An adaptive hybrid blanking algorithm to mitigate the DME pulse interference on BDS B2a receivers

The performance of BeiDou navigation satellite system B2a signal acquisition and tracking is affected when co-existing with the distance measuring equipment (DME) pulse signals in the same frequency band. To mitigate the detrimental impacts of DME interference on the B2a receiver, an adaptive hybrid blanking algorithm is proposed, which contains time–domain interference detection and frequency–domain interference suppression modules. With flexible configurations, the proposed algorithm is capable of optimizing the interference mitigation according to the strength of the detected DME signals indicated by jammer-to-noise ratio (J/N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{J}}/{\text{N}}$$\end{document}). A laboratory testbed is first built to collect simulated B2a data contaminated by DME interference. An empirical model is established to relate J/N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{J}}/{\text{N}}$$\end{document} with kα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{\alpha }$$\end{document}, which is the key parameter of the notch filter that affects the performance of the proposed algorithm. To verify the performance of the proposed algorithm, static and dynamic outdoor experiments are conducted near 2 DME stations close to the Beijing Capital International Airport. The carrier-to-noise density ratio (C/N0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{C}}/{\text{N}}_{0}$$\end{document}) and code tracking errors are analyzed with different mitigation methods applied, including pulse blanking, notch filter and hybrid blanking. Results show that the proposed adaptive hybrid blanking algorithm can achieve the maximum C/N0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{C}}/{\text{N}}_{0}$$\end{document} and minimum code tracking error. In particular, when applying the proposed algorithm, the mean C/N0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{C}}/{\text{N}}_{0}$$\end{document} is improved by up to 3.32 dB compared with that when no mitigation method is applied. This study contributes to the development of novel DME interference mitigation approaches to improve the robustness of airborne GNSS receivers.


