
Technical Article • September/October 2016
Like a pilot boat helping navigate a cargoladen ship into port, the Galileo E6C pilot signal can lead the E6B data signal component to improved performance.
The Particular Importance of Galileo E6CShare via: Slashdot Technorati Twitter Facebook The Galileo E6 signal is centered at 1278.75 MHz, and comprises three signals: an authorized signal (E6A, the publicly regulated service, PRS plus two civilian signals), a data component (E6B), and a pilot component (E6C). Both E6B and C are modulated using binaryphase shift keying (BPSK) code division multiple access (CDMA) memory codes, having lengths of 5,115 chips and chipping rates of 5.115 Mcps. The pilot signal further employs a secondary code, at a rate of one ksps, with a length of 100 symbols, while the data signal carries symbols at a rate of one ksps, being a halfrate encoded 500bps message. This distinguishes the Galileo E6B signal as having the highest symbol rate and the highest data rate of any GNSS signal. As such, it is quite interesting to study the signal in terms of tracking and data delivery performance. To this end, in this article we will first provide a study of the theoretical bounds on processing the E6 signal and, secondly, examine the behavior of current E6enabled GNSS receivers.
Theoretical Bounds Carrier Synchronization. We can characterize carrierphase tracking in a GNSS receiver, when operating in its linear region, by the phase domain model presented in Figure 1. Under this model, the effective noise bandwidth of the phase lock loop (PLL) can be estimated from the closedloop transfer function:
Equation (1) (see inset photo, above right, for all equations) where the PLL filter is denoted by F(z), the numerically controlled oscillator is defined by NCO(z), typically modelled as an integrator, and the discriminator gain, in rad/rad, is given by K_{D}. From this transfer function, the phase tracking jitter can be predicted as: Equation (2) where N_{θ} represents the equivalent noise floor after the discriminator, and accounts for the squaring loss that the nonlinearity of the carrier phase discriminator can induce, such that it increases as the prevailing carrier to noise floor ratio, C/N_{0} is reduced. Both K_{D} and N_{θ} depend on the discriminator used in the PLL, and the received signal characteristics generally influence the choice of discriminator. When an unknown data sequence modulates the signal, a Costasstyle discriminator is employed, which is insensitive to BPSK modulation, while a purePLL discriminator is used when a pilot signal is available. The tracking performance of PLLs that use either of these discriminators, although similar under nominal conditions, can diverge significantly under weaksignal conditions. In particular, the effective gain of the discriminator diminishes rapidly, and the region of phase errors over which the discriminator provides a proportional response contracts. These two factors can result in sporadic cycleslips, or loss of lock, when the receiver experiences any appreciable phase dynamic. In particular, the linear region plays an important role in determining PLL performance. The linear region of an ideal discriminator would extend from –π to +π, for a pure PLL, and from –π/2 to +π/2, for a Costas PLL. Although this is achieved under high C/N_{0} conditions, under nominal operating conditions, this region is smaller, and contracts as the received signal power reduces, with the onset of this contraction occurring earlier for the Costas PLL. Figure 2 depicts the carrierphase tracking jitter and discriminator linear region for a typical purePLL and CostasPLL for a range of C/N_{0}. The curves depict the 3σ bound for typical PLL configurations for a receiver processing the Galileo E6B and E6C signals, having a 20hertzbandwidth and a onekilohertz loop update rate. The curves represent a static receiver; so, the estimated 3σ bound has been further offset by a phase margin, Δθ. The latter term reflects any residual stress that the PLL might experience, such as receiver dynamics, oscillator phase noise, or physical vibration and shock. Also included is the estimated linear region of the two classes of PLL discriminator, which can be seen to converge to 180 and 90, respectively, for the purePLL (E6C) and for the CostasPLL (E6B). These curves offer some insight into the performance that might be observed for a receiver that either processes the Galileo E6B signal alone or employs the pilot signal E6C. In terms of thermal noise–induced phase error, a similar level of tracking error will be observed in either case when the prevailing signal strength is high. As this signal quality reduces below 40 dBHz, however, the E6Bonly receiver probably will perform more poorly. We may examine the relative magnitude of the tracking jitter curves and the discriminator linear region in terms of cycleslippage or lossoflock. Specifically, we can observe the phasemargin, or difference between the linearregion and the 3σ bound. As this margin is reduced, the probability of the receiver experiencing a cycleslip increases, and, once the 3σ exceeds the linear region, the probability of lossoflock is drastically increased. From Figure 2 one can surmise that the E6Bonly receiver will not be capable of tracking the carrier below approximately 38 dBHz, while a receiver that processes E6C might maintain carrier synchronization below 25 dBHz. Of course, these figures assume a static receiver, and exclude factors such as receiver motion and multipath, both of which will bias these results, likely further favoring the E6C case.
