To be in line with the current TM-A defined for GPS L1 C/A and to be conservative, the lower bound of Δ is taken equal to zero for 𝐵𝑃𝑆𝐾(10)-modulated signals. For this signal it is not possible to use the proposed technique to limit the upper bound of the TS (selection in the TS of a distortion based on its impact on the tracking error and differential tracking error) as shown in 6.3.1.1. By consequence, another method copying the ICAO TM-A developed for GPS L1 C/A signal is proposed.
6.3.1.1 Use of the proposed methodology
Figure 6-5 shows on the left the tracking error observed by the reference station when tracking a signal affected by a TM-A with different values of Δ running from 0 to 117 ns. On the right, is shown the worst differential error seen among all reference/user receiver configurations combinations.
Figure 6-5. Impact of the TM-A for GPS L5 and Galileo E5a signals for different Δ. On the left, impact on the reference station tracking error. On the right, impact on the worst differential tracking error.
From Figure 6-5 (left), the tracking error seen by the reference station is always lower than 20 m whatever the value of Δ is. As a consequence, it is not possible to use the criterion about the impact of a distortion on the reference station tracking error to limit the TS.
From Figure 6-5 (right), the worst tracking error entailed by a TM-A distortion increases when Δ increases. Consequently, it is not possible to apply the criterion about the impact of a distortion on the
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differential tracking error to estimate the upper bound of Δ. It is noticeable that for Δ values lower than or equal to 50 ns, the differential tracking errors are lower than 1 m and are by consequence not a threat for the considered DGNSS users. Nevertheless, to be in line with GPS L1 C/A TM it is decided to keep small Δ values in the TS.
To conclude, the strategy to estimate the Δ upper bound from the two proposed criteria (tracking error observed by reference and worst differential tracking error that affect DGNSS users) does not allow the reduction of the TS.
6.3.1.2 Proposition of a TM-A
Based on the above results, it is proposed to keep the range of Δ (in second) of GPS L1 C/A TM-A:
−1.2 𝐸5𝑎 (𝐿5) 𝑐ℎ𝑖𝑝𝑠 ≤ Δ ≤ 1.2 𝐸5𝑎 (𝐿5) 𝑐ℎ𝑖𝑝𝑠
Figure 6-6 illustrates correlation functions affected by TM-A distortions with different Δ values.
Figure 6-6. Distorted GPS L5/Galileo E5a correlation functions for different values of Δ filtered by a 6th-order Butterworth (24 MHz).
From Figure 6-6, it can be seen that the correlation peak is still visible for high Δ values even if strongly flattened. The legitimacy of distortions with high Δ values could be discussed. Indeed, if the distorted signal cannot be tracked by any considered receiver, it is not necessary to include this distortion in the TM. Two distorted signal features that could prevent the tracking can be defined:
- A too low amplitude of the correlation function at tracking correlator outputs level. The worst case is considered: a user’s receiver tracks a TM-A distorted signal (Δ = 1.2 chips) with a correlator spacing equal to 1.2 chip. From Figure 6-6, the amplitudes of the correlation function at tracking correlator outputs are equal to 0.67 in nominal conditions and 0.23 on the distorted correlation function which represents a factor of 3. It means that the receiver will observe a 4.7 dB Signal-to-Noise Ratio (SNR) loss when tracking the distorted signal compared to a nominal one. A 4.7 dB difference between two GNSS signals received by the same antenna/receiver is a typical order of magnitude in nominal conditions, for example
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between a low elevation satellite and one at high elevation. The consequence is that the loss of correlation function amplitude entailed by the distortion does not prevent the tracking.
- A flat zone which includes the two tracking correlator outputs. From Figure 6-6, it is noticeable that the two tracking correlator outputs are on the flat zone when the signal is affected by a 𝛥 higher than 0.6 chip. Nevertheless, depending on the implementation of the discriminator, the behavior of the DLL when both correlator outputs used for the tracking are on a flat zone will be different. This difference in the receiver behavior can become a threat for DGNSS users. By consequence, it is important to take into account even distortions with high 𝛥 values.
6.3.2 Galileo E1C TM-A
As introduced previously, the digital failure of 𝐶𝐵𝑂𝐶(6,1, 1 11⁄ )-modulated signal is more difficult to design because of the presence of sub-carriers. The presence of several components in the signal entails a multiplication of distortion threats.
6.3.2.1 Proposition of digital distortions
No occurrence of EWF has been observed on Galileo signals. Payload knowledge could help to make choices among the large number of conceivable digital failures. However, the lack of information about a payload miss-functioning prevents the selection. In this section, only the two most likely digital distortions that could affect a Galileo E1C signal are presented and are called digital distortion 1 and digital distortion 2.
The scheme on Figure 6-7 presents the Galileo E1 signal generation [Navipedia, 2015]. Only the bottom part (highlighted green box) is of interest in the E1C component generation.
Figure 6-7. Galileo E1 signal generation block scheme [Navipedia, 2015].
Digital distortion 1: A lead/lag on the falling transitions of all signal components after modulation. It is possible to imagine that only 𝐵𝑂𝐶(6,1) or 𝐵𝑂𝐶(1,1) transitions are affected by this lead/lag but because the distortion occurs after modulation, it is most likely that a delay will appear on every transitions.
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The impact on the signal and on the correlation function, of such a signal distortion is shown in Figure 6-8 on the left and on the right respectively for Δ = 0.05 chip (in blue the undistorted signal, in red the distorted signal).
Figure 6-8. Impact of digital distortion 1 on the signal (left), and on the correlation function ( right).
