Research Article
Detection and elimination method for deception jamming based on an antenna array
International Journal of Distributed Sensor Networks 2018, Vol. 14(5) Ó The Author(s) 2018 DOI: 10.1177/1550147718774466 journals.sagepub.com/home/dsn
Shuyan Ni, Jianhua Cui, Naiping Cheng and Yurong Liao
Abstract A global positioning system is an important way of locating an aircraft, while deception jamming can affect the positioning accuracy of such navigation. Considering this, a detection and elimination method for deception jamming is proposed based on a specially designed array for the aircraft. The jamming is detected by comparing the double-difference observation of the carrier phases of two different signals to a certain threshold derived according to the measurement errors of the receiver. To estimate the jamming direction with high accuracy, meanwhile considering the feasibility of airborne installation, a novel configurated array combining medium-length baseline with short baseline is designed, and a fast method to solve the integer ambiguity is discussed. After jamming detection, the nulling of the array beam is pointed to the jamming source through the orthogonal vector weighting to suppress jamming. The validity of the method is verified by computer simulations. Keywords Deception jamming, antenna array, carrier phase, double difference, integer ambiguity
Date received: 1 June 2017; accepted: 16 March 2018 Handling Editor: Riccardo Colella
Introduction A global positioning system (GPS) offers advantages by virtue of its high-precision and all-weather conditions: GPS has been widely used in military systems, such as on-board missiles and unmanned aerial vehicles, which also promote the development of jamming technology against GPS. Deception jamming, as a typical jamming mode, misleads GPS receivers by emitting similar signals to those from the GPS or transmitting real satellite navigation signals, resulting in inaccurate positioning results.1 Deception jamming uses a low transmit power, which is only slightly higher than that of normal navigation satellite signals to make a receiver wrongly judge deception signals as navigation signals to be captured and tracked, thus jamming normal navigation. From the perspective of detection and elimination of deception jamming, there are many current and recent research projects available: Psiaki et al.2 detected
deception jamming signals by using the double-antenna method or the single moving-antenna method.3 The double-antenna method detects the jamming through the difference in carrier phases of two antennae. Due to the short baseline between the two antennae, the method shows a limited estimation precision and needs to solve the integer ambiguity with a high complexity. While the single moving-antenna method detects jamming based on the related information from navigation signals received at different times, but has a limited anti-jamming ability. Montgomery et al.4 detected Department of Optical and Electrical Equipment, Equipment Academy, Beijing, China Corresponding author: Naiping Cheng, Department of Optical and Electrical Equipment, Equipment Academy, Beijing 101416, China. Email:
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 deception jamming based on the error between the observed and the expected value of the carrier phase difference of double antennas, which is easy to implement but requires the attitude of the antennas. Daneshmand et al.5 proposed a detection and elimination method for deception jamming by using antenna arrays and eliminated deception jamming by adjusting the weight of each antenna array. Moreover, the gain is formed in the direction of the desired signals, but the jamming elimination method presents low accuracy. This article concerns both the detection and the rejection of deception jamming based on an antenna array applied in an aircraft. To detect the jamming, a method based on the double-difference observation is proposed, which is easy to implement, and its confidence is analysed. To estimate the direction of the jamming, a novel array according to the aircraft structure is designed, and a fast method to solve the integer ambiguity is discussed, for high accuracy and high speed, respectively. Then, to suppress the jamming, a nulling method is also discussed combined with practical applications. Simulation results have verified the validity of the proposed method. The rest of this article is organized as follows. Section ‘Detection model for the antenna array’ presents the detection model for the antenna array as a basic. The high-accuracy detection method of deception jamming is proposed in section ‘High-accuracy detection of deception jamming’. Elimination of deception jamming signals is discussed in section ‘Elimination of deception jamming signals’. Computer simulations for detecting and elimination are done in section ‘Computer simulations’ to prove validity of the methods. Conclusion remarks are given in section ‘Conclusion’.