Data Recovery For the two E6Bonly modes of demodulation, the ultimate performance depends on the level of carrier synchronization that is maintained during the demodulation operation. At the same time, for the differential E6B mode relative to E6C, only the received signal strength plays a role. For coherent demodulation of each E6B data symbol, carrierphase alignment must be maintained, keeping the local carrier replica either in phase or in antiphase, with the received signal rendering the entire signal to the inphase correlator value, (I_{i}^{B}). We can then achieve symbol demodulation by making either a hard or softdecision on the sign of this value. Once the receiver identifies a preamble, the polarity of the sequence can be ascertained, and the remainder of the symbols, interpreted. For example, the hard decision may take the form: d̂_{l} = sign(I_{i}^{B}) (3) where d̂_{l} denotes the estimate of the i^{th} data symbol, and the superscript, B, denotes E6B. For the differential demodulation of successive E6B symbols, the requirements for carrier synchronization are reduced such that the frequency of the received signal and local carrier replica should be equal, but the absolute phase need not be aligned. Assuming that the signals are maintained at an approximately constant but arbitrary phase, a receiver can determine whether two successive symbols are the same, or different, by checking whether the correlator values undergo a phase inversion. Specifically, a receiver may arbitrarily assume that the first symbol is +1 and construct a sequence of symbols relative to this assumption. The decision as to whether the current symbol is the same as the previous can be expressed as: ĉ_{l} = sign(I_{i}^{B}I^{B}_{i}_{}_{1} + Q_{i}^{B}Q^{B}_{i}_{}_{1}) (4) such that –1 indicates that the successive symbols differ. Again, once a preamble has been identified, the polarity of the entire sequence can be corrected, if necessary. For example, in this case, the hard decision for the n^{th} symbol may take the form: Equation (5) Finally, for the differential demodulation of the E6B symbols relative to E6C, the requirements for carrier synchronization are, again, only that of frequency equality. Assuming that the signals are maintained at an approximately constant arbitrary phase, the absolute sign of the data symbol can be determined by examining the relative phase of the data and pilot component. For example the hard decision for the n^{th} symbol may take the form: d̂_{l} = sign(I_{i}^{B}I_{i}^{C} + Q_{i}^{B}Q_{i}^{C}) (6) where the superscript C denotes E6C. Note that, although the coherent integration period is limited to one millisecond for E6B, it may be extended significantly for the E6C component. In terms of data demodulation, Figure 3 depicts the predicted symbolerrorrate (SER) for a variety of tracking modes versus C/N_{0}. Beginning with the most sensitive scheme, the differential demodulation of the dataonly channel, the “E6B Diff” curve shows the SER trend of a receiver that operates only on the E6B signal and does not require phaselock with the signal. The demodulation scheme, in principle, should provide correct demodulation even in the presence of large phase errors or small frequency errors. However, due to the large number of symbols between each synchronization pattern, or preamble, the scheme is highly sensitive to noise. As a result, it performs the most poorly of the three schemes examined failing to provide any useful information below a C/N_{0} of 38 to 40 dBHz. Moving next to the coherent demodulation of the E6B signal, the “E6B Coh” curve shows the SER trend of a receiver that operates only on the E6B signal but which does require phaselock with the signal. In this case the SER in the moderate to highC/N_{0} region is very close to the theoretical baseband errorrate of Equation (7) However, performance is contingent upon the phase error being small. As the C/N_{0} is reduced, the nominal phase error grows with the result that the SER increases. Ultimately the receiver will lose lock, resulting in a complete loss of phasecoherence and data extraction. For the receiver configuration assumed in this case, this occurs at a C/N_{0} of approximately 33 dBHz. Depending on the receiver configuration, this threshold may vary. Within this region, however, the carrierphase tracking threshold of the receiver determines data availability. Finally, in Figure 3 the curves “E6BC Diff 1 ms” and “E6BC Diff 100 ms” indicate the differential demodulation of the E6B data signal relative to the E6C pilot signal. In this case, the data is determined by the relative phase of the two signal components and is independent of the absolute phase of the received signal pair. This implies that phaselock is not required, provided that the frequency error is small relative to the symbol rate. The difference between these two curves is the coherent integration period applied to the pilot signal, which can be extended arbitrarily. Note that this need not necessarily be the same as that applied by the PLL. Examining the curves, one can see that a moderate SER is maintained even for very low C/N_{0} values and that the increase in coherent integration on the pilot signal can yield a SER asymptotically equal to the theoretical bestcase.
