Full-domain collaborative deployment method of multiple interference sources and evaluation of its deployment effect

Yue Wang, Fuping Sun, Xian Wang, Jinming Hao, Kai Xiao

School of Geospatial Information, The PLA Information Engineering University, Zhengzhou 450001, Henan, China

Keywords:Jamming effect Multiple interference sources Collaborative deployment Effect evaluation Defense capability

ABSTRACT This paper realizes the full-domain collaborative deployment of multiple interference sources of the global satellite navigation system (GNSS) and evaluates the deployment effect to enhance the ability to disturb the attacker and the capability to defend the GNSS during navigation countermeasures.Key evaluation indicators for the jamming effect of GNSS suppressive and deceptive jamming sources are first created,their evaluation models are built, and their detection procedures are sorted out, as the basis for determining the deployment principles.The principles for collaboratively deploying multi-jamming sources are developed to obtain the deployment structures (including the required number, structures in demand,and corresponding positions)of three single interference sources required by collaboratively deploying.Accordingly, simulation and hardware-in-loop testing results are presented to determine a rational configuration of the collaborative deployment of multi-jamming sources in the set situation and further realize the full-domain deployment of an interference network from ground,air to space.Varied evaluation indices for the deployment effect are finally developed to evaluate the deployment effect of the proposed configuration and further verify its reliability and rationality.

1.Introduction

The secure application of the global satellite navigation system(GNSS) in navigation countermeasures is a significant strategic concern.However, the successive captures of American drones by Iran since 2010 [1] and the spoofing attack tests of drones and yachts by the United States (US) [2] demonstrate that GNSS is extremely vulnerable to interference and deception.To secure GNSS safe application under navigation countermeasures (whose narrow meaning focuses on GNSS jamming and anti-jamming[3]),with the development and testing of related technologies and devices, studying relevant evaluation methods of GNSS jamming in the context of this countermeasures has attracted significant attention.The effective realization of this direction is not only beneficial in updating GNSS internal systems, maintaining its external facilities, and optimizing related performance, but also in reducing the threats of GNSS suffered during countermeasures and enhancing its defense capability.Existing relevant evaluation can be divided into two types[4],i.e.,performance evaluation which is for several performance and performs the modeling and detection,and decision-making evaluation which is for the subsystems in navigation countermeasures and selects their corresponding optimal defense measure.The two is complemented each other.

There are some studies on the performance evaluation and decision analysis of single interference technologies for navigation countermeasures:①For building the performance index system,Li et al.created the jamming-oriented indices to evaluate defensive effect of anti-jamming technologies including the adaptive filtering and inertial navigation aiding [5]; however, the qualitative indices were too many in the index system to put into practice.Then,Heng et al.and Wang et al.respectively designed the quantitative indices for evaluating GNSS suppressive [6] and deceptive jamming effect[7].②For the performance evaluation, Ceccato et al.and Psiaki et al.detected the performance of GNSS spoofing[8]and evaluated the anti-spoofing effect of GPS receivers[9];however,the detection methods of some evaluation models were not completely built to carry out the quantitative analysis and performance improvement effectively.Thus, Wang et al.perfected the detection methods of GNSS jamming devices and evaluated their threatening effect[10].③How to efficient utilize the obtained performance evaluation results and make the optimal decision is the primary concern of decision makers participating in navigation countermeasures;thus,for the decision-making evaluation, Wang et al.determined the optimal spoofing strategy from the aspects including weight determination [11], index reduction [12], and dynamic decisions[13].Among these researches above, even for the fullest research,its evaluation objective was a single interference source or a singlejamming oriented defensive technique, and the obtained results were scattered and one-sided, which cannot effectively evaluate the jamming effect on a target threating the GNSS in navigation countermeasures.

Navigation confrontation is significantly more complex: Environments with single interference sources are unrealistic while multi-jamming sources including GNSS suppressive jamming and deceptive jamming is the norm;different deployment structures of multiple interference sources used in navigation countermeasures can impact different effect on disturbing a threatening target.Therefore, based on evaluation results of different jamming effect,investigating the collaborative deployment of GNSS multiple interference sources is more relevant.Furthermore,there are some existing researches on the deployment of GNSS interference sources and the relevant methods for multiple interference sources:①For the deployment structure determination, Tang et al.and Han et al.Gai et al.respectively proposed the deployment structures of single interference sources including GNSS suppressive jammers[14,15] and GNSS retransmitted spoofers [16].②For the methods related to multiple interference source, Liu et al.built the location method of GNSS multiple interference sources[17];Lu et al.Bo et al.and Zhao et al.respectively proposed the suppression methods of multiple interference sources for array radars used in radar countermeasures [18] and the methods performing multiple false targets jamming under this confrontation [19,20]; and Aguilera et al.and Bar-Yehuda et al.respectively developed the cancellation method of multiple interference sources for autonomous devices used in network countermeasures [21] and the bandwidth allocation algorithms of multiple interference sources under this confrontation [22].Even though realizing the collaborative deployment of GNSS multiple interference sources is vital to improve its defense capability,this direction is rarely covered in the above studies, let alone its deployment effect evaluation.

Given the above limitations and lack of studying the collaborative configuration of GNSS multiple interference sources under navigation countermeasures, this paper is to improve the defense capability of GNSS during navigation countermeasures by proposing and evaluating a rational multi-jamming collaborative deployment configuration as one defense system, organized into six sections:Sections 1 and 2 present the background,significance,references, feasibility, advantages, and deficiencies of the collaborative deployment of GNSS multiple interference sources under navigation countermeasures.Section 3 creates key evaluation indicators with their models and detection methods for the jamming effect of three single-jamming sources included in the multiple interference sources, as the basis for determining the deployment principles.Section 4 develops the principles for collaboratively deploying multi-jamming sources,which cover the ground,air,and space.Section 5 provides the simulation and testing results and then determines suitable deployment structures of three singlejamming sources in the set situation, to propose a rational multijamming collaborative deployment configuration.Section 6 evaluates the collaborative deployment effect of the proposed configuration and verifies its rationality by developing various evaluation indices of the deployment effect.Finally,the conclusions and future work are given in Section 7.