Detection model for the antenna array The uniform circular array with its core (Figure 1) is used: it has seven array elements. Element 0 located at the centre of the circle is used as a reference element, while elements 1–6 are uniformly distributed around the circle with radius R and the reference element at its centre. To ensure that there is no integer ambiguity, the
International Journal of Distributed Sensor Networks distance R between any two adjacent elements is smaller than the half of the carrier wavelength l, that is, R\l=2. The coordinate system is established by taking the reference array element as the origin (Figure 1). The angle of array element n (n = 1, 2, . . . , 6) relative to the positive direction of the x-axis is bn = (n 1)p=3. Assuming that the incident direction of signals is (u, u), where u and u represent the pitch angle and azimuth, then the actual phase difference of signals received by array element n and the reference array element is Dun =
2p R cos u cos (u bn ) l
Therefore, the direction vector of the array in the (u, u) direction is a(u, u) = 1
eDu1
. . . eDu6
T
ð2Þ
After application of the PN code and carrier synchronization, the observations of carrier phases only include the fractional part of the actual carrier phases, but exclude the integer part. In addition, considering various internal and external errors affecting the receiver, the observations of the carrier phases can be expressed as6 2p l (d + Dd + cDt r cDt s + cDg c + cDg t cDg i + cDg m ) N + e f=
ð3Þ
where d, Dd, c, Dtr , Dt s and Dg c represent the distance from an antenna array element to a satellite, the orbit error of the navigation satellite, the propagation velocity of electromagnetic waves, the clock error of the receiver, the clock error of the satellite and the delay error caused by signal lines in the receiver, respectively. Furthermore, Dg t , Dg i , Dg m , N and e indicate the delay error in the troposphere, the delay error in the ionosphere, the multi-path error, the integer number of carrier phases and the measurement noise, respectively. If the carrier phase of a signal source is observed by using two array elements, the phase difference of the two measured array elements is known as a single difference, while the difference between single difference measurements of two different signal resources is called a double difference. For a signal source, the single difference obtained by using the reference array element 0 and array element n is Dfn = fn f0
Figure 1. Model for the antenna array.
ð1Þ
ð4Þ
When two array elements receive the same signal, (1) orbit errors, (2) clock errors of the satellite and (3) the clock errors of receivers with the same source of each array element are same. Moreover, (4) the distance between array elements is far smaller than that between
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satellites, so the errors from the troposphere and ionosphere are almost the same. (5) The line length of each channel, in line layout, is consistent, which ensures the same delay error in each signal line. (6) Due to a few reflectors being between the navigation satellite and the array elements, the multi-path error can be ignored. (7) Due to the limitation of the baseline length, the integer number of carrier phases of the two array elements is the same. Therefore, Dfn can be simplified to 2p 2p dn + e n d0 + e 0 l l 2pDdn 2p + Den = = ½R cos (u bn ) cos u + Den l l ð5Þ
Dfn =
where Den = en e0 and Ddn = dn d0 . As for the different signals, superscripts are used to represent different signal numbers, Dfin and Dfnj denote the single differences of array element n and the reference array for signal i and j, respectively. The double difference of carrier phases obtained by subtraction between two single differences is expressed as Dfijn = Dfin Dfnj = 2p 2p ij (Ddni Ddnj ) + (Dein Denj ) = Ddn + Deijn = l l ð6Þ
where Ddnij = Ddni Ddnj and Deijn = Dein Denj .
P Deijn 6s = P Deijn 0:04p = 0:9973
ð8Þ
In other words, if two PN code signals are generated by the jamming source, the double difference of carrier phases is Dfijn 0:04p and the confidence therein is 0.9973. For two actual navigation signals, due to different directions, as the first term exists in equation (6), there is only a small possibility that the double difference is so small. And considering that, there are several pairs of elements in the array, there is little chance that all double differences are so small, which provides better robust than the double antennas. Therefore, when the double difference of the corresponding carrier phase PN code signals measured by the receiver is of different Dfij 0:04p, it is considered that the signal source n corresponding to the two PN codes represents deception jamming. Taking this method for detection, we only need to calculate the double difference based on the observation value of carrier phase, then by comparison with 0:04p, the jamming can be detected, which is very simple to implement.
