A Model to Evaluate Jammer Influences on Ranging Measurements

Abstract

Recently, number of intentional jamming has increased significantly. If GNSS jammers are activated, user receivers can be largely influenced due to the vulnerable characteristic of the GNSS (Global Navigation Satellite System) signal. When the reception power of the jamming signal and that of the navigation signal are similar, the C/A (Coarse Acquisition) chip delay error can occur in the delay locked loop. To evaluate the jamming effect, a new measurement model is formulated based on previous research works. The new model explains how the jamming to signal ratio affects the ranging measurement accuracy and other parameters. To evaluate the validity of the newly formulated model, the experiment results of the previous research works under actual jamming environment are utilized. By evaluating the consistency of the carrier-to-noise ratio (C/N0) and the position error with the actual jamming environment, the validity of the newly formulated model is verified.

1. INTRODUCTION

The satellites located around 20,000 km higher than the ground are transmitting navigation signals to the earth in Global Navigation Satellite Systems (GNSSs), which are operated by the U.S., Russia, EU, and China. The received signal power on the ground is very weak as -160 dBW. Thus, signals are highly sensitive to intentional jamming or surrounding environments (Grant et al. 2009).

A jamming technique refers to the transmission of intentional strong disturbance signals to the frequency band used in navigation signals thereby preventing users from receiving navigation signals. Thus, if an intentional jamming occurs, ranging measurements cannot be received normally, thereby making the calculation of user’s navigation solution difficult. In addition, navigation signals cannot be tracked continuously or will be lost within seconds to minutes (Choi & Ko 2015).

The jamming technique applied to GNSS signals can be divided into the wideband and narrowband types. The wideband jamming refers to the technique that wideband-modulated signals put jamming effects over the frequency band of navigation signals. This technique consumes large power and cost. In contrast, the narrowband jamming is the technique that narrowband-modulated signals put a jamming effect in a specific GNSS frequency band, which is easy to produce by using a small-size jammer. For wideband jamming, studies have been conducted mainly on imposing hostile Gaussian noise over GNSS frequency bands. On the other hand, for narrowband jamming, there have been several different studies: tone jamming type of continuous wave, sweep jamming type with varying frequency, pulse jamming type that is effective to a direct sequence spread spectrum system, and harmonic frequency jamming type (Kim 2013).

In addition, various anti-jamming techniques have been studied to effectively cope with jamming attacks in a navigation warfare environment. For example, studies on beam steered array technique that increases the gain by forming a very narrow beam width and controlled reception pattern that forms a null to the jammer direction have been conducted (De Lorenzo et al. 2006). Furthermore, a front-end filtering technique that blocks jamming signal using a bandwidth filter with sharp cutoff and measuring a jamming to noise ratio in automatic gain control have been studied.

A pre-processing technique that removes jamming and interference signals using digitalized signal samples before navigation signals are modulated in the receiver, a code and carrier tracking loop technique, a technique to estimate the position of multi-jammers by using multiple monitor stations, and a combined technique with inertial navigation systems and multiple navigation signals have been studied (Fu & Zhu 2011). According to the navigation signal frequency, anti-jamming techniques can be divided into two cases where the same frequency bands of existing navigation systems are used or other separate frequency bands are used.

To deal with jamming effects in more detail, this paper proposes an effective model describing jammer influence on ranging measurements. The proposed model can be applied when the jamming signal power is similar to the navigation signal power in a navigation warfare situation. It should be noted that the signal tracking loop does not work and no ranging measurement can be generated when the jamming signal power is larger than the navigation signal power. The proposed model explains how the number of visible satellites, the carrier-to-noise ratio (C/N0), and the jamming-to-signal ratio (J/S) affects ranging measurement errors. The validity of the proposed ranging error model is indirectly verified by utilizing the existing jamming experiment results reported in the previous research works.

2. JAMMING INFLUENCE MODEL OF RANGING MEASUREMENTS

Table 1. Comparison of ranging measurement influence by jamming signal power.

Case	Signal strength	Result
Case 1 Case 2 Case 3	Jamming signal ≪ Navigation signal  Jamming signal ≥ Navigation signal Jamming signal ≫ Navigation signal	Normal operation (Receive the normal navigation signal) Obtain the navigation signal (Include ranging measurement error) Navigation signal unable (Cannot receive the navigation signal)

 

When jamming attacks occur in navigation warfare situations, the effects on navigation measurement can be divided into three cases according to the relative power between the jamming signal and the navigation signal as presented in Table 1. Case 1 in Table 1 refers to the normally received navigation signal as no jamming effect on the user’s receiver is determined. In this case, the received jamming signal intensity is weaker than that of the navigation signal. Case 2 refers to the case where the jamming power and the navigation signal power are similar. In this case, errors in ranging measurements might be enlarged as the jamming signal influences receiver operation. In general, ranging error increases in proportion to the influence level on the ranging measurement. Case 3 refers to the case where the jamming signal power is much larger than the navigation signal power. In this case, users cannot receive the navigation signal as the jamming signal overrides the navigation signal (Glomsvoll 2014).