Receiver Tests Data Recovery. Data recovery performance of the two receiver configurations receivers was assessed using a simulated constellation of signal measurements. A simulationbased test was chosen to ensure repeatability and reliability of the results. An adhoc reference scenario was simulated which which synthesized signals over a wide range of signaltonoise ratios — from that which induced moderate to high data loss to that which did not affect data recovery in any way. The effective C/N_{0} observed at the receiver was selected across a range of 25 to 50 dBHz, in steps of one decibel. For each particular C/N_{0}, the interference was first omitted, allowing the receiver to acquire the satellite signals, and subsequently introduced at a fixed power. We then collected navigation symbols in sets of 1,000 symbols according to the prevailing C/N_{0} and used these to compute the effective BER. Figure 4 presents the results of these tests, providing the measured SER, equivalent BER and theoretical curves. The measured results show reasonably good agreement with the theoretical model over the regions for which BER curves can be computed. In Figure 4, these regions are bounded on the righthandside by the limited observation time, which makes it difficult to observe very low error rates, and on the lefthandside when the receiver fails to provide navigation data. Examining the results, the receiver that only processes the data signal clearly fails to provide data measurements below a C/N_{0} of approximately 33 dBHz. At this point, the receiver appears to have lost lock on the signal. In contrast, with the aid of the pilot signal, the other receiver continues to provide data, albeit with an increasing error rates. One further observation that we can make is that the curve representing the BER for receiver number two exceeds that which would be expected, whereas that of receiver number one does not. This observation aligns with the notion that the onset of carrier tracking problems influences the data recovery performance more for nonpilot aided receivers Measurement Quality & Availability. To assess the effect of the pilot signal on the availability and quality of the positioning observables, we conducted a zerobaseline test. A roofmounted GNSS antenna connected to an RF splitter provided an unattenuated feed to a reference receiver and, via an adjustable attenuator, to the two receivers under test. Using this configuration, we logged a precise set of observations from the reference receiver, while measurements from the receivers under test were logged for a range of controlled C/N_{0} conditions. One of the receivers under test was configured to perform dataonly tracking of Galileo E6B, while both the second and reference receiver, were configured to perform datapilot tracking of Galileo E6BC. The test was conducted on when two Galileo satellites were visible to the reference antenna at elevations of greater than 45 degrees and at C/N_{0} greater than 50 dBHz. Measurements, including C/N_{0}, carrierphase, and pseudorange were logged at one hertz over a period of one hour. During this time the attenuator provided a controlled reduction in received signalstrength, from 0 to 30 decibels. The upper subplot of Figure 5 shows the average observed C/N_{0} for the two satellites. The reference receiver observed C/N_{0} of approximately 50 dBHz on both satellites throughout the test. Zerobaseline doubledifference pseudorange, denoted here by Δ_{2}ρ, and carrier phase, denoted here by Δ_{2}θ, measurements were then computed to ascertain what influence the availability of the pilot signal has on the measurement quality. The doubledifference between the reference receiver and each of the receivers under test is shown in the second and third subplots of Figure 5, which depicts the threesigma computed over two minute windows. In this case, as the three receivers were connected to the same antenna, the magnitude of the doubledifference should be representative of the thermal noise contribution to the measurements which, in this case, is dominated by the noise of the receiver processing the attenuated signal. In terms of availability, the two receivers clearly behave differently under weaksignal conditions, with the dataonly receiver (number two) failing to provide pseudorange and carrierphase measurements below 37 and 35 dBHz, respectively. In contrast, receiver number one, which processes the pilot signal, can provide relatively accurate measurements to a C/N_{0} of approximately 25 dBHz. In terms of carrier phase measurement quality, at high C/N_{0} the receivers exhibit a similar level of thermal noise–induced error; however, as the signal strength is reduced, the error increases more rapidly for receiver number two, showing good agreement with the theoretical results of Figure 2.