Introduction
Civil aviation relies heavily on the position, velocity and time (PVT) services provided by the global navigation satellite system (GNSS) operational in L-band.However, the L-band spectrum is quite crowded because of the occupation of various terrestrial aviation systems, such as distance measuring equipment (DME) and tactical air navigation system (TACAN).Due to the fact that the signal powers of terrestrial systems are much stronger than GNSS signals when arriving at airborne GNSS receivers, GNSS receivers are compromised by these signals transmitted on the same or nearby frequency band (Ioannides et al. 2016).
According to RTCA (RTCA 2004), DME and TACAN ground station emissions are identified as the main thread to L5/E5.The effects of DME pulse interference on GNSS L5/E5a as well as BeiDou navigation satellite system (BDS) B2a receivers are widely discussed in the literature (Bastide et al. 2004;Gao et al. 2007;Garcia-Pena et al. 2020;Huang et al. 2022).Various pulse interference mitigation methods for L5/E5 receivers have been proposed, which include the time-domain, frequency-domain and time-frequency approaches, etc.
The time-domain method contains pulse blanking.Analog technology and digital version of pulse blanking were first proposed by Hegarty et al. (2000) and Grabowski and Hegarty (2002), respectively.This algorithm mitigates pulse interference by zeroing out the samples with amplitudes exceeding the pre-determined threshold.It was recommended by the Interagency GPS Executive Board (IGEB) to minimize the impact of DME on GPS L5 receivers (Kim and Grabowski 2003).Because of its simplicity and effectiveness, pulse blanking has been widely used to mitigate DME 164 Page 2 of 15 interference and other types of interference, such as swept jamming (Borio 2016).However, the bell-shaped structure of the DME pulse and the modulation over the pulse duration make it impossible to eliminate all the interference components, thus leading to an increased noise floor (Bastide et al. 2004).Additionally, those useful GNSS signals covered by DME pulses are also eliminated at the same time.Considering these disadvantages, pulse blanking is more applicable to situations where the pulse interference has a low duty cycle.
The frequency-domain methods mainly include frequency-domain adaptive filtering (FDAF) and notch filter.FDAF estimates the spectral features of the incoming signal by performing a fast fourier transform (FFT) and filters out the interference component in the frequency domain (Raimondi et al. 2006).In fact, the effectiveness of FDAF is related to the number of samples in FFT.Adopting more FFT points contributes to better performance, while increasing the complexity of the computation load (Raimondi et al. 2008;Ojeda et al. 2013).In comparison, the notch filter has the advantages of low computational requirements and high implementation efficiency.It has been proven to be effective in mitigating continuous wave interference (Borio et al. 2008;Gamba et al. 2012), narrow-band interference (Borio et al. 2006;Raasakka and Orejas 2014) and swept-frequency jamming signals (Borio et al. 2014;Falletti et al. 2020).DME signal is narrow-band interference with high spectral density at certain frequency, thus suitable for notch filter.Compared with pulse blanking, the notch filter method can preserve more desired signal, although it also removes the useful component at the DME interference frequency.
Both time-domain-only and frequency-domain-only mitigation methods have major flaws (Gao et al. 2016).The hybrid blanking algorithm was proposed by combining the advantages of pulse blanking and notch filter (Gao et al. 2013).In this algorithm, the pulse interference is detected through a sliding window in the time domain and filtered out by a notch filter in the frequency domain.Therefore, hybrid blanking can maximize the remaining useful GNSS signal.In fact, the performance of the hybrid blanking is heavily influenced by the effectiveness of the adopted notch filter, which is determined by the selected notch frequency and bandwidth.The adaptive notch filter (ANF) is widely adopted to track the frequency variation of the interference by an additional adaptive block (Kang et al. 2014;Qin et al. 2020).In addition, adaptive bandwidth notch filters are designed to optimize the mitigation performance against narrow-band interference (Nguyen et al. 2014;Ferrara et al. 2018) by setting the bandwidth of the notch filter based on the estimated interference bandwidth.By contrast, less research has been conducted to investigate the approach to adjust notch filter to cope with different interference powers.Considering that the DME interference arriving at the aircraft GNSS antenna can vary continuously and significantly during the flight, it is essential to implement a flexible mitigation approach that can adjust the configurations according to the interference characteristics.
From this perspective, a DME pulse interference mitigation algorithm based on adaptive hybrid blanking is proposed.Based on the simulated B2a signals in different cases that are contaminated by various levels of DME interferences, the optimal notch filter parameters that drive the hybrid blanking to achieve the best performance are determined in each case.A mathematical model is established to correlate the incoming interfered signal strength to notch filter parameters.By applying the proposed algorithms in the open-sky experiment where the DME-interfered B2a signals are collected near Beijing International Airport, the performance of the proposed algorithm is fully validated.
The next section introduces the DME signal and its effects on B2a signal, followed by a detailed description of the conventional DME interference mitigation algorithms and the newly proposed adaptive hybrid blanking algorithm.The establishment of the empirical model adopted in adaptive hybrid blanking is then provided, followed by results and a discussion of the performance validation of the proposed algorithm.Finally, conclusions and remarks are withdrawn.

DME signal and its effects on B2a signal
DME is a widely used pulse-ranging system and a competitive candidate to provide alternative positioning, navigation and timing (APNT) services.The airborne DME interrogator transmits a pulse pair sequence toward the ground omnidirectionally.Once the ground DME transponder receives the interrogation signal, a reply signal is sent to the aircraft with a fixed time delay.The reply signal composes of the same pulse pair sequence as the interrogation signal but modulated on a different frequency, depending on the reply channel of the ground transponder.The receiver of the airborne DME interrogator then calculates the slant range with respect to the ground transponder by measuring the propagation time of the pulse pair sequence (Dovis et al. 2012).
DME frequencies are distributed in 1 MHz intervals throughout the 962-1213 MHz band.There are four operating modes for DME, i.e., X, Y, W and Z modes, as illustrated in Fig. 1.The 1151-1213 MHz band is assigned as DME reply frequencies for X mode, which partly overlaps with the BDS B2a frequency band, i.e. 1166.22-1186.68MHz, thus causing potential signal interference.
Figure 2 shows a simulated DME pulse pair operating in X mode.Each pulse can be modeled as a Gaussian function, indicated by the red line, with a width of 3.5 μs.The two pulses are 12 μs apart (Anyaegbu et al. 2008).A typical DME pulse pair is expressed by where = 4.5 × 10 11 s −2 determines the pulse width.Δt = 12 × 10 −6 s is the inter-pulse interval.The repetition rate of pulse pairs is one of the most important parameters of the DME system.A higher repetition rate tends to produce more adverse effects on B2a signals.The maximum reply capability of the DME ground transponder is approximately 2700 pulse pairs per second (ppps) (Musumeci et al. 2014).
Figure 3 provides an example of the DME-interfered B2a signal by comparing the cross-ambiguity function (CAF) magnitude of clean and DME-interfered B2a signals.In the top panel, when there is no interference, it is clear that the correlation peak is dominant.By contrast, in the presence of DME pulse interference in the bottom panel, the correlation peak becomes relatively less prominent, which indicates a decrease in the correlation performance, thus affecting the signal quality.