Table 2. Description of parameters on signal propagation in free space.

Parameter

Description

\( (EIRP_j)_{dB} \) \( (J_t)_{dB} \) \( (G_t)_{dB} \) \( (J_r)_{dB} \) \( (L_p)_{dB} \) \( d \) \( f_j \) \( \lambda_j \) \( c \) \( (G_j)_{dB} \) \( (L_f)_{dB} \)

Effective isotropic radiated power (EIRP) \( =(J_t)_{dB} + (G_t)_{dB} \) Jammer transmission power (dBW) \( = 10\log_{10} (J_t)_W \) Jammer transmission antenna gain (dBic) Received jamming signal power (dBW) \( = 10\log_{10} (J_r)_W \) Free space propagation loss (dB) \( = 20\log_{10} (4\pi d / \lambda_j ) \) Distance between jammer and user (m) Jamming frequency (Hz) Wavelength of jamming frequency (m) \( =c/f_j \) Speed of light (m/sec) Receiver antenna gain toward jammer direction (dBic) Signal loss by receiver front-end filtering (dB)

 

To calculate the level of influence on the ranging measurement, the received jamming signal power needs to be calculated. Considering the free space path loss, it can be calculated by Eq. (1) considering the distance between jammer and the receiver, the jammer’s transmission power, and the jamming frequency band (Kim 2013). The variables related to Eq. (1) are summarized in Table 2.

\(\begin{aligned}\left(J_{r}\right)_{d B} &=\left(E I R P_{j}\right)_{d B}+\left(G_{j}\right)_{d B}-\left(L_{p}\right)_{d B}-\left(L_{f}\right)_{d B} \\ &=\left(J_{t}\right)_{d B}+\left(G_{t}\right)_{d B}+\left(G_{j}\right)_{d B}-\left(L_{p}\right)_{d B}-\left(L_{f}\right)_{d B} \\ &=10 \log _{10}\left(J_{t}\right)_{W}+\left(G_{t}\right)_{d B}+\left(G_{j}\right)_{d B}-20 \log _{10}\left(\frac{4 \pi d}{\lambda_{j}}\right)-\left(L_{f}\right)_{d B} \end{aligned}\)(1)

Based on Eq. (1), the jamming to signal ratio (J/S)_dB in dB unit can be calculated by Eq. (2) where (S_r)_dB denotes the received navigation signal power. Fig. 1 shows the (J/S)_dB variation according to the distance between the jammer and the receiver with f_j = 1575.42 MHz, G_t = 3 dB, G_j = 6 dB, and L_f= 3 dB, and S_r = -157.5 dB.

\((J / S)_{d B}=\left(J_{r}\right)_{d B}-\left(S_{r}\right)_{d B}\)    (2)

The jamming to signal ratio computed by Eq. (2) is affected

Fig. 1. Comparison of J/S variation with jammer power and jamming distance.

by the carrier-to-noise ratio (C/N₀)_dBHz at the receiver, the threshold value (C/N₀)_eff,dBHz, the antenna gain towards the satellite (G_svi)_dB, the antenna gain towards the jammer (G_j)_dB, the jamming resistance quality factor Q, and the code chip rate R_c (Kaplan & Hegarty 2005). By re-arranging Eq. (3) with regard to (C/N₀)_dBHz, Eq. (4) can also be obtained.

\((J / S)_{d B}=-\left(G_{s v i}\right)_{d B}+\left(G_{j}\right)_{d B}+10 \log _{10}\left[Q \cdot R_{c}\left(10^{-\frac{\left(C / N_{0}\right)_{e f f, d B H z}}{10}-10^{-\frac{\left(C / N_{0}\right)_{d B H z}}{10}}}{10}\right)\right]\)      (3)

\(\left(C / N_{0}\right)_{d B H z}=-10 \log _{10}\left(\begin{array}{ccc}10 {-\frac{\left(C / N_{0}\right)_{e f f, d B H z}}{10}} & & {\frac{(J / S)_{d B}+\left(G_{s v i}\right) d B^-{\left(G_{j}\right)} d B}{10}} \\ & {-\frac{1}{Q \cdot R_{c}} 10} & \end{array}\right)\)      (4)

Fig. 2 shows the change in (C/N₀)_dBHz according to the changes in jamming distance from the receiver when G_svi=1.5 dB, Q = 2.22, R_c = 1.023 Mcps, and (C/N₀)_eff,dBHz = 28 dBHz. When J_t = 0.01 W and all the other variables are the same as those used in generating Fig. 1, (C/N₀)_dBHz can be calculated using (J/S)_dB computed according to the change in jamming distance. As verified in Fig. 2, (C/N₀)_dBHz cannot be calculated when the jamming distance was 800 m or shorter as (J/S)_dB is calculated to a large value. However, (C/N₀)_dBHz increased as the jamming distance increased when the jamming distance was 800 m or longer.