2.Overview of the collaborative deployment of multiple interference sources

Deceptive jamming is effectively performed when GNSS receiver is subjected to the high-power suppressive jamming during a brief un-locked recapture phase.Therefore,suppressive jamming is firstly carried out, whose purpose is to interfere with various threatening targets (enemy aircraft, guided weapons, etc.).Subsequently,spoofing is implemented,where the purpose of generative spoofing is the radars in enemy aircrafts and the guided weapons, and the purpose of retransmitted spoofing is usually enemy aircrafts.Their deployment concepts and feasibility analysis are listed below.

(1) Radar,early warning system,and other measures are used for the detection and tracking of the threatening target,in order to obtain its approximate location.

(2) The ground directly below either side of air routes of the threatening target, evenly deploys suppressive interference sources.

Feasibility and Advantages

Relative to spoofing, suppressive jamming technology is more mature [23]; Thus, we can precisely estimate the number of jammers, their locations, and deployment structures in this paper.Specifically,various control stations are also deployed on the ground to regulate the positions of carrying platforms,control the instructions sent to spoofing simulators and the time delay caused by retransmitted signals, and further receive reconnaissance information on threatening targets obtained by the early warning system, radars,and various sensors [24].

(3) Swarms of unmanned aerial vehicles(UAVs)are deployed in the air, as carriers to carry generative spoofing sources.

Current Relevant Methods

①The low cost of drones enables their use as baits in enemy airspace.For example, Han et al.[25] falsified the decoys through track spoofing to induce enemy antiaircraft fire in response to them, in order to deplete enemy’s air-defense resources and expose the location of its threatening target.②Based on the grasped approximate location of the target, UAVs,as carriers of various types of sensors and other auxiliary components,were firstly used by Ferhati et al.[26]to keep dynamic tracking of the target through RF and electro-optical sensors,and then used by Wang et al.[13] to perform instantaneous or continuous, dynamic, and concealed deceptive tasks through spoofing simulator and inertial measurement unit.

Feasibility and advantages

①Spoofing attacks generated in UAVs can either continuously transmit normal data packets to the target’s network channel from the inside,in order to make the network node mistakenly think that the real data packets are being transmitted and then keep it silent or in receive state [27], or broadcast satellite navigation signals containing false navigation messages from the outside, so that the targeted receiver would calculate the wrong position information and then be deceived into the vicinity of the preset spoofing position.Accordingly,②the use of on-demand deployment,flexible and maneuverable UAVs with the inertial navigation system and sensors, as the carriers for carrying the generative spoofing sources and performing deceptive tasks,has the advantages including consuming high-

cost enemy weapons at a small cost, dynamically obtaining high-value reconnaissance intelligence, normally navigating even suffering from interference, and completing deceptive tasks in a hidden way; however, INS would accumulate the error because it has not obtained the corrections of GNSS within the signal recapture time [28].Therefore, the survivability and stability of UAVs also need to be focused on.

(4) Low earth orbit(LEO)small-satellite systems are deployed in space, as platforms to carry retransmitted spoofing sources.

Existing deployment methods

Retransmitted spoofing sources consist of two sections: front and back ends [29], with the front end being GNSS receivers,which realizes the reception and frequency conversion amplification of GNSS signals,and the back end being GNSS repeaters,completing mixing of retransmitted signals and the transmission of spoofing signals.Most existing these sources are deployed on the ground[30];their performance such as related distance measurement, link delay calibration, and signal delay control all determine the smooth implementation of retransmitted spoofing tasks.However, the reconnaissance and targeted destruction of interference sources deployed on the ground are relatively easy to achieve.

Feasibility and advantages

①Compared with the ranging accuracy obtained by the groundbased retransmitted spoofing sources,satellite-borne retransmitted spoofing sources afford the obvious advantage, i.e., interplanetary distance measurement can be achieved by optical means such as lasers[31]as well as quantum communication[32],which can reduce the number of error sources and considerably improve the ranging accuracy.②Compared to the ground-based interference source is prone to destruction,satellite-borne retransmitted spoofing sources can realize the formation flying,large constellation networking,and fast spatial response capability;and hence,high temporal resolution,revisit rate,and resistant destructiveness usually belong to them.

3.Construction of evaluation indicators for the jamming effect

Single-frequency interference,band-limited Gaussian noise and matched-spectrum interference are selected as interference signal patterns of GNSS suppressive jamming,and retransmitted spoofing and generative spoofing are selected as interference signal patterns of GNSS deceptive jamming.Owing to length limit, here, we only propose key evaluation indices and their mathematical models,which form great theoretical basis and data foundation for studying the collaborative deployment.

3.1.Key evaluation indices for GNSS suppressive jamming effect

Definition of indicator 1 Relationship between the tracking threshold of the phase-lock loop(PLL) and the minimum jamming-to-signal ratio (J/S)min: The dynamic stress on the code tracking loop can be negligible when a stable carrier tracking loop is used.Therefore, in the full digital simulation, the carrier tracking error σJPLL(ignoring the effect of thermal noise in the receiver) generated by the PLL under various suppressive interference sources should be first calculated by referring to a previous study [33].

Based on the σJPLL, the evaluation models of the equivalent carrier-to-noise ratio (C/NJ)effcorresponding to the singlefrequency interference, bandwidth Gaussian-noise interference,and matched-spectrum interference can be obtained as follows:where BPis the noise bandwidth of PLL; R0(·) is the band-limited autocorrelation function of the pseudorandom code; βris the correlation bandwidth of GNSS receiver front-end; Psis the desired signal power; J/S is the jamming-to-signal ratio; PJ’ is the multiaccess interference power; βJand fJ0are the interference bandwidth and sits center frequency; Nois the number of visible satellites transmitting the desired signals; NJiand PJiare the type number of the i-th interference and its power, respectively.

From a previous study [3], the empirical tracking threshold of PLL for the arctangent discriminator (σPLL) can be obtained.

Here,θeis the dynamic stress error of the PLL,including only the error caused by the errors of Doppler frequency estimation of GNSS/INS.Under such a basis, the relationship between the σJPLLand (J/S)mincan be determined.

Definition of indicator 2 Relationship between the average acquisition time(Tavq)and the J/S:To resume operation as soon as possible after GNSS receiver loses lock, the C/A code must be first quickly acquired.Thus, from the existing research [34], Tavqof C/A code is the product of the total number of search cells (Nsearch) and their average residence time(Tdwell), which can be evaluated as follows:

where fdmaxand Δfdare the maximum Doppler shift and its search step; Lcand ΔLcare the sequence length of pseudo-random code and its search step; Pdis the detection probability;Pfais the falsealarm probability; Tsis the pre-detection integration time; k1is the misjudged work factor.When the search/lock policy is continuously correct for n times,k1can be expressed below.

where,Q(a,b)denotes the Marcum Q-function;This the detection threshold.When the jamming effect alone is considered,the noise power (σn) represents only the interference power at this point.