Conventional DME interference mitigation algorithms
A typical structure of a GNSS receiver is shown by the green blocks in Fig. 4. The incoming signal y(t) received at the antenna is filtered, down-converted and digitalized to intermediate frequency (IF) samples y[n] by the radio frequency (RF) front-end.If no interference mitigation procedure is implemented, the IF samples are parsed by the baseband signal processing module directly, which includes parallel channels for signal acquisition and tracking.Then, the pseudorange, carrier phase measurements and related navigation messages are obtained and used to solve the PVT results.
In order to mitigate the pulse interference on GNSS receivers, an interference mitigation component is implemented before the acquisition stage, as shown by the red block in Fig. 4. Different pulse interference mitigation approaches can be applied.In this section, the widely used pulse blanking, notch filter and time-frequency hybrid blanking approaches are discussed.These conventional algorithms are realized in this study to serve as references in evaluating the performance of the newly proposed approach.

Pulse blanking
Pulse blanking is a simple method to mitigate pulse interference by zeroing out those samples that exceed the predefined threshold, which is given by where T h is the threshold.In this analysis, the threshold is set according to Musumeci et al. (2014), which assumes that the samples output by the analogue-to-digital converter (ADC) follows a Gaussian distribution in the interference-free environment.Thus, a blanking threshold is pre-set based on the required false alarm probability p fa .
Figure 5 shows an example of the pulse blanking performed on a typical modulated pulse pair of DME signals.It is apparent that the pulse blanking is not able to suppress the entire DME pulses due to the tails of the Gaussian pulse and the modulation over the pulse duration.As a result, a large portion of the pulse interference is remained, thus still affecting the performance of the receiver in processing the B2a signals. (2)

Notch filter
The basic principle of a notch filter is to attenuate the power of interference component at a certain frequency.
There are three widely used ways to implement a notch filter, i.e., fast fourier transform (FFT), finite impulse response (FIR) and infinite impulse response (IIR) notch filter.Considering that the IIR-based notch filter has low computation cost and high implementation efficiency (Borio et al. 2008), a one-pole IIR notch filter is employed, which is given by where z 0 is the zero of the transfer function that determines the frequency of the notch.k ∈ [0, 1) is the pole contrac- tion factor that determines the width of the notch.z 0 and the notch frequency f nf are connected by where T s is the time sampling interval.The 3-dB attenuated bandwidth of the notch filter can be approximated as (Dovis 2015) where f s is the sampling rate.Figure 6 presents the mag- nitude responses of the notch filters with different k .It is clear that k obviously influences the width and depth of the notch.A smaller value of k results in a deeper and wider notch.Therefore, it is important to select a proper value of k in interference mitigation.Compared with pulse blanking suitable for pulse interference, a notch filter generally performs better for continuous wave interference, which manifests as narrow-band interference in the frequency domain.Because DME interference can be considered as narrow-band interference with high spectral density at a certain frequency, notch filter is also applied to mitigate DME interference.However, the B2a signal energy at the notch frequency is also removed even if no interference occurs.Therefore, an interference detection module in the time domain is needed, which determines whether to trigger the notch filter.A typical example is the hybrid blanking algorithm, which is given in details next.

Hybrid blanking
Considering that both pulse blanking and notch filter have their inherent drawbacks, hybrid blanking is proposed by combining these two techniques (Gao et al. 2013), i.e., to detect the pulse interference in the time domain and perform mitigation in the frequency domain.
Figure 7 illustrates the schematic of the hybrid blanking algorithm.A sliding window is implemented on the input IF samples to detect pulse interference by comparing it to a predefined threshold.If a pulse is detected, the duration of the pulse segment is estimated.A notch filter is then applied to suppress the interference data segment.Finally, the filtered segment is used to replace the original parts and form the output.
For the B2a signal segments superposed by DME pulse interference, hybrid blanking tends to preserve the most useful components compared with pulse blanking and notch filter.Nevertheless, the performance of the hybrid blanking is highly determined by the characteristics of the adopted notch filter, which further depends on the notch parameter selection.