Fig. 2. Calculated C/N0 by jamming distance variation.

When jamming signal power is at the similar level with the navigation signal power during the normal signal tracking process of a navigation receiver, unstable signal delays can occur due to jitter type errors generated in the delay locked loop (DLL) of the receiver. Eq. (5) describes the relationship between the DLL jitter error and (C/N₀)_dBHz (Kaplan & Hegarty 2005). Table 3 describes the variables used in Eq. (5). The jitter error is generated differently according to the correlation between the early-to-late width D of the receiver 

Table 3. Description of parameters on calculating DLL jitter error.

Parameter	Description
\( \sigma_{tDLL} \) \( D \) \( B_n \) \( B_{fe} \) \( T \) \( T_c \) \( b \)	1-sigma jitter error on DLL (chip) Chip interval in Early-to-Late correlator (chip) Code loop noise bandwidth (Hz) Double-sided front-end bandwidth (Hz)  Predetection integration time (sec) Code chip width (sec/chip) Normalized bandwidth (Hz) \( = B_{fe} / R_c \)

 

correlator and the normalized bandwidth \(b\left(=\frac{B_{f e}}{R_{c}}\right).\)

\( (\sigma_{tDLL})_{chip}= \left \{ \begin{array}{lc} \begin{array}{lc}\sqrt{ \begin{array}{l} {B_n \over 2⋅(C/N_0)_{dBHz}} \times D \\ \left [1+{2 \over T⋅(C/N_0)_{dBHz}⋅(2-D)}\right ] \end{array}}~~~~~~~~~~~~~~~~~~~~~~~~~~~,~~~D \geq \frac{\pi \cdot R_{c}}{B_{f e}} \end{array} \\ \sqrt{\begin{array}{lc} \begin{array}{l} \frac{B_{n}}{2 \cdot\left(C / N_{0}\right)_{d B H z}} \\ \times\left(\frac{1}{B_{f e} \cdot T_{c}}+\frac{B_{f e} \cdot T_{c}}{\pi-1} \times\left(D-\frac{1}{B_{f e} \cdot T_{c}}\right)^{2}\right) \\ \times\left[1+\frac{2}{T \cdot\left(C / N_{0}\right)_{d B H z} \cdot(2-D)}\right] \end{array} \end{array}}~~~~,~~~ {R_c \over B_{fe}} < D < {\pi \cdot R_c \over B_{fe} } \\ \begin{array}{lc}\sqrt{ \begin{array}{l} {B_n \over 2⋅(C/N_0)_{dBHz}} \times \left ( {1 \over B_{fe}\cdot T_c } \right ) \\ \left [1+{1 \over T⋅(C/N_0)_{dBHz}}\right ] \end{array}}~~~~~~~~~~~~~~~~~~~~~~~~~~~,~~~D \leq \frac{R_c}{B_{fe}} \end{array} \end{array} \right \} \)      (5)

Since the jitter error calculated by Eq. (5) is in chip length unit, it is converted to m unit by Eq. (6) that can be interpreted as the ranging measurement error. Fig. 3 shows the change in the 1-sigma jitter error (σtDLL)m in m unit according to the change in (C/N₀)_dBHz when B_n = 0.2 Hz, T = 0.02 sec, D = 1 chip, and b =2. The figure verifies that the jitter error rapidly increases as (C/N₀)_dBHz decreases

\(\left(\sigma_{t D L L}\right)_{m}=\left(\sigma_{t D L L}\right)_{c h i p} \cdot\left(\frac{c}{R_{c}}\right)_{m / c h i p}\)       (6)

Fig. 3. Calculated 1-sigma error of DLL jitter by C/N0 variation.

In summary, ranging measurement errors of a receiver affected by a jammer can be modeled by Eqs. (1-6) that describes the DLL error considering the jamming to noise ratio, the antenna gain towards the satellite, the antenna gain towards the jammer, and the carrier-to-noise ratio.

3. INDIRECT VERIFICATION OF DESIGNED MODEL

Although actual verification of the ranging measurement error model is highly desirable, it is difficult to transmit real jamming signals for experiment due to the strict national radio wave regulations. In addition, even if jamming signals are generated and applied using GPS simulators, it cannot be considered as an actual verification due to the use of simulated signals. Accordingly, this study performed a verification on the jammer’s influence model on ranging measurements indirectly rather than directly through the user’s receiver jamming influence tests, which were performed in the preceding studies. Glomsvoll (2014) installed a user receiver on the shore and mounted a jammer in a boat to perform a test of identifying the jamming influence on user receivers, moving the boat from 1,300 m away from the user receiver and approaching the shore slowly. The test overview performed by Glomsvoll is shown in Fig. 4, in which a user receiver is installed at location D, and a boat mounted with a jammer moves toward location D straightly from location B.