Definition of indicator 3

Relationship between the gain of GNSS receiving antenna in the interference direction (Grj) and the suppressive distance (Drj): Grjdirectly affects the effective suppressive distance and the effect of implementing suppressive jamming.In the full physical test,as Grjis a function of the arrival angle (αj, angle to the vertical) of jamming signals, and αjis related to the GNSS receiver’s height (hr),interference source’s height (Hj), and Drj, the αjcan be calculated.

After an interference signal has entered the antenna lobe range of the receiving antenna,the Grjvaries with the αj.According to the derivation of a previous research [11], the following mathematical model can be induced to calculate the Grj.

During tests,(Hj-hr)can be set as 3 km,6 km,9 km,and 10 km in that order, and the interfering sources are usually deployed above GNSS receivers to avoid their occlusion.

Definition of indicator 4 Relationship between the equivalent isotropic radiate power(EIRP)and the Drj: In the full digital simulation, referring to a previous study[35],the power of the interference signals received by GNSS receiving antennas can be expressed in decibels as the following equation:

where EIRPjand λjare the EIRP of the interference source and its wavelength; when Prjis set to the minimum value, i.e., the minimum interference power (Prj)minis at the receiver’s RF front, the maximum suppressive distance (Drj)maxcan be obtained.

Definition of indicator 5

Relationship between the continuous suppressive operating distance (Lj)and the destruction probability of the threatening target to a given protected object (Pk): In the full digital simulation, after finishing the division of interference force zones, the relationship among VG, ΩG, and Ljof a threatening target can be obtained by combining the requirements of the protected target for Pkand Ragiven in a previous study[36].Thus,with the determination of the Lj, the Pkcan be approximated below.

where VGand ΩGdenote the velocity of the threatening target and the drift rate of its angular error, respectively; Rais the range of damage to the protected object; Ljis the distance from the threatening target to the protected object when the target enters the interference force zone and loses lock.

3.2.Key evaluation indices for GNSS deceptive jamming effect

Definition of indicator 1 Maximum spoofing scope (SSp,Rmax): In the full digital simulation,referring to previous findings [37], if a spoofer propagates in free space and the effect of topography and earth curvature are not considered, its maximum spoofing distance can be evaluated below.

If free space loss and other environmental effect are not considered and the earth is a uniform sphere whose radius is RGl,its maximum spoofing distance of the spoofing source whose height is HSp, can be obtained as follows:

Based on DSp,Rmax(Loss)and DSp,Rmax(Earth),the smallest one is selected as the maximum distance of a spoofing source under tests,and the maximum spoofing scope can be obtained with this distance as radius and the source as the center of the scope.

where PSp,Rrepresents the spoofing power received by GNSS receiver;PSp,Tis the transmitting power of a spoofing source;GTand GRare the transmitting antenna gain of spoofing source and receiving antenna gain of receiver; DSp,Ris the distance between spoofing source and receiver; λSpis the spoofing wavelength, and COlis the additional loss.

Definition of indicator 2

Success rate of spoofing (ω): It can evaluate the spoofing effect under different power conditions for spoofing signals.In the full physical test,the spoofing distance and signal power are specified,and tests are repeated n times(10 epochs are counted as one test).If the obtained RMSE(s) does not exceed 0.50 m and the mean absolute deviation of pseudo-range MAD(ρ) does not exceed 10 m[38], the deception is considered as success.

where mean (ρ0i) represents a mean pseudo-range of (xsi0, ysi0,hsi0), and ρrirepresents a pseudo-range of (xsi, ysi, hsi).

If the tests are performed successfully for g times,the ω and its relationship with the test number can be determined.

Fig.1.Simplified planar projection of the deployment structure of suppressive jammers.

Fig.2.Retransmitted spoofing model with one interference source.

Fig.3.Retransmitted spoofing model with multiple sources.

Definition of indicator 3

Accuracy of the pseudo-range rate (σv): It is one of the important indicators to measure the rapidity of GNSS deceptive jamming.In the full physical static test,the test steps are as follows.

Firstly, setting the relative speed between the user and the satellite as 0, the carrier frequency value (f0) of the counter is recorded.Then,setting the relative speed between the user and the satellite as 1000 m/s, the carrier frequency value (fi) is recorded.Furthermore, calculating the carrier frequency deviation of the ith test as fdi= fi- f0, the standard deviation between the relative velocity (vi) and the set velocity (v0) can be obtained after n tests.

Fig.4.3-D design of the single-chain constellation (44 satellites) (front view), the conventional δ constellation (170) (side view), and the RGT constellation (160) (top view) and their 2-D design results.

If the σvis less than or equal to 0.005 m/s, this performance passes the test.The smaller the σvis,the better the spoofing effect of the spoofing source under test is.

Definition of indicator 4

Timing accuracy of the synchronous clocks (Δt): It is one of the important indices to measure the time synchronization capability of GNSS deceptive jamming.In the full physical static test,the test steps are as follows.

Firstly,the spoofer is opened,the antenna is disconnected after being positioned for 24 h,and the output information related to the time difference is recorded for 1 h.Then,the deviations(Δtfi)of the first 100 points in the information and the deviations (Δt1i) of the last 100 points in the information are summed and averaged to obtain this indicator.

If the △t is less than or equal to 200 ns/h, this performance under test is effective.The smaller the Δt is,the better the spoofing effect of the spoofer under test is.

Definition of indicator 5

Power control accuracy (ΔPtest): It is one of the most important indicators to measure the stability of GNSS deceptive jamming.In the full physical static test[39], the test steps are as follows.

Firstly,the original output power of a spoofer is set to+30 dBm according to its power control resolution which is ≤0.5 dB in real time.Then, as the output power is decreased 3 times in turn with an interval of 0.5 dB, respectively outputting as Ptest1, Ptest2, and Ptest3.Finally, they are modeled by using the power meters as follows:

If the ΔPtestfulfills the condition in Eq.(18),this performance is up to standard.The smaller the ΔPtestis, the better the spoofing effect of the spoofer under test is.