Adaptive hybrid blanking algorithm
Hybrid blanking combines the advantages of pulse blanking and notch filter, while in practice, it is not reasonable to apply fixed notch filter parameters in DME interference mitigation for different situations.To keep the useful B2a signals to the maximum while eliminating interference properly, an adaptive hybrid blanking algorithm is proposed in this study.
As discussed in the previous subsection, the pole contraction factor k of the notch filter determines the width and the depth of the notch.A smaller value of k indicates a stronger suppression capability.Theoretically, a smaller k should be chosen to mitigate stronger interference, while applying a too small k leads to excessive loss of the desired B2a signal.On the other hand, for less stronger interference, a relatively larger k should be used, while the interference cannot be completely removed if k is too close to unity.Therefore, it is necessary for the receiver to apply an optimal k to cope with DME interference of different powers.
In this analysis, jammer-to-noise power ratio ( J∕N ) is exploited as an indicator of the interference strength in the received B2a signal (Borio 2017).The J∕N computation is based on the received data without a requirement of prior knowledge of the interference power, thus it is perfectly suitable in practical applications.In this study, the empirical model to select k based on the J∕N of the input signal is established, which is provided in detail in the next section.
Figure 8 demonstrates the schematic of the proposed adaptive hybrid blanking algorithm, which consists of four steps.
Step 1 Detecting DME interference pulses in the time domain.By passing the input signal through a sliding window, as shown in Fig. 7, the DME interference is detected and the duration of the interference data segment is estimated.
Step 2 Determining the center frequency f nf of the inter- ference.The power spectral density (PSD) of the interference data segment detected in Step 1 is estimated by FFT.By comparing with the normal PSD level, the frequency band where interference occurs is estimated and the center frequency f nf is derived.With f nf , z 0 is calculated by ( 4) and sent to the notch filter.
Step 3 Calculating J∕N and selecting an optimal k .The J∕N of the interference data segment is calculated with (6).Based on the empirical statistical model established in the next section, the optimal k is derived and fed to the notch filter.
Step 4 Performing notch filter.The interference data segment is filtered by the notch filter with the parameters determined in Steps 2 and 3.The original portion with interference detected is then replaced by the filtered data.With the steps above, the DME interference is optimally removed.The processed samples are then input to the acquisition stage.Otherwise, if no interference is detected in the first step, the receiver performs signal acquisition directly.
Compared with the hybrid blanking proposed by Gao et al. (2013), the main improvement is that an J∕N calcu- lation module is used in order to provide an optimal k for the notch filter applied in the proposed algorithm in different interference situations.Therefore, the proposed algorithm is able to optimize the capability of the hybrid blanking by attenuating the pulse interference without excessive loss of the desired B2a signal.It should be mentioned that this algorithm can be applied to cases of multiple interference sources with different central frequencies.However, in the presence of pulse collision, the proposed algorithm may perform differently which worth a further investigation.

Empirical model establishment to adjust k ˛ according to J/N
This section describes the experimental setup for collecting simulated B2a signals interfered by the DME pulses in the laboratory.Based on the collected data, the statistical model between J∕N and k is established.

Simulation of DME-interfered B2a signals
An experimental testbed was developed to collect the B2a data under different DME interference, as shown in Fig. 9.The BDS B2a signals were generated by a Spirent GSS9000series GNSS simulator, which can simulate the BDS constellation with flexible configurations.The simulation situations were precisely repeatable, making it perfectly suitable for this analysis.The output power level was set to − 103 dBm in order to simulate real B2a signals output by the active GNSS antenna.An Aeroflex Nav-2030-series Avionics Signal Generator was also applied to simulate DME signals with adjustable carrier frequencies, power levels and pulse repetition rates.An RF combiner was applied to superimpose the impacts of DME interference on the BDS B2a signals.
The contaminated B2a signal was then processed by an in-house software-defined radio (SDR) BDS B2a receiver developed at Beihang University.It consisted of an RF frontend, which is a Universal Software Radio Peripheral (USRP) X310, and a baseband signal processing module.The specific parameters adopted by the USRP X310 are listed in Table 1.With the USRP, the RF signal was down-converted to the baseband, sampled at a rate of 20 MHz and digitalized to complex 16-bit data.The digital data were further processed by the acquisition and tracking modules.
DME interferences with different carrier frequencies, pulse repetition rates and powers were simulated, as listed in Table 2.In this analysis, it is assumed that the receiver is exposed to a single DME interference source.The DME power levels in each case increased from − 85 to − 60 dBm  at a step of 1 dB.Thus, a total of 78 groups of DME interference superposed on B2a data were generated and collected.
A group of clean B2a data was also generated and processed for comparison purpose.

