Front. Phys.Frontiers in PhysicsFront. Phys.2296-424XFrontiers Media S.A.106347410.3389/fphy.2022.1063474PhysicsOriginal ResearchInfluence of sweep interference on satellite navigation time-domain anti-jammingLi et al.10.3389/fphy.2022.1063474LiBaiyu12QiaoJia2LuZukun2*YuXiaoyou3*SongJie2LinBaojun4LiXianghao21Scientific Research Department, National University of Defense Technology, Changsha, China2College of Electronic Science and Technology, National University of Defense Technology, Changsha, China3College of Computer Science and Electronic Engineering, Hunan University, Changsha, China4Innovation Academy for Microsatellites of Chinese Academy of Science, Shanghai, China
Edited by:Siming Liu, Southwest Jiaotong University, China
Reviewed by:Youfeng Cheng, Southwest Jiaotong University, China
Changli Li, Nanjing University of Information Science and Technology, China
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The global navigation satellite system (GNSS), represented by global positioning systems (GPS), is widely used in various civil and military fields and represents an essential basis for space-time information services. However, the radar signals partially overlap with the frequency band of satellite navigation signals, seriously affecting the normal reception of weak satellite navigation signal power. To further improve anti-jamming with sweep interference in the time domain, this paper focuses on the sweep interference scenario, studies the influence of the sweep interference on time-domain-adaptive anti-jamming, and proposes a timing reset based on the adaptive filter. The proposed method can effectively deal with the influence of sweep interference on time-domain-adaptive anti-jamming and can suppress interference and protect signals at the same time. Simulation experiments verify the effectiveness of the anti-jamming method proposed in this paper. Under the typical simulation scenarios, the influence time of the frequency sweep interference on the navigation signal is less than 1 m when the timing reset period is 1 m, which is significantly reduced compared to traditional methods. The proposed anti-jamming method is of great significance for improving the survivability of satellite navigation receivers in sweep interference scenarios.
global position systems (GPS)sweep interferencetime domain adaptive anti-jammingtiming resetadaptive filer62003354National Natural Science Foundation of China10.13039/5011000018091 Introduction
The Global Navigation Satellite System (GNSS) is satellite-based all-weather navigation, positioning, and timing system [1–3]. At present, the leading satellite navigation systems used around the world are the US GPS (Global Positioning System), the Chinese Beidou-3 global satellite navigation system, the Russian GLONASS (Global Navigation Satellite System), and the European Galileo system [4–7]. With the deterioration of the electromagnetic environment and the escalation of interference complexity, including concepts such as electronic warfare and navigation warfare, which have received a great deal of attention in modern combat systems, anti-jamming has become an essential function of satellite navigation receivers [8–11].
The anti-jamming technologies comprise the time/frequency domain anti-jamming technology, based on a single antenna, and space-domain anti-jamming technology, based on the antenna array [12, 13]. Space-domain anti-jamming technology can also be combined with other domain algorithms to form space-time and space-frequency technology. Antenna array anti-jamming technology uses multiple antenna array elements and vector weighting to cancel interference according to the difference in the signal direction angle and the interference direction angle [14, 15]. The single antenna has irreplaceable advantages in some application backgrounds compared to array anti-jamming technology, mainly reflected by the small size and convenience of the single antenna. The antenna can be customized according to the shape of the installation platform [16–19].
Time-domain anti-jamming technology based on linear estimation represents basic adaptive filtering theory [20]. It occupies fewer resources in developing and implementing the Field-Programmable Gate Array (FPGA) and other hardware and can be easily modularized. It can effectively suppress traditional narrowband interference, such as narrowband interference and sweeping-frequency interference. However, satellite navigation signals are usually in the L-band. Ground air traffic radars, active earth exploration satellites, satellite-to-ground mobile communication satellites, and aviation radio navigation, among others, are also in this frequency band [13, 21–23]. If the same frequency is used between different systems, there will be mutual interference between the different systems. For example, the air traffic control radar uses chirp signals, which overlap with the frequency point of the satellite navigation signal. Due to the weakness of the satellite navigation signal, air traffic control radar has a severe impact on the navigation signal. Due to the particularity of the air traffic radar signal, it has not received much attention from scholars. In an experiment in 2021, the author team found that sweeping-frequency interference not only deteriorates the performance of the air traffic control radar’s satellite navigation receiver but also seriously impacts time-domain adaptive anti-jamming performance.