4.Development of the co-deployment principle of multiple interference sources consisted of three single-jamming sources based on the built evaluation indices

To obtain a rational configuration of the collaborative deployment of multi-jamming sources, the principle for effectively deploying three single-jamming sources including the groundbased suppressive interference sources, satellite-borne retransmitted spoofing sources, and UAV-borne generative spoofing sources should be firstly developed below.

4.1.Deployment principle of ground-based suppressive jammers

According to the division principles of interference force zones[40],that is,①the disturbed zone is defined as the region in which the Tavqof the C/A code under interference condition exceeds 10 times that under no interference condition (Tavq0), ②the semifailure zone is defined as the region in which a pseudo-range measurement is output with error and the Pdcaused by the interference is less than 0.16, and ③the invalid zone is defined as the zone that causes GNSS receivers to lose lock, based on the evaluation indices of the suppressive jamming effect, the interference force zones can be obtained below.

Number of GNSS suppressive jammers required for deploying Based on the knowledge of geometry, it is common to deploy the jammers directly below the both sides of the target’s route,in order to ensure that the target cannot fly out of the interference force zone even deviating its route, shown in Fig.1.

Then, according to Fig.1, different interference force zones formed by suppressive jamming should be modeled as a sphere,with Lj(i) denoting the effective suppressive operating distance of the ith source.

The minimum number of suppressive interference sources (Nj)required by this deployment can be determined when the following constraints are satisfied.Its evaluation model and related constraints with their computing formulas are below.

Fig.5.Simplified graph of the multiple satellite-borne retransmitted spoofing model.

Fig.6.Transient jamming area of a drone carrying a spoofer.

Fig.7.Jamming area of a decoy generated by the spoofer.

Fig.8.Schematic of the generative spoofing threatening to the target.

where constraint 3 indicates that the allocation interval between two adjacent sources in the horizontal direction,Δ|xj(i)-xj(i+1)|,is less than or equal to half the sum of the effective suppressive operating distance of adjacent interference sources,(Lj(i) + Lj(i+1)).

Positions of GNSS suppressive jammers required for deploying In the full digital simulation, assuming that the airway of the threatening target is a straight line and the width of the force zone is the distance between two jammers in the Z-axis direction,the Xcoordinate of the jammer closest to the center of the protected object (xMN), and the fixed increment of the (i+1)-th jammer

Fig.9.Schematic of the continuous generative spoofing mode.

Fig.10.Plotting of 3-D mesh plots,3-D curve plots,and 3-D surface plots based on Matlab built-in functions including meshc(x,y,z)(top left),meshz(x,y,z)(top right),plot3(x,y,z) (middle), surfc (x, y, z) (bottom left), and surfl (x, y, z) (bottom right) for Lj required by the threatening targets with different parameters.

relative to the ith one,Δ|xj(i) - xj(i+1)|, can be determined.

Assuming that the known continuous suppressive operating distance is Lj,the minimum number of jammers,(Nj)min,required at this point can be calculated, provided that the constraints in Eq.(21) are satisfied.

If the coordinate of the plane projection of the jammer closest to the protected object is[xj(0),yj(0)]=(|xMN|,-drj),the position of the ith jammer can be sequentially derived to realize the full

deployment of suppressive jammers, shown in Fig.1.

where Drjis the distance between any jammer [xj(i), yj(i)] and a threatening target O;drjis the horizontal distance from the jammer to the route; the symbol 「.∙⏋denotes rounding upwards; rjis the maximum jamming radius of the interference force zone projected onto the plane of a target, roughly equivalent to the maximum suppressive distance (Drj)max.

4.2.Deployment principle of satellite-borne retransmitted spoofers

GNSS retransmitted spoofing is achieved by receiving and delaying GNSS signals,which are amplified and then retransmitted through sending antennas.This spoofing includes two classical models, as shown in Figs.2 and 3.

Multi-station retransmission can realize regional mapping, and its mapping error and scale factor(≤10)are mainly determined by positions of carrying platforms; However, single-station retransmission can only realize point-to-point mapping.Thus, it is necessary to deploy multiple repeater-equipped small satellites,which is equal to a constellation deployment problem.

Fig.11.Division schematic of the force zones for GNSS suppressive jamming.

Fig.12.Curves of suppressive distances (Drj) with EIRPj based on the interference force zones and height differences (Hj - hr).

Number of GNSS retransmitted spoofers required for deploying Considering the difficulties in controlling small satellites and their high deployment cost, it is necessary to determine the basic structure of the constellation deployment.To maximize the benefits of the deployment, the selected structure should take the service performance of constellation such as coverage and interplanetary links and the economy into account; its instantaneous coverage rate and coverage time ratio should be maximized,revisit time as well as the launch cost and deployment difficulty should be minimized.Based on the above principles, the frequently-used single-chain, multi-chain, conventional δ, and common-track(RGT) constellations are taken for example, and their structures are shown in Fig.4; from Fig.4, as the single-chain constellation cannot meet the instantaneous coverage of the latitude zone and the conventional δ and RGT constellations both require more satellites which lead to higher deployment costs, a multi-chain constellation can be considered as the basic structure for deploying.

Fig.13.Curve of average capture time Tavq with the J/S.

If a multi-chain structure can meet the following constraints determined by the evaluation results of spoofing effect and the constraints based on the service performance of constellations,it is an effective multi-chain constellation.Then, its basic parameters including the number of satellites (NSa), orbital planes (PWay) and phase factors(FPh),need to be calculated,in order to carry repeaters and complete deploying as part of the multi-jamming source collaborative configuration.

Firstly, the range of the phase difference between two contiguous satellites (Δu) can be determined based on the range of the continuous coverage control factor (εOc).Subsequently, the phase configuration parameter (MPc) corresponding to the minimum γadcan be selected according to the image of γadand MPcdrawn on the range of Δu as follows:

where αsfand R ⊕are the sensor’s half-field angle and its corresponding mean radius of the earth; hSais the mean orbit altitude;γadis as the ratio of right ascension difference to declination difference, and smaller γadusually corresponds to a steeper link undulation and better coverage uniformity.Next, the range of NSacan be obtained from the MPcand the range of Δu.

where (ΔxF,ΔyF, ΔhF) and (ΔxR, ΔyR,ΔhR) respectively denote the coordinate differences of F′and R′relative to their respective neighborhood origins F and R;A and B are respectively the domain matrices of the satellite position relative to the preset false point and the repeater position relative to the real random point,whose evaluation models are as follows:

where KPhis the integer coefficient that uniquely determines an integer within FPh∊[0, PWay- 1]; and n, an odd number set as 3 herein [41], represents the number of chains in a multi-chain structure.