Positioning and Benefits of E6 Triplefrequency GNSS may enable both rapid and reliable ambiguity resolution for long baseline, realtime kinematic (RTK) positioning. The use of more signals from each GNSS satellite improves timetofirstfix (TTFF). For instance, triplefrequency RTK has been shown to give a considerably higher success rate than dualfrequency. Threecarrier ambiguity resolution can always be achieved by direct application of the leastsquares ambiguity decorrelation adjustment (LAMBDA). We can also find certain linear combinations for Galileo, using both carrier phase and code measurements, so that the speed and reliability of ambiguity fixing can be improved. Such combinations frequently involve the use of the E6 carrier phase. The tradeoff, however, is that the noise of these combinations is much higher than the original carrierphase measurement noise. The target here is to give qualitative statements about the expected performance when using, for instance, the LAMBDA method on specific dual, triple, and quadruplefrequency Galileo signals. A simplified model of the phase observation including the ionospheric effect can be written as: Equation (8) Tropospheric delay, receiver and satellite clock errors, and phase biases are considered known and are not shown. ρ is the geometric distance, Equation (9) is the slant ionospheric delay at frequency f_{F}, λ_{F}N_{F} is the phase ambiguity, where λ_{F} is the wavelength at frequency f_{F} and N_{F} is the integer ambiguity, and includes the unmodeled effects, such as measurement noise and multipath. Full phase alignment for triplefrequency measurements L_{1}, L_{2}, and L_{3} is achieved when L_{1} = L_{2}= L_{3}, which, when setting the unmodeled effects to zero, gives: Equation (10) for which the phases’ internal range difference ΔL_{Max} is zero and thus ΔL_{Max} = 0, where ΔL_{Max} = max(L_{1} – L_{2}, L_{1} – L_{3}). Figure 6 shows a simulation for Galileo when the ionosphere is considered unknown within plus/minus one meter at the E1 frequency. The internal range differences are displayed as a function of phase range, and the horizontal axis shows the phase range in meters around the correct range at zero. At the correct range, and in the absence of thermal noise and multipath, ΔL_{Max} is zero. The figure shows how the different phase ranges agree at a given range. The simulation, based on the principle of cycling through possible phase ambiguities for the first two carrierphase signals and calculating the ionosphere correction, provides phase alignment. This ionosphere is then applied to all phase measurements. The vertical axis illustrates how well the phase alignment ΔL_{Max} can be used to separate the correct ambiguity from the other candidates. The higher ΔL_{Max} is for the erroneous candidates, the greater the chance of selecting the ambiguities pointing to the correct range. Dualfrequency provides relatively poor performance, as then there is no redundancy in the ionosphere observations, so, all candidates are zero on the yaxis. Thus, we can see how triplefrequency, using the E5aE5bE1 signals, introduces some redundancy and, consequently, provides improved performance and increased separation from the other ambiguity candidates. However, introduction of the fourth frequency, E6, drastically improves this separation. With fourfrequency Galileo signals, about twothirds of the ambiguity candidates can be eliminated based on an internal phase range comparison. Interestingly, separate studies show that a triplefrequency Galileo solution, using E1E5abE6, provides similar performance to that of the quadruplefrequency case shown in Figure 6.
Conclusion Unlike its E1 or E5a counterparts, which have 4 and 20millisecond symbol periods, respectively, the E6B signal has a very limited capacity for correlation gain. As such, although it might be reasonable to process the E1B or E5aI signals in isolation, it proves more of a challenge to do so for the E6B signal. Indeed, our work has demonstrated, both via theoretical modeling and tests using receivers, that the use of the E6C pilot signal can provide meaningful improvements to receiver performance. In terms of data extraction on the E6B data signal, the use of the E6C pilot signal for synchronization can provide a noticeably reduced symbolerrorrate and a correspondingly increased availability of the E6 navigation message. As for carrierphase positioning, the E6C pilot signal appears to improve both measurement availability and measurement accuracy. This improvement in measurement accuracy, extends further to the performance of RTK solutions. Adding the Galileo E6 signal clearly provides significant benefits with respect to carrierphase ambiguity resolution when ionospheric effects are considered largely unknown. It is also noteworthy that the observations made here have considered a relatively benign scenario. First, the experiments have considered a static scenario. In a practical usage case, which would include receiver motion, the carrier synchronization would be stressed. This is likely to elicit a further disparity between the dataonly and the datapilot tracking of the signal, both in terms of data and ranging capability. Second, the experiments have considered only the case of thermal noise, both in the theoretical model and in the attenuation of the live GNSS signals. In reality, the spectrum in the vicinity of the E6 signals is frequently occupied by moderate to high power telecommunication transmissions, including analog and digital video broadcast, such as DVBS. These signals can cause a significant degradation to the received GNSS signal quality. In such cases, the increased integration period offered by the pilot signal and the improved isolation offered by the secondary code can be of considerable benefit. In summary, the Galileo E6C signal seems to serve an important dual purpose: as a facilitator for the use of the dataservices carried by its accompanying E6B signal and as an enabler for quadruplefrequency carrierphase positioning, a unique feature of Galileo.
Additional Resources ManufacturersThe GNSS simulator used in the tests described in this article was the GSS8000 from Spirent Communications, Paignton, United Kingdom. The GPS splitters and attenuator were from MiniCircuits, Brooklyn, New York USA. Identification of the GNSS receivers has been withheld under the terms of a nondisclosure agreement with the researchers.Author Profiles
James Curran
Tor Melgard Copyright © 2018 Gibbons Media & Research LLC, all rights reserved. 