Sweeping-frequency interference is a type of narrowband interference that takes place quickly. Traditional methods believe that time-domain-adaptive anti-jamming can effectively solve frequency sweep interference. However, according to our measurements in 2021, this is not the case, and we have reproduced the experimental scene. The sweeping-frequency interference will lead to the degradation of the time domain-adaptive anti-jamming performance. This paper mainly analyzes the mechanism of this phenomenon and proposes solving the time-domain-adaptive anti-jamming problem in the sweeping-frequency interference scenario.
The structure of this paper is as follows: Section 2 introduces the mathematical models studied in this paper, including the mathematical models of time-domain anti-jamming and sweeping-frequency interference. Section 3 analyzes the influence of sweeping-frequency interference on time-domain anti-jamming and provides theoretical analysis and simulation verification. Section 4 proposes a time-domain anti-jamming method under the condition of sweeping-frequency interference and verifies the proposed method via simulation. Section 5 builds an experimental verification platform and uses experimental instruments to verify the results analyzed in this paper and the proposed method. Finally, the conclusions of this paper are presented.
2 Mathematical model2.1 Time domain adaptive anti-jamming
In the satellite navigation receiver, the antenna receives the navigation signal transmitted from the satellite and preprocesses the navigation signal through the radio frequency channel. These preprocesses include low-noise amplification, frequency mixing, filtering, intermediate frequency amplification, and other links, which can be collectively referred to as analog signal processing. Then, the analog signal is converted into a digital signal through an analog-to-digital converter (ADC). Digital signal processing is usually carried out in the FPGA and Digital Signal Processor (DSP). Signal flow is carried out in the FPGA, and the DSP is responsible for signal control and scheduling. The receiver functions include digital down-conversion (DDC), anti-jamming, acquisition, tracking, and other types of processing, and, finally, output PNT information. Anti-jamming processing is part of digital signal processing. The framework of the satellite navigation receiver is shown in Figure 1.
Satellite navigation receiver architecture.
The structure of the single antenna-based time-domain-adaptive anti-jamming filter is shown in Figure 2 [24, 25]. where xn is the input baseband signal, yn is the anti-jamming output signal, and en is the error signal processed by the anti-jamming process.
The time-domain anti-jamming filter structure.
The conventional adaptive algorithms for time-domain anti-jamming include the Least Mean Square (LMS) algorithm, which is based on the Minimum Mean Square Error (MMSE) criterion, and the Least Squares (LS) algorithm, which is based on the Recursive Least Squares (RLS) algorithm [26–28]. Among them, the LMS algorithm proposed by Widrow and Hoff in 1957 has the advantages of simple principles and no need for complex matrix inversion, and this method is widely used [29]. This paper only analyzes the LMS algorithm.
The output of the filter is set as yn. Then, we can obtain:yn=wHnxnwhere wn represents the filter weight vector at time n, and xn represents the sampled data vector input to the filter.
The desired signal of the filter is set as dn. Then, the error of the filter en can be expressed asen=dn−yn=dn−wHnxn
The iterative formula for the weight coefficient of the LMS algorithm is as follows:wn+1=wn+μxne*nwhere e*n is the conjugate transpose of en. μ is the step factor, and its value must satisfy0<μ<2λmaxwhere λmax is the maximum eigenvalue of the correlation matrix, and the algorithm can only be converged when the step size factor satisfies Formula (4).
The filter structure used in this paper is a commonly used odd-order bilateral tap transversal filter; that is, it is a filter with an interpolation structure. Constraining the middle tap coefficient always to be one ensures that the weight vector does not converge to all zeros. The filter architecture is shown in Figure 3 [30–33]. Where z−1 denotes that the signal is delayed by one sampling point, w denotes the weight coefficient of the anti-jamming filter, and w* denotes the conjugate transpose of w.
The architecture of the time-domain anti-jamming filter.