Positions of GNSS retransmitted spoofers required for deploying

Based on the determined small-satellite constellation with better benefits, the following method can be used to select suitable satellites in the constellation as platforms to carry retransmitted spoofing sources (called repeaters for short), in Fig.5.

The number (NSp) of the platforms to carry the repeaters are usually larger than 4 in actual countermeasures.Therefore, to obtain a more satisfactory mapping result, i.e., the shape of the neighborhood of the real random point R΄must be as similar as possible to that of the preset false point F΄, the mapping relationship between the two can be improved according to the principles and models of the classic four-station retransmitted spoofing [37],and established as follows:In the full digital simulation, the distance from the real random point to the preset false point(ρF,R)is significantly shorter than the distance from the real point to the satellite (ρR,Sa).Thus, we set |ρF,Sa| ≈|ρR,Sa| to improve the computational efficiency.When repeater is located on the line from the real point to the corresponding satellite and the following conditions are satisfied,

It is easy to obtain A=B.It can be seen from Eq.(29)when A=B≠0 and[ΔxFΔyFΔhF]T=[ΔxRΔyRΔhR]T,the optimal mapping effect is achieved.Thus,the evaluation model of 3-D position coordinates of each repeater at this point can be obtained below.

where(xSansat,ySansat,hSansat)and(xSpNSp,ySpNSp,hSpNSp)are respectively the positions of the nsat-th satellites and the NSp-th repeaters;ρF,Sa1and ρR,Sp1are the distance of satellite-1 from a preset false point and that of repeater-1 from a real random point.

Fig.14.Curve of minimum interference signal (Prj) and its (Drj)max.

4.3.Deployment principle of UAV-borne generative spoofers

UAV-borne generative spoofers with their flexibility and better concealment are suitable for performing multi-class instantaneous or continuous spoofing tasks(such as spoofing the radar which is as the eyes of a threatening target and always one of its prime targets of the defender) during countermeasures.Accordingly, assuming that the antenna pitch beamwidth of the UAV and its azimuth beamwidth are φUAVand θUAV, and the heights of the UAV and a threatening target(such as an enemy aircraft) are HUAVand Hplane,the instantaneous interference areas of a drone and its decoy to a threatening target are shown in Figs.6 and 7.

Table 1 Collection of the design results of the chain constellations based on the basic single-chain parameters.

Table 2 Comparison of the coverage performance and visibility of different constellations to target points and target areas.

Fig.16.3-D design with top and side views (top) and 2-D design results for the selected small-satellite constellation (bottom).

4.3.1.Number of GNSS generative spoofers required for deploying

Model 1 On the premise of meeting the constraints in Eq.(25),the model of a transient interference area formed by the UAV during its flight,as shown in Fig.6, can be obtained as follows:

Fig.17.Coverage performance (left) and visibility analysis (right) of different small-satellite constellations for the target point.

Fig.18.Coverage performance and visibility analysis of different small-satellite constellations for global (left) and target area (right).

Table 3 Inter-satellite link performance comparison of different small-satellite constellations.

Table 4 Comparison of the number of decoys generated by each spoofer group.

where RRmaxis the maximum reconnaissance distance of the threatening target; RJmaxis the maximum jamming distance of a decoy;φUAVand θUAVare the beam widths of the azimuth and pitch angles of interference antennas, respectively.

Model 2

If the absolute value of the difference of azimuth angles of adjacent drones relative to the threatening target ΔαUAVis not greater than θradar,the interference area of the generated decoy,shown in Fig.7,can be modelling and quantified.

where ΔRFDminand ΔRFDmaxare the minimum and maximum retransmission delay distances;RFDis the distance between a decoy and the threatening target; αUAVand αFDare respectively the azimuth angles of the UAV and its generated decoys relative to the threatening target;θradarand φradarare the beamwidths of azimuth and pitch angles of the target’s radar main lobe.

Model 3

The number of single-layer drones (NUAV) to be deployed as the interval of ΔLUAVcan be calculated according to the following models, provided that the azimuth angle (θITO) of the threatening target to the protection channel are known.

Fig.19.Simulation of a typical false track and its status tracked by a threatening target.

Similarly,the number of deployment layers of drones(MUAV)can be determined by acquiring the corresponding pitching angle (φITO).

where kfalseis the number of decoys generated by one drone in one scanning period of a threatening target;IUAVis the total number of drones present in the main lobe of the target’s radar antenna.Therefore, the sum of drones to be deployed is obtained as NUAVtotal= MUAVNUAV, in order to complete the UAV-borne generative spoofing task.

4.3.2.Positions of GNSS generative spoofers required for deploying

The short-time local generative spoofing is difficult to achieved the effect and purpose of the continuous generative spoofing;thus,the drones carrying the generative spoofers must form a network.The relay mode of each spoofer group is as shown in Figs.8 and 9:After UAV1and UAV2finish spoofing, UAV2and UAV3continue to deceive until relaying to UAVNUAVtotal-1and UAVNUAVtotal; and then,the continuous false tracks can be formed, and this spoofing task would be completed.

In the full digital simulation, the interference is carried out by UAV2and UAV3as UAV1stops working, setting the first decoy generated by UAV2and UAV3is the nlocus-th point in the false plot and with reference to a previous study[30]and Fig.9,the distance delay (Δtnlocus) required to generate the nlocus-th point and its spoofing opportunity (Tnlocus) can be calculated below.

Table 5 Comparison of interference resource requirements.

Fig.20.Validation of the deployment structure based on different angular distances and false tracks generated by spoofers.

Fig.21.Simplified graph of a rational configuration for the collaborative deployment of multiple interference sources.

where Rnlocus,αnlocus,and θnlocusare the distance between the nlocusth point and the threatening target, and their corresponding azimuth angle and angular distance,respectively;Tradar0is the instant when radar starts scanning counterclockwise from 0°; c is the speed of light;R23is the distance between a spoofer group(UAV2&UAV3) and a threatening target, whose model is below.

here,vfalseis the velocity of the decoy moving in a straight line from west to east, and Tscandenotes the radar scanning period.