Direction estimating of jamming
High-accuracy detection of deception jamming Jamming detection Deception jamming is generally emitted by a jammer through a single antenna, showing the same location and direction for different PN code signals, while real navigation signals are generated from various directions. The deception jamming is detected on this basis. For two actual navigation signals, due to different directions, the first term exists in equation (6) Ddnij = Ddni Ddnj 6¼ 0. As to the deception jamming sources, in the single differences Dfin and Dfnj of the array element n and the reference array element for two different PN code signals i and j with the same jamming source, because Ddni = Ddnj , the double difference is Dfijn = Dein Denj = Deijn
obtained. According to the current level of the receivers, the track error of carrier phases is generally smaller than 1% of the carrier wavelength,8 that is, jej 1% 3 2p = 0:02p. With respect to the normal distribution e;N (0, s2 ), P(jej 3s) = 0:9973. Therefore, it can be considered that 3s ’ 0:02p. In addition, owing to Deijn ;N (0, 4s2 ), then
ð7Þ
In general, the measurement error of carrier phases is the normal distribution of e;N(0, s2 ).7 According to the characteristics of the normal distribution, the single difference error Den = en e0 ;N (0, 2s2 ) and the double difference error Deijn = Dein Dein ;N(0, 4s2 ) are
After detecting the interference, the direction of the jamming is estimated by using the single difference of carrier phase of the jamming signal. Let bn = ½ R cos bn R sin bn comprise the x- and y-coordinates of array element n and n = ½cos u cos u cos u sin uT consist of the x- and y-coordinates of the unit vector in the direction of incident signals projected on the xoy-plane, then the single difference Dfn in equation (5) can be written as Dfn =
2p bn n + Den l
ð9Þ
The single differences of carrier phase between array elements 1–6 and the reference array element are adopted to construct observation vector Df = ½Df1 , . . . , Df6 T , then 3 2p 6 l b1 n(u, u) + De1 7 7 6 7 6 2p 6 b2 n(u, u) + De2 7 Df = 6 7 = Bn + De l 7 6 . 5 4 2p b2 n(u, u) + De6 l 2
ð10Þ
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where B = (2p=l)½ b1 b2 b6 T and De = ½De1 , . . . , De6 T represent the coefficient matrix and the error vector, respectively. To minimize the error, the cost function G(n) = Bn Df is constructed, and the least squares method is used to solve for vector n n = (BT B)1 BT Df = ½x, y
ð11Þ
Then the pitch angle and azimuth of incident jamming signals can be further calculated as
u = arctan (y=x) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u = arccos ( x2 + y2 )
ð12Þ
For the given circular array, to avoid the existence of integer ambiguity which influences the estimation accuracy, the single difference Dfn = 2pDdn =l + Den \p has to be satisfied, that also means Ddn \ (p Den )l=2p. Given that Den ;N (0, 2s2 ), according to the characteristics of the normal distribution there is pffiffiffi P(jDen j 3 2s) = 0:9973. If the distance between element n and the reference element satisfies pffiffiffi R\(p 3 2s)l=2p = 0:486l (giventhat 3s ’ 0:02p) ð13Þ
then, for signals from any directions the ambiguity condition Ddn R\(p Den )l=2p is satisfied with a confidence of 0.9973. So the distance R should be designed under the constraint of equation (13). For the L1 carrier of GPS that is R\0:486 3 0:19m = 0:0925m.