Statistically modeling k ˛ as a function of J/N
To select an optimal k based on the interference strength represented by J∕N , an empirical model is established.For the simulated B2a data in each millisecond, the J∕N is cal- culated by where the total power P total is estimated as the sample vari- ance of the received signal.The noise power N is determined by the variance of the samples when no pulse occurs.Figure 10 presents the variation of J∕N as a function of DME interference powers in different cases.Generally, the J∕N in each case increases gradually with the increase of the interference power.Under the same interference frequency, a higher pulse repetition rate contributes to a higher J∕N .When the pulse repetition rate is 2700 ppps, the signals with the DME interference frequency closer to the B2a center (6) J∕N = 10 ⋅ log 10 P total − N N frequency result in slightly higher J∕N , as the blue and red lines show.Thus, J∕N is an effective parameter that reflects the effect of the DME signals with different interference frequency, pulse repetition rate, and most importantly, the interference power on the B2a signal.Therefore, it is selected to indicate the characteristics of the DME interference.
To indicate the B2a tracking performance and select the optimal k that potentially achieves the best interference mitigation performance, the carrier-to-noise density ratio ( C∕N 0 ) of the processed B2a signal is calculated.It should be noted that the notch frequency of the notch filter is set to the center frequency of the simulated DME signal.With the increase of k , C∕N 0 grows slowly and slightly, followed by an obvious drop.The increase in C∕N 0 is due to the fact that more useful energy is preserved with the decrease of the notch width which is determined by k , while the drop is attributed to the interference component that is not eliminated.This trend is particularly evident when the interference power is stronger.On the other hand, it can be seen that under different DME interference power levels, the k that maximizes the C∕N 0 is different.The maximum C∕N 0 is achieved when k is 0.97, 0.95, 0.90, 0.84 0.76 and 0.66 for the interference power of -85, -80, -75, -70, -65 and -60 dBm, respectively, as marked by the red circles in the figure.This phenomenon conforms to the previous theoretical analysis that smaller k should be chosen for stronger interference.Therefore, choosing a proper k is significant to the design of the hybrid blanking algorithm, especially under strong DME interference.It should be noted that the results based on the data collected in   Cases 2 and 3 are similar to that of Case 1, thus not shown here.Moreover, the input C∕N 0 values are relatively high.This is because if the input C∕N 0 value is too low, it may degrade the receiver performance, which is mixed with the influence of an improper k , thereby contaminating the modeling process.
Based on the estimated J∕N and the optimal k deter- mined for each simulated B2a signal under DME interference in different cases, the variation of the optimal k as a function of J∕N is presented in Fig. 12.As the fig- ure shows, the optimal k decreases gradually with the increase of J∕N .In our analysis, the value of J∕N is used to represent the overall impact of the interference of different parameters, including frequency, pulse repetition rate and power.By fitting the three cases with a signal fit, the established model can be applied in different interference situations, thereby improving its feasibility and applicability.In order to mathematically model k as a function of J∕N , the k is modeled with an empirical function defined as The MATLAB curve fitting tool is applied to solve the coefficients a and b, which is 0.017 and − 2.034, respectively.The sum of squares due to error (SSE) and R-square of this fit is 0.0587 and 0.9768, respectively, indicating that the model can represent the trend well.Therefore, the empirical model is applied for the parameter k selection in the adaptive hybrid blanking algorithm.
It should be noted that there may be extreme interference situations that may cause k lower than 0 according to (6).In this case, k is set to 0.1 to maintain the effec- tiveness of the algorithm while eliminating as much interference as possible.With the statistical empirical model developed in this section, k can be altered accordingly based on the measured J∕N levels.The open-sky experiments are conducted near 2 DME stations, which are respectively, about 12 and 31 km from the Beijing Capital International Airport.With the data collection platform shown in Fig. 13 established on a car running on the road near the DME stations, as shown in Fig. 14, the B2a data are collected following the same setup listed in Table 2.