2.2 Mathematical model of sweeping-frequency interference
Sweeping-frequency interference is a commonly used modulation method in the radar field, and its complex signal expression is as follows [34]:xt=exp−j2πfttwhere ft represents the frequency of the sweeping-frequency interference, which changes with time. Chirp is a typical swept frequency that varies linearly with time.
Assume that the sampling rate is 16.25 MHz, the frequency change range is linear from 0.05 MHz to 0.1 MHz, and the frequency change rate is 0.16 GHz/s. One cycle of the sweeping-frequency interference time-domain waveform is shown in Figure 4, and it can be seen that the frequency changes linearly [35].
The time-domain waveform of sweeping-frequency interference.
Assume that the sampling rate is 16.25 MHz, the frequency change interval is 1 MHz, and the frequency change rate is 1 MHz/ms. Linear frequency modulation includes two frequency modulation methods: continuous frequency modulation (CFM) and discontinuous frequency modulation (DFM) [36, 37]. For CFM, the frequency increases linearly from 3 Mhz to 4 MHz in the first millisecond and from 12 Mhz to 13 MHz in the 10th millisecond. In the case of DFM, the frequency remains 3 MHz in the first millisecond and becomes 4 MHz at the beginning of the second millisecond; in the 10th millisecond, the frequency remains 12 MHz and becomes 13 MHz at the beginning of the 11th millisecond (The beginning of the 11th millisecond not shown in the Figure 7B).
The frequency variation expressions of the CFM and DFM are as follows:fCFMt=ktfDFMt=kntwhere k represents the slope, which is the rate of change of the frequency with time. t indicates the continuous time. n represents time in non-continuous continuous increments, and its mathematical expression is as follows:nt=am−1am−1≤t<amm=1,2,3,...where a is the duration of frequency discontinuity.
The spectral characteristics of CFM and DFM are shown in Figures 5, 6, respectively. Each type of swept interference shows the spectrogram at 10 different times, and each interval is 1 m. The spectral characteristics can be shown via Power Spectral Density (PSD).
Frequency domain characteristics of CFM interference.
Frequency domain characteristics of DFM interference.
To express the frequency domain characteristics in the different periods more clearly, Figure 7 shows the time-frequency diagram of the generated sweeping-frequency interference data [38, 39]. Among them, the x-axis represents frequency, the y-axis represents time, and different colors represent different signal amplitudes. Red represents the most robust signal amplitude, and blue represents the weakest signal amplitude. It can be seen that the frequency change is consistent with the simulation settings. Figures 7A, B represent chirp signals, where the frequency of the signal changes linearly over time. Figure 7A shows the CFM, whose frequency changes are continuous, and Figure 7B shows the DFM, whose frequency changes are discontinuous, showing a step-by-step growth trend consistent with the expected effect.
Time-frequency domain characteristics of sweeping-frequency interference. (A) CFM (B) DFM.
3 Influence of sweeping-frequency interference on time-domain anti-jamming
In scenarios applying a satellite navigation receiver, the signal power is about 30 dB lower than the noise power, and the interference power is more than 10 dB stronger than the noise power. Therefore, the reference signal of the time-domain-adaptive filter is usually set to 0, which is set to the minimum power guideline. On the one hand, the noise will not be suppressed under the constraint of the weight vector. On the other hand, the interference signal belongs to the narrow band in the bandwidth and can be suppressed by the adaptive filter.
Suppose that the swept interference hops from frequency f1 to frequency f2. After time-domain-adaptive anti-jamming, a null is formed at the frequency point f1. When the interference frequency jumps to f2, the anti-jamming weight vector at the frequency point f1 is used as the baseline, and then a null is formed for the interference at the frequency point f2. Since the minimum power criterion is adopted, when the interference frequency hops from frequency f1 to frequency f2, the null at frequency f1 will still be retained, and a null will be formed at frequency f2. If the interference frequency is always frequency hopping or sweeping within the bandwidth of the navigation signal, then the spectrum will form several nulls after adaptive anti-jamming processing.