Figure 2. Medium-length baseline antennae.
on the relationship between medium and short baselines a faster and easier solution is discussed below. Assuming short-baseline element n is collinear with medium-length element m, given that Ddm = lDdn , the difference between the carrier phases of element m and the reference element is theoretically l times that of element n, the integer number can therefore be estimated by using the measurement value of Dfn , that is N = floor
0
Dfm = Dfm + 2pN
ð14Þ
Therefore, to obtain the complete carrier phase difference, the integer number N needs to be calculated. There are many ways to solve integer ambiguity. Based
ð15Þ
To analyse the confidence of equation (15), the actual single difference of the medium-length baseline is represented as
Measures taken to improve accuracy When the jamming direction is solved by using the circular array with its core, the estimation accuracy is limited due to the short baseline. To improve the estimation accuracy and considering the feasibility of airborne installation, two elements with medium-length baselines9 are arranged collinear with elements 1 and 2 of the original short-baseline array (Figure 2), numbered 7 and 8. The length of the baseline is designed to be lR. Assuming that the single difference observation of the new element m (m = 7, 8), and the reference array element for the carrier phases is Dfm , due to the existence of integer ambiguity on the longer baseline, the 0 observation Dfm is only the fractional part of the carrier phase difference Dfm , that is
Dfm lDfn = floor 2p 2p
Dfm =
2p 2p Ddm = lDdm = lDfn lDen l l
ð16Þ
pffiffiffiffi Given that lDen ; N (0, 2ls2 ) and P(jDen j 3 2ls) =p0:9973, considering the maximum error value is ffiffiffiffi 3 2ls in the confidence of 0.9973, only when the fractional part of lDfn satisfies pffiffiffiffi pffiffiffiffi lDfn 3 2ls\2p mod \2p 3 2ls 2p
ð17Þ
There is no cycle skipping. In other words, when the equation (17) is satisfied, the integer number can be calculated by N = floor(lDfn =2p) with a confidence of 0.9973. The single difference of carrier phases ranges from 0 to 2p with a uniform distribution, that is, the reliabilpffiffiffiffi ity for equationpffi (17) is only (2p 2 3 3 2ls)= 2p = 1 0:02828 l, given that 3s ’ 0:02p. Take a certain type of unmanned aerial vehicle as an example, the short baseline is designed as 0.09 m based on equation (13), and the medium baseline is designed as
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1.84 m, considering the aeroplane structures, so l = 20:4 and the reliability is 87.2%. Allowing for the fact that the rotation of the aeroplane can avoid such invalidity, owing to the double difference of carrier phases being related to the azimuth and change in pitching of antenna array elements. By combining the integer part obtained by use of the above method, with the fractional part obtained through measurement, the single difference between carrier phases of the long baselines is obtained. Then combining with the estimating method for directions outlined in section ‘Direction estimating of jamming’, the more accurate direction of jamming signals can be obtained.
Elimination of jamming signals To eliminate the deception jamming signals, according to the signal vector received by each array element, if a set of weight coefficients v can be found such that vH aJ = 0, the output signal weighted with v changes to13–15 y(t) = vH r(t) =
p X
vH a(ui , ui )Si (t)
i=1
+ vH a(uJ , uJ )
q X
Jj (t) + vH e(t)
ð20Þ
j=1
=
p X
vH a(ui , ui )Si (t) + vH e(t)
i=1
Elimination of deception jamming signals After detecting the jamming signal direction, the array weights are designed to suppress the jamming signals while making the maximum gains of array beams point to the desired signals.