5.Determination of three single-jamming sources deployment structures required by the construction of a multi-jamming sources confgiuration based on example simulations

Through the scene setting and the case-based simulations,based on the related principles created above, the relatively more suitable deployment structures of three single-jamming sources in the set situation can be determined as follows,in order to construct a rational configuration of the collaborative deployment of multijamming sources.

5.1.Deployment structure of GNSS suppressive interference sources

Deployment condition 1When the velocity(VG)of the threatening target is 670 km/h and its angular error drift rate(ΩG)is 0.1°/h,the required Ljcan be obtained as 222 km based on Fig.10.Moreover,jammers are deployed 10 km directly below the either side of airway of the target (Hj= 0.5,hr=10.5 km),and its EIRPjof matched-spectrum jamming signals is 1 kW.

Table 6 Parameter comparison of different configurations of multi-jamming sources and three structures of single-jamming sources.

Table 7 Basic definition of each evaluation index of deployment effect and its mathematical model.

Table 8 Comparison of simulation results of five evaluation models corresponding to four configurations and three structures.

Deployment condition 2 Considering a P(Y) receiver assisted with the C/A code as an example,based on the interference force zones in Fig.11 and their respective suppressive distances (Drj) in Fig.12, the interference power differences needed by the RF front-end of the jammer between the disturbed zone and the semi-failure zone and between the disturbed zone and the invalid zone are calculated as 1 dB and 3.5 dB, and their corresponding differences of Drjare respectively 2.8 km and 8.5 km.

Deployment condition 3

According to the above division principles,the maximum received power of the C/A code is set to-153 dBW[12],the antenna gain of the receiver pointing at the satellite is set to 1.5 dB,and Pfais 0.1.To determine the minimum jamming power(Prj)minrequired by its RF front-end in the interference zone when the receiver uses the C/A code to recapture GNSS signals, it is necessary that (Tavq)min>10(Tavq0).From the article[10],Tavq0is 27.31 m when Pfais equal to 0.1.

Accordingly, Fig.13 shows that when (J/S)min= 47 dB, it can be determined that the (Prj)minis equal to -104.5 dB; and based on Fig.14, the maximum suppression distance(Drj)maxcorresponding to the (Prj)mincan be obtained as 25.3 km.

Deployment structure determination

Based on the above, the effective suppressive operating distance Lj(i) of the ith source is 46.4 km, which satisfies the first, second,and fourth constraints in Eq.(21).Furthermore, it can be determined that the configuration interval of suppressive jammers in the horizontal direction should not exceed 46.4 km according to the third constraint.Finally, as calculated by Eq.(23), the number of deployed sources shall be no less than 5, to ensure a seamless coverage.

Finally,assuming that the current Prjis-116.9 dB,as calculated by Eqs.(9)and(22),the suppression distance Drjcorresponding to Prjis obtained as 20 km and the configuration interval Δ|xj(i) - xj(i+1)| is 43.648 km.Thus, the 3-D position coordinates of 8 suppressive jammers can be obtained in Eq.(39), and further the seamless deployment structure of these jammers is obtained.

5.2.Deployment structure of GNSS retransmitted spoofing sources

Deployment condition setting

Following a previous study [41], when setting the average orbit height(hSa)as 800 km and continuous coverage control factor(εOc)as[0.8,1.2],we obtain Δu ∊[19.62°,29.73°]as per Eq.(26).In the range of Δu, the point diagram of γadwith relation to MPcis obtained according to Eq.(26).It is observed from Fig.15 that γadis minimum when MPc= 2.

Accordingly,the value range of NSacan be determined as an even number between[37,55]based on Eq.(27),and hence,NSan∊[114,162].Using Eq.(28) to further calculations, we can determine PWay∊[19,27],PWayn∊[19,27],FPh∊[16,24],and FPhn∊[10,18];and their related chain-shaped design results are summarized in Table 1.

Deployment structure determination

In the full digital simulation where the simulation time is set to 24 h,for less revisit and low coverage of the LEO satellites,we select the percentage of coverage time, visibility time, revisit time, and accuracy factor (DOP), etc., as the evaluation indices for the coverage performance and visibility analysis; they have been defined and mathematically modeled in a relative study [42].The coverability and visibility of various chain constellations (132/22/13,126/21/12,114/19/10,which are selected from Table 1 according to the constraints in Eq.(25)),conventional δ constellation(170/17/0), and RGT constellation (160160/10) to the target point (Xining),the target area (latitude -15°to 45°, longitude 0°-110°), and the globe are evaluated and simulated through STK,whose simulation results are in Table 2.

Referring to the previous findings [42], the maximum revisit time based on the target point and target area, TRvmax(Point) and TRvmax(Area), their mean revisit time, TRvmean(Point) and TRvmean(Area),their coverage time ratio,αCt(Point) and αCt(Area),as well as the root mean square error(RMSE)and standard deviation(SD)of the accuracy factors,DOPRMSEand DOPSD,are set for determining these constraints from service performance of constellations.If all indicators of a constellation can satisfy their constraints in Eqs.(25)and (40), it should be selected.

Table 2 shows that compared with other constellations,only the three-chain constellation (132/22/13) can meet the given constraints in Eqs.(25)and(40).Therefore,the most suitable structure for deploying GNSS retransmitted interference sources is the constellation has 132 satellites, 22 orbital planes, and 13 phase factors, whose ascensional difference of ascending nodes is 16.36°and phase difference is 24.55°;and its designs are shown in Fig.16.

Verification of deployment results

For the verification method, it carries out based on two kinds of reference data: ①the evaluation results of the coverage performance and visibility to the target point, the target area, and the globe corresponding to different constellations, and ②the performance parameters of inter-satellite link of constellations.For the first point, according to Table 2, related service performance evaluation results are in Figs.17 and 18.For the second point, considering the distribution characteristics of the chain-shaped constellation,the selected constellation(132/22/13)needs a total of four closed links,while the conventional δ constellation(170/17/0)requires at least 10 noncoplanar orbit links, the RGT constellation(160/160/10) needs only one closed link but with less robust; and performance parameters of the inter-satellite links for three constellations are listed in Table 3.

From Figs.17 and 18,①the αCt(Point)and αCt(Area)of 132/22/13 are the largest, its TRvmax(Point), TRvmax(Area), TRvmean(Point),TRvmean(Area),DOPRMSE,and DOPSDare the smallest;and hence,its coverage performance and visibility for target points and target areas are the best; ②all results of 132/22/13 can meet the given constraints.Therefore, from the service performance of constellations, the verification of the constellation selected in this section would been completed.