Collection of open-sky DME-interfered B2a data
Table 3 lists the details of the three interference situations for the open-sky signal collection, which includes 1 static test and 2 dynamic tests.The distance between the DME station and the car is about 2-3 km, which is a reasonable configuration to simulate the worst case occurred when the aircraft flies over the station.In addition, two satellites with relatively high and low elevation angles are selected for each situation.
Figure 15 shows the real-time spectrum of the incoming signal around the B2a band calculated by the PolaRx5S receiver in Situation 1.It is clearly shown that there is a spike at about 1181 MHz, which is exactly the DME station operation frequency.

DME interference mitigation with the adaptive hybrid blanking algorithm
The performance of the newly proposed adaptive hybrid blanking algorithm in mitigating the real DME interference in the Situations listed in Table 3 is presented.The Figure 16 shows an example of the variation of B2a samples before (top) and after (bottom) performing adaptive hybrid blanking in the time domain in Situation 2. The pulse pairs are clearly observed in the top panel in a random way, while in the bottom panel with the proposed algorithm implemented, the pulse interferences are significantly suppressed.
Figure 17 presents an example of the received B2a signal PSD before and after applying adaptive hybrid blanking.In the top panel, an obvious spike occurs at around 4.5 MHz away from the central frequency of B2a signal, which is consistent with the transmitting frequency of the DME station in Situation 2. With the mitigation algorithm applied, the spike at the same frequency in the bottom panel is significantly suppressed.Thus, the effects of the DME interference on the B2a receiver are reduced.

Mitigation performance validation in situation 1
In this section, the performance of the proposed adaptive hybrid blanking algorithm is evaluated and compared with other mitigation algorithms by processing the interfered B2a signal collected statically.PRN 41 with an elevation of 45° and PRN 33 with an elevation of 76° are selected for the analysis.Based on the C∕N 0 values computed by the B2a SDR receiver at a rate of 5 Hz, the averaged C∕N 0 in each second is calculated.Additionally, the standard deviation of the code tracking error is estimated which is determined by the normalized early-late magnitude (NELM) discriminator implemented in the B2a receiver.
Figure 18 shows the averaged C∕N 0 computed in each second of PRNs 41 and 33.It should be noted that when no mitigation technique is applied in this situation, the tracking process is not performed because no satellite is acquired.It can be seen that hybrid blanking provides a higher C∕N 0 than notch filter and pulse blanking, while the adaptive hybrid blanking algorithm provides the highest C∕N 0 in most time.Especially for PRN 33 in the bottom panel, the C∕N 0 values under the adaptive hybrid blanking algorithm are significantly higher.
Table 4 lists the mean C∕N 0 of both PRNs when differ- ent pulse interference mitigation algorithms are applied.Apparently, the highest mean C∕N 0 is achieved when adap- tive hybrid blanking is applied, which is about 3.5, 3.0 and 2.0 dB higher than pulse blanking, notch filter and hybrid blanking, respectively.
Figure 19 compares the root mean square (RMS) of the code tracking error of PRNs 41 and 33 under different mitigation methods.It can be seen that for both PRNs, the RMS of code tracking errors has the minimum value when adaptive hybrid blanking is applied, which is about 0.09 and 0.06 chips for PRNs 41 and 33, respectively, indicating that the proposed adaptive hybrid blanking algorithm provides excellent suppression performance in the static situation.

