proposed RFI detection scheme for the HWRS SAR system

Fig.3 illustrates the flowchart of the proposed RFI detection scheme for the HWRS SAR system.After range compression, the SAR data are transformed into the range-frequency azimuthtime domain.According to previous study [15],the RFI environments could be categorized into the time-stationary narrow-band (TSNB) and time-varying wide-band (TVWB) interference.Further, a two-step RFI detection and mitigation filter is applied in parallel.As initial RFI detection is done using statistical hypothesis testing procedures, there are some data samples to be incorrectly classified as RFI.Here, the maskmerging method introduced in [15] is adopted to denoise initial detections.Finally, the notch filter is applied to mitigate the RFI and obtain RFI-clear raw data.

1) TSNB Interference Detection

Due to the temporal coherence of TSNB RFIs, they can form peaks in the range spectrum,and cause the SIR in the coherence estimation window along the frequency to be larger than the SIR along the azimuth [15].Therefore, the coherence coefficients estimated by the samples in the azimuth are larger than those in the range frequency.Accordingly, to detect TSNB RFI, the coherence between them-th channel and the first channel is estimated byNsamples in azimuth dimension.

2) TVWB Interference Detection

Due to their wide bandwidth nature, TVWB would make SIR in the coherence estimation window along azimuth larger than that along range [15].Therefore, the coherence coefficients estimated by the samples in the range frequency are larger than that in the azimuth.Accordingly,to detect TVWB RFI, the coherence between them-th channel and the first channel is estimated byNsamples in range frequency dimension.

wherel0is the initial frequency bin to estimate the coherence, Δθrepresents the phase gradient of the interferogram.

4 Experiments

To demonstrate the validation of the proposed RFI detection scheme, a real SAR data collected from an experimental C-band 5-channel SAR system is adopted.The main parameters of the system are listed in Tab.1.This multichannel HRWS SAR system works in the side-looking and Scan-SAR mode.The distribution of the antennas is along azimuth, in which the middle antenna transmits chirp signal, and all of the antennas receive echoes.The speed of the aircraft is about 110 m/s, and the Doppler bandwidth is approximately 958 Hz.Since the PRF of the system is only 200 Hz, the Doppler ambiguity number is approximately five.

Tab.1 System parameters for real measured data

The original SAR data is clean data without RFI.To acquire multichannel SAR data with RFI, the TSNB and TVWB RFI is artificially injected into the original SAR data for demonstration.The parameters of RFIs are listed in Tab.2.

The estimated correlation between them-th channel and the first channel is shown in Fig.4.Fig.4 (a) and Fig.4 (b) represent the estimated coherence along azimuth between the first channel and the 2nd and 5th channel, respectively.Fig.4 (c) and Fig.4 (d) represent the estimated coherence along range between the first channel and the 2nd and 5th channel, respectively.It is shown that the presence of RFI would lead to obvious anomalies in the coherence map, which is consistent with the previous theoretical derivations and beneficial for subsequent RFI detection.

Tab.2 RFI parameters in the experiments

Fig.5 compares the imaging results for the simulated dataset.Fig.5(a) depicts the imaging results without RFI, and Fig.5(b) depicts the image with strong RFI strip artifacts, which obscure the region of interest.Fig.5(c) shows the imaging results after applying the proposed detection scheme and notch filtering.It is shown that the RFI artifacts have been clearly eliminated and well recover the underlying land covers.

5 Conclusion

RFI poses a significant threat to HRWS SAR systems with biased echo measurements and image artifacts.This paper investigates the spatial decorrelation phenomenon among channels due to the presence of RFI.In this context, two fully decorrelated channels are employed to detect RFI, and a two-step RFI detection scheme is applied to detect TSNB and TVWB interference.Experimental results validate the effectiveness of the analysis and the proposed scheme.

Fig.4 Estimated sample coherence among channels: (a) the estimated coherence along azimuth between the first and the 2nd channel; (b) the estimated coherence along azimuth between the first and the 5th channel; (c) the estimated coherence along range between the first and the 2nd channel; (d) the estimated coherence along range between the first and the 5th channel

Fig.5 Comparison of imaging results: (a) original SAR image; (b) SAR image with RFI; (c) SAR image after RFI mitigation by the proposed scheme