Figures 5, 6 show sweeping-frequency interference scenarios using the traditional time-domain-adaptive anti-jamming method. Figures 8, 9 show the spectrum after anti-jamming in each period. Time-domain-adaptive anti-jamming can form nulling at the interference frequency. As the interference frequency changes, the nulls at the original interference frequencies are still retained. The more the interference frequency changes, the more nulls are formed and the greater the equivalent effect on the navigation signal.
Spectral characteristics after anti-jamming (CFM).
Spectral characteristics after anti-jamming (DFM).
The time-frequency analysis was performed on the data after anti-jamming to more clearly analyze the time-domain-adaptive anti-jamming process caused by sweeping-frequency interference. The time-frequency analysis results are shown in Figure 10. The time-frequency analysis of the sweeping-frequency interferenceshows that although the interference frequency has changed, there is still a null at the original interference frequency. When the interference frequency scans the entire signal bandwidth, several nulls appear in the signal spectrum, disturbing the signal spectrum structure and affecting the navigation signal demodulation.
Time-frequency domain characteristics after anti-jamming. (A) CFM (B) DFM.
4 Time-domain anti-jamming method for sweeping-frequency interference
Under the conditions of the above simulation test scenarios representing continuous frequency modulation and discontinuous frequency modulation, taking the first weight coefficient of the weight vector as the analysis object, the modulus value of the weight coefficient in the continuous and discontinuous frequency modulation scenarios is shown in Figure 11 [40–42]. For the continuous frequency modulation interference, the change in the weight coefficient is relatively gentle, and there is no jumping point.
However, for discontinuous frequency modulation, due to the frequency hopping of the interference, the weight coefficient generated by the adaptive filter also hops along with it. The weight coefficient experiences a relatively large jump when the interference frequency changes. In addition, even if the weight coefficients jump, the adaptive filter will quickly make the weight coefficients converge [43, 44]. In the context of this experiment, the convergence time is about 2us. For the reception of satellite navigation signals, data anomalies of this order of magnitude can be ignored.
Through the above analysis, the convergence time of the adaptive filter is negligible compared to the reception of the satellite navigation signals, and the abnormal anti-jamming processing shown in Figures 8–10 is caused by past interference; then, the filter can be reset according to the time to solve the problem caused by the sweeping-frequency interference to the adaptive anti-jamming filter. Figure 12 demonstrates the time-domain anti-jamming algorithm flow chart based on timing reset.
Algorithm flow chart based on timing reset.
Set the timing reset period to 1 m. According to the above simulation scenario, the weight coefficient value under continuous frequency modulation and discontinuous frequency modulation is shown in Figure 13. The results demonstrate that the improved time cost is meager, the convergence time is less than 1us, and the impact on the quality of the navigation signal is negligible.
Impact of timing reset on adaptive convergence. (A) CFM (B) DFM.
Under the experimental conditions shown in Figures 8, 9, a timing reset method for the adaptive anti-jamming filter is adopted, and the timing reset period is 1 m. In the continuous frequency modulation and discontinuous frequency modulation scenarios, the spectrum after anti-jamming is shown in Figures 14, 15.
Spectral characteristics after anti-jamming based on timing reset (CFM).
Spectral characteristics after anti-jamming based on timing reset (DFM).
Compared to Figures 8, 9, the experiment in this section shows that the spectrum has been significantly improved after anti-jamming, and only a null is formed at the interference frequency point, effectively protecting the signal energy and demonstrating an anti-jamming effect.
In the case of continuous frequency modulation and discontinuous frequency modulation interference, a time-domain-adaptive anti-jamming method based on timing reset is adopted. The time-frequency analysis was performed on the data after anti-jamming, and the results are shown in Figure 16 to describe the process of adaptive anti-jamming more clearly.
Analysis of time-frequency characteristics after anti-jamming based on timing reset. (A) CFM (B) DFM.
Compared to Figure 10, the method proposed in this paper only forms nulls around the interference frequency points, and the past interference will not affect the existing interference suppression for a long time, showing good anti-jamming performance.
In order to demonstrate the performance superiority of the improved algorithm more clearly, the time-frequency analysis and PSD nulling width after anti-jamming is demonstrated and compared with the proposed and traditional method. Under different discontinuous frequency modulation interference scenarios, the time-frequency analysis is shown in Figure 17, and the PSD nulling width is presented in Table 1. The interference bandwidth is 0.5 MHz, and the sweeping frequency speed is 1 MHz/ms. The null width of 10 m is continuously observed, and the timing reset period is 1 m.