From Table 3, ①compared with other constellations, the distance between noncoplanar orbit inter-satellite links of the threechain constellation selected herein is the longest, which can be used as a supplement to its coplanar orbit inter-satellite links;accordingly, the constellation can achieve full connectivity while others cannot; and ②the angle parameters of the three-chain constellation are comparable to the conventional δ constellation whose directional angle performance is relatively better.From the performance of inter-satellite links of constellations, the verification of the constellation selected is completed.

5.3.Deployment structure of GNSS generative spoofing sources

Simulation situation

With the threatening target located at the origin(0,0,15)(its unit is km, same as below), the X-axis and Y-axis positive directions are respectively set to 0°and 90°, and radar scans counterclockwise from 0°at time 0 at an interval of 6 s and its main lobe width is set as 1°.As calculated by Eqs.(35) and (36), four layers with at least three spoofers per layer need to be deployed at an interval of 750 m.After determining the approximate location of the threatening target, assuming that there are 4 spoofers (UAV1-UAV4) respectively deployed at (0, -50,15), (0.75, -50, 15), (1.5, -50, 15) and(2.25,-50,15),it can be seen from Fig.8 their θ1locusand R1locusare set as 0°and 50 and angular distances of adjacent drones(θ12,θ23,θ34)are all set to 0.86°.Also, these spoofers can be covered with the threatening target simultaneously.

Depoyment simulation test 1

If the generated decoys start from the starting point (0, -200,15)after 5 cycles of radar scanning and move in the radial direction of 80°, oblique direction of -55°, and tangential direction of 0°at a speed of 350 m/s,the number of decoys generated by each spoofer group can be determined in Table 4.

From Table 4,when the proposed deployment method is used to simulate close radial motions, the angular variation among the decoys in the scanning period is small, and therefore, continuous generative spoofing can be achieved with less spoofers; while simulating the tangential motion, the angular variation is large,making this method difficult to achieve continuous generative spoofing.As the decoys close to radial motions are the focus of the simulation during actual countermeasures, the deployment method in this study can largely meet the requirements of the antagonistic game.

Depoyment simulation test 2

Based on Test 1,the decoys can be used as the measurement data of the threatening target.Supposing that its range error and angle error are 50 m and 0.1°,and the 3/4 sliding-window approach and extended Kalman filter method are adopted for track initiation and state estimation,persistent false tracks can be obtained as shown in Fig.19.

Fig.19 shows that the false tracks generated by the built deployment method can effectively deceives the threatening target,and make this target to steadily track the decoys.

Deployment structure determination Based on the above results,the radar main lobe width should be set to 1.6°when the spoofers are deployed, UAV1-UAV14should be respectively deployed at(0,±50,15),(±1.35,±50,15),(±2.7,±50,15)and (±4.05, ±50, 15), and the angular distance between each adjacent spoofers is 1.54°,where the generated decoys would move from the starting point(0,-300,15)in the radial direction of 80°at a speed of 350 m/s.Other conditions are same as Test 1.

Validation of deployment results

To validate the deployment structure, based on the simulation results obtained, as exemplified using UAV1-UAV4, we present the effect of different performance parameters on the number of spoofers required to generate 20 decoys in Table 5.Furthermore,the relationship between the number of decoys and the ability of the threatening target to track decoys is presented in Fig.20.

From Table 5, the larger the desired radar main lobe width during the deployment, the greater the distance between decoys and the radar, and the larger the angular distance between each adjacent spoofers are, the smaller number of spoofers required to generate a certain number of decoys.

From Fig.20, the spoofers can generate more decoys continuously when the distance between decoys and the threatening target with larger radar main lobe width is increased, and their spoofing continuity is stronger.When the number of spoofers is constant, the proposed deployment structure is more effective in performing long-range continuous generative spoofing on the target.

6.Proposal of a rational configuration for multiple interference sources based on the obtained single-source structures and evaluation and verification of the deployment effect and its rationality

6.1.Determination of a rational configuration

Based on the created deployment principles of suppressive jammers, GNSS repeaters and generative spoofers, and the simulation results and verified results of the built effective and suitable deployment structure of each single interference sources,a rational configuration for collaboratively deploying multiple interference sources can be determined, shown in Fig.21: ①Layer 1: For the ground layer, 8 suppressive jammers are uniformly deployed 8.660 km away from the both sides of the air route of a threatening target, their position coordinates are in Eq.(39), and their deployment interval is 43.648 km.② Layer 2: On the air layer,UAV1-UAV14with generative spoofers are respectively arranged in(0, ±50,15), (±1.35, ±50,15), (±2.7, ±50,15), and (±4.05, ±50,15)around the circle, whose adjacent angular distances are all set to 1.54°; their generated decoys would move from the starting point(0,-300,15)in the radial direction of 80°.③Layer 3:On the space layer, the multi-chain small-satellite constellation, consisting of three single chain(44/22/19)and four closed inter-satellite links,is deployed as the platforms to carry GNSS repeaters; its phase factors, ascensional difference, and phase difference are respectively set to 13°, 16.36°, and 24.55°.Finally, based on Fig.21 and the following evaluation indices,the collaborative deployment effect of the proposed configuration can be evaluated and its rationality can be further verified.

6.2.Evaluation of the proposed configuration and verification of its rationality

Given that the evaluation indices of the deployment effect of satellite-borne repeaters have been proposed as the verification for the effective deployment of retransmitted spoofing sources, only the five evaluation indices (coverage rate of interference sources,average risk index,mean time between incidents,ground/air/space collision safety PELOS,G,PELOS,A,PELOS,S,and total collision safety)are selected for evaluating the deployment effect of the singlejamming source deployment structures in the configuration proposed and the collaborative deployment effect for multi-jamming sources corresponding to the various configurations with different setup parameters in Table 6 and verifying the rationality of the proposed configuration through further comparisons.Owing to length limit, we present only simplified mathematical models of each evaluation index (refer to Refs.[34,43] for detailed derivations), as shown in Table 7; and their corresponding simulated evaluation results are compared in Table 8.