Therefore, only if a set of weight coefficients orthogonal to aJ is found, the jamming signals can be elimi1 H nated. Let Q = E aJ (aH J aJ ) aJ , because h i 1 H QH aJ = E aJ (aH a ) a J J J aJ 1 H = aJ aJ (aH J aJ ) aJ aJ = 0
Array incident signal model Supposing that there are p navigational satellites which send signals in the direction of (ui , ui )( i = 1, . , p) and a deception jamming source in the direction of (uJ , uJ ) emitting deception jamming signals with q PN codes, the q PN codes produced by jamming are the same as the PN codes of p actual navigation satellites, the vector of the received signals of the array is10,11 r(t) =
p X
a(ui , ui )Si (t) + a(uJ , uJ )
i=1
=
p X i=1
q X
ai Si (t) + aJ
y(t) = =
Jj (t) + e(t)
ð18Þ
j=1
pffiffiffiffiffi Si (t) = pPffiffiffiffiiffiDi (t t i )Ci (t t i )e jfi + j2pfi t Jj (t) = Pj Dj (t t j )Cj (t t j )e jfj + j2pfj t
p X i=1 p X
H
(QQH a(ui , ui )) a(ui , ui )Si (t) + QQH a(ui , ui ) (a(ui , ui )Q)H Qa(ui , ui )Si (t)e(t)
ð22Þ
i=1
where aJ = a(uJ , uJ ) and ai = a(ui , ui ). e(t) is the receiving error vector. Si (t) and Jj (t) indicate the ith GPS signal and the jth deception jamming signal received by the reference array element, respectively. That is12
The matrix Q is orthogonal to aJ . Let weight vector be v = Qh(H is a column vector), then vH aJ = 0. To make the main beam point in the specific direcwhile inhibiting jamming, let tion (ui , ui ) h = QH a(ui , ui ), then,
Jj (t) + e(t)
j=1 q X
ð21Þ
ð19Þ
where Pi and Pj represent the signal powers of the ith GPS signal and the jth deception jamming signal, respectively, Di (t) and Dj (t) indicate their data, Ci (t) and Cj (t) are PN codes, and t i and tj stand for the propagation time-delays. Moreover, fi and fj denote the initial phases, while fi and fj are the Doppler frequency shifts of the two signals to their receivers.
However, considering that the direction (ui , ui ) of the actual satellite is unknown at the moment, we can only point the beam to a certain direction (u, u) for searching. If the jammer exists at startup, we have to search in the whole airspace until one satellite enters the beam. As the main lobe of the seven-element circle array is wide, and there are several navigation satellites in the airspace, the process will not take long. If the beam is tracking a satellite signal when the jammer impinges, we can use the direction of this satellite for searching. As long as any GPS satellite enters the beam, the positions of actual satellites can be settled utilizing the navigation message.
Computer simulations
Simulation 1: detection of deception jamming signals
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International Journal of Distributed Sensor Networks
Figure 3. Observed double differences of carrier phases in the presence of jamming: (a) 3D view and (b) xoz-plane view.
Supposing that, there are four navigational satellites (S1–S4 with PN codes 1–4) and a deception jamming source J, which emits four jamming signals which are consistent with the PN codes of S1–S4, and the signal to interference ratio is –10 dB. The measurement error of carrier phases in the software-defined ratio (SDR)
receiver is set to be random value with the normal distribution of e;N (0, s2 ) when s = 0:02p=3. Equivalent to wavelength of carrier L1 which is 0.19 m, that is, s = 0:02p=3=2p 3 0:19 m = 0:00063 m. Assuming that the absolute locations of jamming and the four navigational satellites at a certain moment are
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Figure 4. Interference detection probability.
S1 = ½3472964, 19696155, 20000000 S2 = ½5773500, 10000000, 20000000 S3 = ½8845515, 7422268, 20000000 S4 = ½18793852, 6840402, 20000000 J 1 = ½1975, 5426, 10000
By using the projected point of the jamming source on the ground as a centre, a square measuring 100 km 3 100 km is established. The detected doubledifference values of carrier phases of array element 1 and reference element to every two PN code signals are shown in Figure 3: the units in Figure 3 are metres and the carrier phase is equivalent to the wavelength. Both three-dimensional (3D) view and xoz-plane view are given in the figure, and the title DDij represents the double difference of PN code signal i and j. On the basis of the proposed detection method, the threshold is set to be 0:04p, that is 0.0038 m equivalent to wavelength. It can be seen from the simulation figures that in the neighbouring jammed areas, all the double difference of carrier phases are no more than 0.0038, while in other areas most are far larger than 0.0038. This verifies the feasibility of the detection method proposed in this study. To count the detection probability and the falsealarm probability, the aircraft walks through all the locations of the set area with a step of 500 m and 40,000 steps in total. At every step, the jamming is detected with a random carrier phase error set in the receiver in the normal distribution of e;N(0, s2 ). Then according to the results of the 40,000 times of detecting, the detection probability and the false-alarm probability are calculated. The variance s is set from 0 to 2 mm (which has been equivalent to wavelength) with a step of 0.1 mm. With every value of s, the same process above is implemented, and then the detection probability and the false-alarm probability with s are shown in Figures 4 and 5.