Digital distortion 2: A lead/lag on the 𝐵𝑂𝐶(1,1) sub-carrier or/and on the 𝐵𝑂𝐶(6,1) sub-carrier falling transitions at the signal square wave generator level (before modulation). This distortion was introduced in [Phelts et al., 2006] for 𝐵𝑂𝐶(1,1) signal. In Figure 6-9, the lag on 𝐵𝑂𝐶(1,1) and 𝐵𝑂𝐶(6,1) transitions is similar. To be conservative and take into account most of possible cases, two independent parameters are defined:
- Δ11 : the lead/lag parameter on 𝐵𝑂𝐶(1,1) sub-carrier component (before modulation).
- Δ61 : the lead/lag parameter on 𝐵𝑂𝐶(6,1) sub-carrier component (before modulation).
The impact on the signal and on the correlation function of such a signal distortion is shown in Figure 6-9 on the left and on the right respectively for Δ11 = Δ61= 0.05 chip (in blue the undistorted signal, in red the distorted signal).
Figure 6-9. Impact of digital distortion 2 on the signal (left), and on the correlation function ( right).
1 1 1 -1
𝑇𝑐
𝑇𝑐
1 1 1 -1
𝑇𝑐
𝑇𝑐
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In Figure 6-10 is represented in red the Galileo E1C signal generation level where the digital distortion 1 appears and in green where digital distortion 2 appears.
Figure 6-10. Galileo E1C signal generation unit and digital distortions.
6.3.2.2 First TM-A TS limitation based on physical considerations
Two TM-A are proposed to take into account each proposed digital distortion for the new Galileo E1C signal:
- TM-A1: A lead/lag (Δ) on every signal falling transitions after modulation. Only one parameter is necessary (digital distortion 1).
- TM-A2: A lead/lag on the 𝐵𝑂𝐶(6,1) ( Δ61) and on the 𝐵𝑂𝐶(1,1) ( Δ11) sub-carrier falling transitions at signal square wave generator level (before modulation). Two parameters are necessary (digital distortion 2).
Δ, Δ61 and Δ11 parameters range can be fixed observing the shape of signals distorted by the different digital distortions:
- From a certain value of Δ, the distorted signal keeps the same shape because a chip is composed of one positive and one negative sub-chip. It entails that from a certain value of Δ (Δ = 1.08 chips), increasing the value of Δ (above 1.08 chips) does not change the shape of the signal and the correlation function. From this value of Δ, chips are disappearing and the signal is constant.
- From a certain value of Δ11, the signal keeps the same shape because a chip is composed of one positive and one negative sub-chip. It entails that from a certain value of Δ11 ( Δ11= 0.5 chip), sub-chips (of the 𝐵𝑂𝐶(1,1)) are disappearing. Increasing the value of Δ11 above 0.5 chip does not change the shape of the signal and the correlation function.
- From a certain value of Δ61, the signal keeps the same shape because 𝐵𝑂𝐶(6,1) signal is composed of alternative positive and negative values with the same amplitude. It entails that from a certain value of Δ61 ( Δ61= 0 .08 chip), sub-chips (of the 𝐵𝑂𝐶(6,1)) are disappearing.
Illustrations presented in Figure 6-11 show this concept for different distortions:
1) TM-A1 with Δ = 1.08 chips
2) TM-A2 with Δ11= 0.5 chip ( Δ61 not considered) 3) TM-A2 with Δ61= 0 .08 chip ( Δ11 not considered)
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Figure 6-11. CBOC signals affected by different digital distortions on the top and associated correlation functions on the bottom.
In the three cases, choosing higher values of Δ, Δ61 and Δ11 does not bring any change on the signal.
These limits can be considered as Δ, Δ61 and Δ11 values that entail a saturation of the distortion. By consequence it is not necessary to take into account higher value s of Δ, Δ61 and Δ11.
6.3.2.3 Limitation of the TM-A TS based on the detection capability of the reference station
It is noticeable that some of the distortions with high values of Δ should be easily detected. The range of Δ could be limited by the assumed capability of the reference to detect tracking bias larger than 20 meters.
Using this condition, Δ and Δ11 can be decreased to 0.12 chip and 0.10 chip respectively, as represented in Figure 6-12. Reference configuration was applied to establish these plots.
By consequence, for TM-A1, the following parameter values are envisaged:
−0.12 𝑐ℎ𝑖𝑝 ≤ Δ ≤ 0.12 𝑐ℎ𝑖𝑝 and for TM-A2,
−0.1 𝑐ℎ𝑖𝑝 ≤ Δ11 ≤ 0.1 𝑐ℎ𝑖𝑝
−0.08 𝑐ℎ𝑖𝑝 ≤ Δ61 ≤ 0.08 𝑐ℎ𝑖𝑝
1 2 3
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Figure 6-12. Tracking error for TM-A1 and TM-A2 and different delta values (Δ and Δ11 ).
6.3.2.4 Proposition of a simplified TM-A
Considering the current GPS L1 C/A digital TM, it is clear that it is assumed that the distortion occurs on the signal after its modulation with the PRN code. However, no information about the Galileo E1C signal generation on-board the payload is available in the literature. Knowing if the three signal components (𝐵𝑂𝐶(1,1), 𝐵𝑂𝐶(6,1), PRN) are generated independently (TM-A2) or as the product of the components (TM-A1) could help to choose between TM-A1 or TM-A2 or both.
Assuming that the digital signal is directly generated as the components product would entails that only TM-A1 should be preserved. It is noteworthy that no digital distortion was observed on Galileo nominal signals. It means that the TM-A1 already takes into account distortions that are not generated by Galileo satellites payload in nominal conditions. Based on these assumptions a simplified TM-A is proposed and consists only in TM-A1.