The results in Table 7 indicate the following:①Larger SSpand SSjare preferrable when Smis given,and thus,f1(P)and f2(P)belong to maximum indicators (↑); otherwise, they are minimum indicators(↓).larger f1(P)and f2(P)for a given range correspond to the better deployment effect of GNSS interference sources.②Smaller f3(P)correspond to the better deployment effect partly, because the effective suppressive area certainly contains the planar area mapped by the effective deceptive range when designing the deployment structure.③ As tMTBIis inversely proportional to fSFR,manufacturers need to design the core hardware with a larger tMTBI,in order to reduce the accident rate of all types of running equipment and optimize their reliability.④Owing to the proportional relationship between the PELOS,G, PELOS,A, PELOS,Sand their hourly accident rates as well as the probabilities of death caused by collisions, PELOSshould be as small as possible to reduce the probabilities of death and accident when Smis given.⑤PELOSis approximately equal to the weighted sum of the PELOS,G, PELOS,A,PELOS,S; and thus, the smaller the PELOSis, the better the deployment effect of GNSS interference sources can be.

According to the evaluation criteria of deployment effect,compared with the evaluation results of different configurations(in Table 6), it follows from Table 8 that: ①except for the tMTBIcorresponding to single-source deployment structures might be better than that corresponding to configurations for collaboratively deploying multi-jamming sources because of related hardware attributes,other evaluation results corresponding to configurations for deploying multi-jamming sources are all better than those for single-source deployment structures.Thus, the defense capability of multi-jamming sources to GNSS is superior to that of the singlejamming sources.②Evaluation results of the configuration proposed in this paper meet their evaluation criteria,and these results are all better than those of other configurations of deploying multijamming sources, and further the rationality of our proposed configuration can be verified.Then, compared the evaluation results of three deployment structures of suppressive,retransmitted,generative jamming sources built in this paper with evaluation results of our proposed configuration,it follows from Table 8 that:①Except for f1(P) in the spoofer deployment, tMTBIin the UAVborne spoofer deployment, and f2(P) in the suppressive jammer deployment, which do not meet the evaluation criteria owing to device-dependent properties, all the evaluation results of three single-source deployment structures in our proposed configuration are far more than their criteria and corresponding deployment effect are sound.② Although each structure in the proposed configuration is rational and valid in its corresponding simulation examples, their PELOS,G, PELOS,A, PELOS,Sand PELOSare still higher,f3(P) also; thus, there is big room for improving related running devices.③In particular, the deployment structure of UAV-borne spoofers has the highest f3(P) and the lowest f2(P), which in turn leads to their highest collision safety;thus,to improve the safety of this type of deployment,the ways including the airspace use,route planning,and drone design can be considered in the future.In sum,based on the above evaluated and compared results,the rationality of the proposed configuration is verified, and corresponding improvements of three single-source deployment structures contained in this configuration would be performed.

7.Conclusions and future work

To realize the ground-air-space collaborative deployment of multiple interference sources,in this paper,①we have created the evaluation indices and developed the principles to realize the fulldomain collaborative deployment of GNSS suppressive and deceptive jammers under navigation countermeasures;②we have proposed a rational configuration for collaboratively deploying multi-jamming sources based on the developed principles and evaluated its deployment effect to verify the rationality of the proposed configuration;and ③we would deploy this configuration to improve the defense capability to GNSS.Specific conclusions and directions for future studies are below.

(1) Based on the created key evaluation indicators for the jamming effect, the principles for realizing the collaborative deployment of GNSS multiple interference sources have been developed: ①For ground-based suppressive jammers, the allocation interval should be no larger than half the sum of the effective suppressive operating distance of adjacent jammers, and the structure having a smaller number of jammers should be selected.②When deploying satellitebased retransmitted spoofers, the selected structure should have larger instantaneous coverage rate and coverage time ratio and smaller revisit time, launch cost, and deployment difficulty.③When deploying UAV-borne generative spoofers, the selected structure should have the ability to continuously generate more decoys with the increase of the distance between decoys and the threatening target having a larger radar main lobe width, and have a larger spoofing success rate.

(2) Based on the established full-domain deployment principles and case-based simulation analysis, a rational configuration for collaboratively deploying multiple interference sources has been proposed: ①The first layer is the ground layer,which deploys 8 suppressive jammers evenly at 43.648 km interval, along 8.660 km on both sides of the threatening target’s air route.②The second layer is the air layer, where UAV1-UAV14with generative spoofers are deployed around the circle at(0,±50 km,15 km),(±1.35 km,±50 km,15 km),(±2.7 km, ±50 km,15 km), and (±4.05 km, ±50 km,15 km),with each angular distance of 1.54°between adjacent spoofers.③The third layer is the space layer,which deploys a three-chain constellation with 132 small satellites and 13 phase factors in 22 orbital planes at an orbital altitude of 800 km and orbital inclination of 53°as the platforms to carry retransmitted spoofers, and builds 4 closed intersatellite links.

(3) Based on the developed evaluation indices of deployment effect, the collaborative deployment effect of the proposed configuration has been evaluated and its rationality has been verified: ①All the evaluation results of the configuration proposed in this paper meet their evaluation criteria, and these results are all better than those of other configurations of deploying multi-jamming sources.② Although each single-source deployment contained in this configuration is rational and effective in its corresponding instance simulation, its total collision safety and the risk index are higher than the corresponding results of this configuration.Therefore, although the rationality of the proposed configuration has been verified, its deployment structures of single interference sources have room for improvement partly; in particular, the deployment of GNSS generative spoofing sources, which affords the highest risk index and collision safety, should be focused on.

(4) Based on the obtained evaluation results, specific suggestions for improving the single-source deployments in the given configuration and further realizing the optimal configuration have been brought forward.①As the safety of UAV-borne generative spoofers is relatively worse, the deployment of the cluster of drones will be improved from the aspects including performing the air traffic control to reduce the probability of conflicts, designing the route network away from crowds or in areas with significant ground cover to reduce the operational risk of flight equipment, and adding the anti-collision design of drones to reduce the probability of collision between them.②Intelligent evolutionary algorithms,such as a hybrid method based on hybrid algorithm and particle swarm optimization,which can realize the global optimality, will be introduced in the future; for the setup parameters of various multiinterference sources configuration, it is possible to obtain the global optimal configuration through constructing the matrix and its corresponding equations and using this method to solve the equations.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China (Grant No.42174047 and No.42174036) and the National Science Foundation Project for Outstanding Youth(No.42104034).