Figure 5. False-alarm probability.
We can see that the detection probability is smooth at the beginning with a high value almost 100%. But when s is over a certain value, it decreases sharply. That is because the detection threshold we set by supposing the error variance of observation receiver is 0.63 mm. When s goes beyond that, the detection performance will suffer from deterioration. From Figure 5, we see that, the low false-alarm probability is related not only to the error, but also to the directions of double navigation signals. When s increases, the curves of DD12 and DD23 increase sharply while the others remain smooth at the zero level. These results can be explained from Figure 3. The double differences from two actual navigation signals are very low for DD12 and DD23 as shown in Figure 3, due to their relative position to the measurement baselines, which may cause a high probability of false alarm. As there are several baselines used in the array, there is little chance that the double difference of every baseline is smaller than the detection threshold, which can be used to reduce the false-alarm probability and improve the robust.
Simulation 2: elimination of deception jamming signals
Supposing that the azimuths and pitch angles of four navigational satellites are S1 (80°, 45°), S2 (50°, 40°), S3 (320°, 60°) and S4 (190°, 45°), the direction of jamming source J is (200°, 60°). The anti-interference beam patterns for each satellite are shown in Figure 6. It can be seen that, a high gain is formed in the direction of S1;S3, meanwhile the interference signal is suppressed. However, as S4 is too near to the direction of interference, it suffers a great loss in gain. As there are more than four navigation satellites visible in the airspace, if
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International Journal of Distributed Sensor Networks
Figure 6. Anti-interference beam patterns for each satellite: (a) 3D view and (b) overlook view.
Figure 7. Two-dimensional time–frequency search: (a) received signals of the array and (b) output signals of the weighted array.
the signal of S4 is too weak to be demodulated, we can choose another one in a different direction. When the PN code of S1 is used for a twodimensional time-frequency search, the input and output of the array are as shown in Figures 7. The sampling frequency is to set be 25 MHz. It can be seen that the jamming signals are suppressed to a significant extent with its correlation value reducing from 3270 to 353, due to the effects of the orthogonal matrix after array weighting.
Conclusion Deception jamming is a serious threat for the aircraft. To counter it, a detection and elimination method is put forward in this article, based on a special antenna array designed for the aircraft. Combining the uniform circular array with added two elements with medium
length, the array can be used both in high-accuracy detecting and in jamming eliminating. In the jamming detection, based on the direction differences of real navigation signals and deception jamming signals, the double-difference observation is used to be compared to a certain threshold related to the measurement errors of the receiver. The detection method is easy to implement, and both the theoretical analysis and the simulation results show its high detection probability. After detecting, the jamming direction is estimated with high accuracy and high speed, due to the extended baseline in the new designed array and the fast method to solve the integer ambiguity. On the basis of the estimated direction, the orthogonal matrix is constructed to eliminate jamming. Then utilizing the signals without jamming, the actual GPS signal, which the main beam should be pointed to, can be searched.
Ni et al. The simulations show that this method can identify and eliminate deception jamming of navigation signals, and ensure the navigation and positioning accuracy of aircraft in a complex environment. Acknowledgements Shuyan Ni and Jianhua Cui contributed equally to this work.
Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.
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