Other genes in the PHTS spectrum

After observing nominal distortions on GPS L1C/A signals collected with high-gain dish antennas, the same approach is used on Galileo E1C signals. Results proposed in this part were obtained with a 1-second observation time. Results on PRN 18 are not presented because from the CDO, the data collection on PRN 18 cannot be trusted.

5.3.2.1 Impact on the correlation function

For Galileo E1C signal, the ideal correlation function that is subtracted to the nominal one is normalized differently than for GPS L1 C/A. The presence of the 𝐵𝑂𝐶(6,1) component makes more difficult the slope normalization. As for GPS L1 C/A, eight hundred and one correlator outputs are visualized and are described as:

𝑐𝑜𝑟𝑟_𝑜𝑢𝑡_𝐸1𝐶(𝑘) 𝑤𝑖𝑡ℎ 𝑘 = 1: 1: 801

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The ideal correlation function is simply an ideal unfiltered 𝐶𝐵𝑂𝐶(6,1, 1 11⁄ ) / 𝐵𝑂𝐶(1,1) correlation function built from eight hundred and one points and with its maximum obtained for 𝑘𝑚𝑎𝑥. The maximum of the correlation function is reached for 𝑘𝑚𝑎𝑥 which is not necessarily equal to four hundred and one.

Figure 5-6 shows the real part of the difference between the ideal unfiltered correlation function (𝑐𝑜𝑟𝑟_𝑜𝑢𝑡𝐸1𝐶) and the one affected by nominal distortions.

Figure 5-6. Difference between correlation functions affected by nominal distortions and an ideal unfiltered correlation function. Galileo E1C.

From Figure 5-6 three main results are noticeable:

- Ringing phenomenon affects the correlation function and the frequency of the oscillation is approximatively equal to 24 MHz as seen with the CDO.

- At −0.5, 0 and 0.5 𝑇𝑐 from the prompt, steps are present. This phenomenon is linked to the fact that the ideal correlation function is not exactly normalized as the distorted correlation function. Such distortions can be induced by the filtering of the 𝐵𝑂𝐶(1,1) component on the signal affected by nominal distortions.

- A high slope affects the correlation function between 0 and 0.25 𝑇𝑐.

- Discontinuities appear at “𝐵𝑂𝐶(6,1) correlation function peaks”, it means for delays from the prompt equal to ±0.08; ±0.17; ±0.25; ±0.33; ±0.42; ±0.58; ±0.67; ±0.75; ±0.83 and

; ±0.92 𝑇_𝑐. Discontinuities are more or less visible and are caused by a change of the correlation function slope and/or a slight error in the normalization of the ideal correlation function that does not match the distorted correlation function. Such distortions can be induced by the filtering of the 𝐵𝑂𝐶(6,1) component on the signal affected by nominal distortions.

It was seen from some GPS L1 C/A collected signals that a distortion can be induced by the receiver in addition to nominal distortions generated by the satellite. The drawback of high-gain antenna measurements is that the distortions induced by the receiver cannot be distinguished from the distortions generated by the satellite because only one signal can be collected at a given time. One advantage of Galileo E1 signals collected with high-gain dish antenna is that two components are available: E1C and E1B. Since antenna and/or digitizer effects will distort both components in the same

5.3 Correlation function observable from high-gain dish measurements

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way, making the difference between distortions that affect the E1C component and distortions that affect the E1B component will remove the common distortions due to the receiver front-end. The problem is that with this approach, a distortion generated at payload level with a similar impact on both components is also removed.

Figure 5-7 gives difference between the ideal and the distorted correlation functions for Galileo E1C and Galileo E1B for one signal (PRN 14).

Figure 5-7. Difference between correlation functions affected by nominal distortions and an ideal unfiltered correlation function. Galileo E1C and E1B. (PRN 14 only)

Figure 5-8 shows the difference between the correlation function distortion on the E1B component and on the E1C component. Compare to nominal distortions visible on Figure 5-6, on Figure 5-8 it is noticeable that:

- High slope which affects the correlation function between 0 and 0.25 𝑇_𝑐 is removed. More generally the amplitude of the distortion is lower because distortions that affect in the same way both components are removed.

- Discontinuities caused by the 𝐵𝑂𝐶(6,1) are enhanced because E1C modulation consists in the subtraction of the 𝐵𝑂𝐶(6,1) component whereas E1B modulation consists in the addition of the 𝐵𝑂𝐶(6,1) component.

- A low frequency phenomenon of 1 MHz is clearly visible and corresponds to a distortion which affects in different way the E1B and the E1C components.

Using the two E1 components to estimate distortions that affect a Galileo E1 signal permits to remove distortions that have the same effect on Galileo E1C and Galileo E1B components. In particular it permits to reduce the amplitude of nominal distortions. Nevertheless, two problems remain with this strategy:

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- Distortions induced by the satellite and having the same effect on E1B and E1C components are removed (if they exist).

- Distortions induced by the receiver and having different effects on E1B and E1C components are still present (it they exist). By consequence, it is not possible to distinguish distortions introduced by the satellite and by the receiver.

Figure 5-8. Difference between nominal distortions on the correlation functions of the E1C and the E1B components.

5.3.2.2 Impacts on the S-curve and the tracking error

Figure 5-9 shows the differential tracking bias generated by nominal distortions for each correlator spacing between 0 and 0.75 𝑇𝑐 with respect to the reference tracking configuration for the data collected at ESA. The correlator spacing of the reference is fixed to 0.25 𝑇𝑐.

From Figure 5-9 it can be seen that around the prompt the differential tracking error varies rapidly for correlator spacing’s smaller than 0.25 𝑇𝑐. For instance, a user who tracks the Galileo E1C PRN 14 with a correlator spacing equal to 0.1 𝑇_𝑐 will be affected by a differential error equal to 0.8 m relatively to a user who tracks the same signal with a correlator spacing equal to 0.15 𝑇𝑐. The phenomenon is also visible with less amplitude on GPS L1 C/A signal. It means that around the correlation function peak, the correlation function is slightly asymmetric. The signal distortion which entails the asymmetry can come as well from the satellite as from the receiver (antenna, digitizer, etc.). From proposed results, it is not possible to isolate the distortion induced by the satellite and the one induced by the receiver.

5.4 Conclusions and problems related to the observation of nominal distortions with high-gain dish antennas

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Figure 5-9. Tracking error function of the correlator spacing for different Galileo E1C PRNs (reference at 𝐶𝑆 = 0.25 chip).

As a matter of fact the S-curve zero-crossing is closely related to the distortion which affects the correlation function on Figure 5-6. By comparing carefully Figure 5-6 and Figure 5-9, plots have similar behaviors but a factor approximatively equal to one hundred has to be applied. By analogy, high differential error variations observed for reference receivers with a tight correlator spacing (below 0.25 𝑇_𝑐) are induced by the distortion visible between 0 and 0.25 𝑇𝑐 on the correlation function. It can be expected that if this distortion, close to the prompt, is removed from the measurement (better calibration of the antenna, use of a measurement based on E1B and E1C, etc.), the differential error should not be so high for differential Galileo E1C users with tight correlator spacing.

5.4 Conclusions and problems related to the observation of nominal