Fig. 4. Experiment overview (Glomsvoll 2014).

The analysis on jamming effect was based on the change in C/N0 measured at the receiver and the calculated horizontal and vertical errors. The jammer used by Glomsvoll transmitted jamming signals at -35 dBW and 1575.42 MHz, which was a frequency band of GPS L1 C/A. Since other jammer-related variables were not disclosed, the same variables that were used to depict Figs. 1-3 were used. Table 4 summarizes the variables used in this indirect verification. Fig. 5 shows the comparison between C/N0 measured when a jammer approached the user receiver for about three min from 1,300 m away and C/N0 calculated from the model formulated in this study. The left side of Fig. 5 shows C/N0 measured in the test and the right side shows C/N0 calculated by the designed model. Fig. 5 verifies that there is similarity between measured and calculated C/N0 values.

Table 4. Description of parameters used in the jamming simulation.

Parameter	Value	Parameter	Value
\( f_i \) \( G_t \) \( G_i \) \( L_f \) \( (C/N_0)_{eff~dBHz} \) \( G_{svi} \)	1575.42 MHz 3 dBic 6 dBic 3 dB 28 dBHz 1.5 dBic	\( Q \) \( R_c \) \( b \) \( D \) \( B_n \) \( T \)	2.22 1.023 Msps 2 Hz 1 chip 0.2 Hz 0.02 sec

 

Fig. 5. Comparison of between the measured C/N0 (left; Glomsvoll 2014) and the calculated C/N0 by designed model (right).

Glomsvoll verified the horizontal and vertical ranging errors of the user receiver while measuring C/N0 at the same time. This study calculated the level of ranging measurement errors using the actually measured C/N0 at the receiver to compare the ranging errors indirectly. The left side of Fig. 6 shows the measured C/N0 value, but the fluctuation of the values is so large that the measured C/N0 value is curve-fitted as shown in the right side of Fig. 6. Signals whose C/N0 is approximately below 30 dBHz could no longer be traced in the receiver.

Fig. 6. Measured C/N0 (left; Glomsvoll 2014) and the curve-ftted measured C/N0 (right).

The DLL errors of eight pseudorandom noise (PRN) were calculated from the curve-fitting C/N0 values, respectively. Glomsvoll did not provide the pseudorange, user position, and satellite positions in detail. Thus, the pseudorange and satellite positions were calculated arbitrarily based on the measured C/N0 to calculate the ranging error, which are presented in Table 5. After applying the DLL delay error to the pseudorange for each PRN, the horizontal and vertical errors were calculated. Figs. 7 and 8 show the comparisons of horizontal and vertical errors. The left sides of Figs. 7 and 8 show the horizontal and vertical errors calculated at the receiver. The right sides of Figs. 7 and 8 show the horizontal and vertical errors generated by the DLL error modeling through the curve-fitting C/N0. Both Figs. 7 and 8 showed that the errors occurred in the actual jamming situation were somewhat larger than the calculated ranging errors by C/ N0, but it was verified that the overall error trends of both methods were similar.

Table 5. Description of the assumed positions and the pseudoranges by C/N0.

SV/User	PRN	C/N0 (dBHz)	Position (LLH)			Pseudorange (m)
			Latitude (deg)	Longitude (deg)	Height (km)
GPS 1 GPS 2 GPS 3 GPS 4 GPS 5 GPS 6 GPS 7 GPS 8	25 12 31 2 4 29 14 20	49.45 48.45 47.95 46.75 46.45 45.15 43.45 36.45	40 70 50 30 10 0 25 20	150 140 120 80 100 170 140 40	19500 20000 21000 20500 21000 20000 24000 20000	19916699.71 21324350.83 21222720.13 22310577.29 22582236.98 23272061.23 24342834.71 25550143.31
User	-	-	37.5975	126.8651	0.063576	-

 

4. CONCLUSIONS

Fig. 7. Comparison of horizontal precision with the actual jamming environment (left; Glomsvoll 2014) and ranging measurement error model (right).

Fig. 8. Comparison of height precision with the actual jamming environment (left; Glomsvoll 2014) and ranging measurement error model (right).

This study proposed an effective error model of ranging measurements of navigation receivers due to jamming. The measurement error modeling was performed based on jammer and receiver-related variables and the rationale that DLL errors may occur in the receiver if the difference between the jamming signal power and the navigation signal power is not large. Although the navigation error occurred in the actual jamming situation were somewhat larger than the ranging errors calculated by the proposed method, it was verified that the overall error trends of the reported actual jamming experiment results and the proposed model showed good consistency.