Comparison of null width of different anti-interference methods.
Jnr (dB)
Method
Time slot (ms)
1st
2st
3st
4st
5st
6st
7st
8st
9st
10st
40
Traditional
1.14
2.17
2.36
1.97
2.48
2.04
2.29
2.04
1.77
1.79
Proposed
1.15
1.14
1.25
1.25
1.32
1.24
1.20
1.18
1.17
1.24
50
Traditional
1.18
2.28
2.42
2.54
2.12
2.27
2.44
2.04
1.95
1.84
Proposed
1.26
1.22
1.28
1.23
1.21
1.25
1.26
1.12
1.15
1.19
60
Traditional
1.43
2.44
3.12
3.89
4.17
4.44
3.88
3.61
3.97
3.76
Proposed
1.37
1.44
1.30
1.40
1.51
1.43
1.20
1.39
1.50
1.44
The results in Figure 17 show that the interference power is inconsistent under different interference signal ratio conditions, but the anti-jamming performance of the proposed algorithm is always better than the traditional algorithm.
The results of Table 1 show that the PSD nulling width of discontinuous frequency modulation interference after traditional anti-interference fluctuates significantly, the maximum nulling width of which is up to 4.44 MHz. The nulling width of the improved algorithm is relatively stable, and the steady-state error is less than 0.2 MHz. It shows that the proposed algorithm only forms a null in the interference frequency band and will not reduce the navigation signal quality.
In traditional methods, when time-domain-adaptive anti-jamming faces sweeping-frequency interference, the frequency of the sweeping-frequency interference changes in real-time, and it is difficult for time-domain-adaptive anti-jamming to adapt to the frequency change. The time-domain-adaptive anti-jamming algorithm usually adopts the power invert criterion. When the frequency of the sweeping interference changes in real-time, the PSD nulling width after the anti-jamming increase, failing the time-domain-adaptive anti-jamming algorithm. According to the simulation experiment, the convergence time of the adaptive algorithm is negligible relative to the reception of the navigation signal, and the sweeping frequency interference affects the entire signal spectrum. The influence of sweeping-frequency interference on the signal spectrum is closely related to the timing reset time. In the simulation scenario of this paper, the influence time of the frequency sweep interference is less than 1 m, and the influence of the frequency sweep interference is compared to the traditional method, demonstrating a substantial reduction. Therefore, this paper proposes an anti-jamming method based on the filter timing reset, which can solve the problems caused by frequency sweep interference. The anti-interference null is always generated in the interference frequency band without affecting the navigation signal, significantly improving the anti-jamming performance of sweeping-frequency interference.
5 Conclusion
This paper proposes a time-domain-adaptive anti-jamming processing method for satellite navigation receivers in the context of the sweeping-frequency interference scenario. This method also solves the problem of sweeping-frequency interference causing the time-domain-adaptive anti-jamming method to fail. It is difficult for the traditional time-domain-adaptive anti-jamming method to adapt to the changes in sweeping-frequency interference. According to the problem of it being difficult for the traditional method to adapt to the change in the interference frequency, a time-domain-adaptive anti-jamming processing method based on the timing reset weight vector was designed. The analysis shows that a time-domain anti-jamming method based on the minimum power criterion cannot suppress sweeping-frequency interference. The simulation verification shows that it is difficult for the traditional method to suppress the sweeping-frequency interference, and even the anti-jamming weight coefficient is disordered. The anti-jamming processing method proposed in this paper reduces the problems caused by the change in the interference frequency. The carrier-to-noise ratio during simulation shows promising results and can improve the anti-jamming performance.
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
Author contributions
BL and JQ performed the theoretical study, conducted the experiments, processed the data and wrote the manuscript. ZL and XY designed the system, provided research suggestions and revised the manuscript. JS and BL helped in performing the experiments. XL provided the experiment equipment and suggestions for the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by the National Natural Science Foundation of China (No.62003354).
The authors would like to thank the editors and reviewers for their efforts to help the publication of this paper.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
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