Mitigation performance validation in situation 2
This section quantitatively analyzes the performance of the proposed adaptive hybrid blanking algorithm in mitigating DME interference based on B2a signals collected in Situation 2. PRN 33 with an elevation of 35° and PRN 38 with an elevation of 75° are selected for the analysis.Figure 20 shows the mean of the C∕N 0 estimated at each second with different interference mitigation methods implemented.The original C∕N 0 values without mitigation are also shown for comparison.It can be seen that for both satellites, the smallest C∕N 0 mostly appears when no mitigation is applied, while obvious improvement can be observed under the pulse blanking and notch filter methods, with an increase of around 1.5 dB-Hz, as listed in Table 5.Furthermore, the hybrid blanking and the adaptive hybrid blanking achieve higher values of C∕N 0 , while the newly proposed adaptive hybrid blanking algorithm generally provides the largest values of  C∕N 0 , indicating that the proposed approach achieves the best performance.It is worth mentioning that even with the mitigation algorithms implemented, there are still obvious fluctuations in the C∕N 0 values.This may be due to the sig- nal fading and blocking caused by the surroundings during the vehicle moving, such as buildings and trees.Table 5 summaries the mean C∕N 0 of PRNs 33 and 38 by applying different interference mitigation algorithms, as shown in Fig. 20.The mean C∕N 0 increases to different extents with the mitigation algorithms.However, the proposed adaptive hybrid blanking achieves the most improvements by about 3.05 and 3.32 dB for PRNs 33 and 38, respectively.
Figure 21 further shows the RMS of the code tracking error of PRNs 33 and 38.The RMS of the code tracking error of PRN 38 is lower than that of PRN 33, which is due to the lower elevation.When these interference mitigation algorithms are implemented, the code tracking errors can be generally reduced.Compared with the conventional interference mitigation methods, the newly proposed adaptive hybrid blanking achieves the smallest code tracking errors, which is 0.09 and 0.06 chips for PRNs 33 and 38, respectively.This again indicates that the proposed algorithm achieves the best mitigation performance.

Mitigation performance validation in situation 3
Similar to the analysis in the previous section, PRN 33 with an elevation of 40° and PRN 41 with an elevation of 71° are selected for the mitigation performance analysis based on the data collected in Situation 3.
Figure 22 shows the variation of the averaged C∕N 0 with different interference suppression methods implemented.C∕N 0 for the original signal is not shown as the signals are not acquired when no mitigation method is applied.It is obvious that when the hybrid blanking and the adaptive hybrid blacking algorithms are applied, the values of C∕N 0 for both satellites are generally larger, which agrees with the results shown in Fig. 20.Additionally, the adaptive hybrid blanking achieves the maximum C∕N 0 , indicating that the proposed algorithm outperforms the conventional ones.Table 6 summarizes the mean of C∕N 0 for PRNs 33 and 41 corresponding to the results shown in Fig. 22.It can be seen that the newly proposed adaptive hybrid blanking algorithm achieves an increase of about 2.5, 2.0 and 1.2 dB compared with pulse blanking, notch filter and hybrid blanking, respectively.
Figure 23 shows the RMS of the code tracking errors for PRNs 33 and 41 when applying different mitigation algorithms based on the B2a data collected in Situation 3. The minimum RMS of code tracking error is observed when the adaptive hybrid blanking is adopted, which is similar to the result shown in Fig. 22.This further validates the superiority of the newly proposed adaptive hybrid blanking.

Conclusions and remarks
This study proposed an adaptive hybrid blanking algorithm to mitigate the adverse effects of DME interference on BDS B2a receivers.An empirical model is built to alter the algorithm configuration according to the interference strength.The performance of the algorithm is validated by processing practical DME-interfered B2a signals.k is a key parameter that affects the performance of the notch filter implemented in the proposed algorithm.
To establish an empirical model to enable adjusting k based on the interference strength indicated by J∕N , a number of 78 groups of DME interference were generated which are superposed on simulated B2a signals processed by an SDR-based B2a receiver.Results show that J∕N is an effective index to represent the DME interfer- ence strength.With this model, the proposed algorithm is capable of adaptively suppressing the DME interference and optimizing the receiver performance according to the DME interference strength.
The performance of the newly proposed algorithm and conventional DME interference mitigation methods including pulse blanking, notch filter and hybrid blanking were compared by processing the open-sky B2a data collected near 2 DME stations close to the Beijing Capital International Airport.Results show that the adaptive hybrid blanking was able to select proper parameters flexibly and generally outperforms the conventional mitigation methods in both static and dynamic situations.It achieves significantly higher C∕N 0 and lower RMS of code track- ing errors.A C∕N 0 increase of up to 3.32 dB is observed compared with that when no mitigation method is applied.
The adaptive hybrid blanking algorithm effectively suppresses the DME pulse interference and significantly improves the B2a receiver performance, which further enhances the robustness of the receiver.In addition to DME signals, the proposed adaptive hybrid blanking algorithm proposed is applicable to any intentional and unintentional pulse interference.The future work will focus on evaluating the mitigation performance of the proposed algorithm in the case of pulse collision.The performance of the proposed algorithm against other types of interference will also be studied.Author contribution YZ, SH and KG initiated the study.ZD, KF provided supports with the software used in the analysis.KG and ZW helped to improve the manuscript.KG, SH and YW helped to collect data.SH analyzed the data and initiated the manuscript.All authors provided critical feedback and approved the manuscript.

Fig. 1
Fig. 1 Frequency allocation of DME and BDS B2a signals

Fig. 2 A
Fig. 2 A DME pulse pair operated in X-Mode

Fig. 4 Fig. 5
Fig. 4 Interference mitigation implemented on a general GNSS receiver

Fig. 6
Fig. 6 Magnitude responses of the notch filter with different k α

Fig. 8 Fig. 9
Fig. 8 Adaptive hybrid blanking schematic Figure 11 shows the variation of C∕N 0 in relation to k under different interference power levels in Case 1.As the figure shows, the variation of C∕N 0 under interference levels of − 75, − 70, − 65 and − 60 dBm is quite similar.

Fig. 10
Fig. 10 Variation of J/N of the DME-interfered B2a signals in different cases listed in Table 2

Fig. 11
Fig. 11 Variation of C⁄N 0 as a function of k α under DME interference of different power levels.The maximum C⁄N 0 achieved in different curves are marked by red circles (7) k = −1 ⋅ exp(a ⋅ J∕N + b) + 1Validation of the adaptive hybrid blanking algorithmTo validate the performance of the proposed adaptive hybrid blanking approach in mitigating DME interference on BDS B2a signals, open-sky experiments are conducted in three different situations to collect B2a data contaminated by real DME signals.The experimental setup and the performance of the proposed algorithm in mitigating the DME interference are presented in this section.

Figure 13
Figure13shows the setups of the B2a data collection for the outdoor experiments.Compared with the setups shown in Fig.9, a GNSS antenna is used to receive open-sky BDS B2a signals.Additionally, a commercial GNSS receiver, Septentrio PolaRx5S, is also included in the experimental setup during the data collection.This receiver is capable of calculating and demonstrating the incoming signal spectrum around the B2a band, thus providing a useful tool to check whether there is DME interference in real time.Since the PolaRx5S solves the position based on GNSS L1 signals which are not interfered

Fig. 12
Fig. 12 Variation of k α in relation to various J⁄N

Fig
Fig. 14 Experimental environment for collecting real DMEinterfered B2a signals

Fig. 16
Fig. 16 Variation of the interfered B2a signal amplitude before (top) and after (bottom) performing adaptive hybrid blanking

Fig. 19 Fig. 20
Fig. 19 RMS of the code tracking errors for PRNs 41 and 33 calculated with different interference mitigation methods applied in situation 1

Fig. 21 Fig. 22
Fig. 21 RMS of the code tracking errors for PRNs 33 and 38 calculated with different interference mitigation methods applied in situation 2 ers and engineers at the National Key Laboratory of CNS/ATM for their advice and interest.The work was carried out with the financial support from the National Natural Science Foundation of China (grant nos.62022012, 62101019, U2033215 and U2233217), the National Key Research and Development Program of China (grant nos.2020YFB0505602), the Civil Aviation Security Capacity Building Fund Project (grant nos.CAAC Contract 2020(123), CAAC Contract 2021(77) and CAAC Contract 2022(110)).

Fig. 23
Fig. 23 RMS of the code tracking errors for PRN 33 and PRN 41 calculated with different interference mitigation methods applied in situation 3

Table 1
Settings of the USRP X310 adopted for data collection

Table 2
Configurations of 3 simulated DME interference cases

Table 4
Mean of C∕N 0 when applying pulse blanking, notch filter, hybrid blanking and the proposed adaptive hybrid blanking algorithms in situation 1

Table 5
Mean of C∕N 0 when applying pulse blanking, notch filter, hybrid blanking and the proposed adaptive hybrid blanking algorithms in situation 2

Table 6
Mean values of C∕N 0 when applying pulse blanking, notch filter, hybrid blanking and the proposed adaptive hybrid blanking algorithms in situation 3