On Generalized Signal Waveforms for Satellite Navigation (797942), страница 66
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However, as we mentioned inchapter 7.8.2, to find the optimum code allocation it would be necessary to evaluate (7.149)and (7.160) for all the possible permutations.Fortunately, since the gains of the different codes are defined in non-decreasing order and thesignal with the lowest power c1 will never have solo chips in the majority vote signal, thenumber of permutations to assess reduces to ten for the case that we multiplex five signals.300Signal Multiplex Techniques for GNSSThe ten standard permutations, as defined by [G. L. Cangiani et al., 2002] are presented next:⎧{G1 , G2 , G3 , G4 , G5 }⎪{G , G , G , G , G }⎪ 1 2 4 3 5⎪{G1 , G2 , G5 , G3 , G4 }⎪⎪{G1 , G3 , G4 , G2 , G5 }⎪{G , G , G , G , G }{g1 , g 2 , g 3 , g 4 , g 5 } = ⎪⎨ 1 3 5 2 4⎪{G1 , G4 , G5 , G2 , G3 }⎪{G2 , G3 , G4 , G1 , G5 }⎪⎪{G2 , G3 , G5 , G1 , G4 }⎪{G , G , G , G , G }⎪ 2 4 5 1 3⎪⎩{G3 , G4 , G5 , G1 , G2 }(7.167)where {g1 , g 2 , g 3 , g 4 , g 5 } = {G1 , G2 , G3 , G4 , G5 } is the particular case that we covered in theprevious two chapters.
As underlined by [G. L. Cangiani et al., 2002], the indexes areincreasing in positions 1, 2 and 3 of (7.167) in order to assure that the majority vote will nevertransmit the signal with the lowest power as solo chip. However, the situation for positions 4and 5 is definitely different since here the order is significant. Indeed, depending on whichsignal occupies positions 4 and 5, this signal could be on I and Q resulting thus in differentefficiency values as we have shown. According to this, twenty permutations are to beevaluated: the ten given by (7.167) plus another ten with positions four and five interchanged.Once the previous equations determine with code set results in the optimum total efficiency,we would only have to form the majority vote of the three selected signals according to thetheory presented in chapter 7.4.7.
In a next step, the resulting majority vote signal would befurther interplex-multiplexed with the other two uncombined signals.Last but not the least, it is important to mention that in principle any interplex solution couldbe employed in the intervote scheme to multiplex all the signals as defended and emphasizedby [G. L.
Cangiani et al., 2002]. In the particular but illustrating case of previous pages fivesignals were intervote-multiplexed using a three-input interplex. Nevertheless, as one canimagine, when the signals to multiplex increase, other interplex solutions could also be used.However, three seems to be a good compromise as then interplex behaves optimally.301Signal Multiplex Techniques for GNSS7.9FDMA vs. CDMAWe have seen in chapter 2 that GPS, Galileo and Compass are or will be using CDMA whileGLONASS is the only one that still employs FDMA for the transmission of its navigationsignals. However, as we have seen in chapter 2.5.3 it seems that the Russian NavigationSystem is moving in the direction of achieving higher interoperability with the American,European and Chinese systems as GLONASS is already taking the first steps to CDMA.In spite of the promising benefits that this change would bring, the main reasons that theRussian GLONASS has used as argument in the past against CDMA are summarized next:••••Existence of single point of failure if all signals are located at E1/L1,FDMA offers improved security protection (not any more true as we explain next),The issue of paying for the new civil signal design,The historical reasons that lead to FDMAThe improved robustness of FDMA versus CDMA has usually been justified by the improvedSSCs that FDMA can achieve.
If we take as an example the C/A Codes of GPS andGLONASS, we can see that the Self SSC of the GLONASS C/A Code is of approximately-57.9700 dB-Hz while for GPS we obtain -61.8008 dB-Hz. The favourable difference for theGPS C/A Code comes from the different employed transmission filters and the lower coderate of the GLONASS C/A Code. However, if we take a look at the SSC between spectraladjacent GLONASS C/A Codes, we can recognize than the spectral separation improves to-69.5604 dB-Hz, providing thus nearly 12 dB of additional protection with respect to CDMA.Moreover, if we take a look at non-adjacent spectra the theoretical isolation is infinite andthus the average of the adjacent SSCs would be of -80.6999 dB-Hz or nearly 22 dB better(considering 14 frequency slots).CDMA achieves higher protection by means of the cross-correlation of the employed codes.These provide in the case of the GPS C/A Gold Codes an additional protection of 24 dB whenno Doppler is considered and of approximately 21 dB when also Doppler is taken intoaccount.
In the case of FDMA there is only one code and thus we have to talk about autocorrelation instead of cross-correlation. Nonetheless, although all the GLONASS satellitesemploy the same code for all the satellites, since the relative Doppler and delay among themcan be considered as random, the final autocorrelation value that two FDMA satellites presentis that of the secondary peaks of the ACF, also in the order of 21 dB with respect to the mainpeak, and thus close to the cross-correlation of GPS C/A Codes. The randomization effectthrough Doppler is similar to the principle of Doppler Division Multiple Access (DDMA).If we consider now the spectral separation and code separation effects together, we can seethat from this point of view FDMA would provide an additional protection of 22 dB with302Signal Multiplex Techniques for GNSSrespect to the CDMA approach.
This has been indeed the main argument used by GLONASSexperts until now. As we can recognize, the implicit assumption behind is that the jammersare narrowband.While the protection against jammers was at the beginning of GNSS of particular importanceand drove most of the decisions that Russia and the USA took to build their respectivesatellite navigation systems, nowadays it is possible to build very wideband jammers.
Thus,the protection that FDMA was supposed to offer against narrowband interferers is not anymore an advantage against CDMA.We can imagine it with a simple example. If we jam a satellite in a CDMA system with anarrowband interferer, we automatically jam all the other satellites since they are on the samecarrier. On the contrary, in an FDMA system the other satellites would result in principleunaffected.
Wideband jammers are however not an issue or at least not as they were at thebeginning when GLONASS argued the FDMA goodness on the basis of its superior jammingprotection. As a result, unless the different satellites used carriers very separated in frequency,with today’s technology one could jam all the FDMA signals at the same time disabling theextra protection that FDMA was supposed to bring.In addition, FDMA is a clear show-stopper for mass market applications since havingdifferent carriers for each satellite poses an important challenge in the design of the receivers.As one can imagine, this makes FDMA less competitive than its CDMA competitor.Moreover, filter design and other synchronization aspects difficult the design of an FDMAreceiver.
Although the problem can be solved as many manufacturers have shown in the pastyears, there is no doubt that if GLONASS wants to really provide mass-market signals, itscivil signals will have to slowly migrate to CDMA.303Signal Multiplex Techniques for GNSS304Conclusions and Recommendations8. Conclusions and RecommendationsIn this last chapter, the conclusions from the research work of this thesis are presented.Furthermore, recommendations for future work activities are proposed.8.1 ConclusionsThis thesis provides a theoretical framework to describe analytically the characteristics of anygeneric navigation signal waveform.
Generalized expressions have been derived andfundamental theoretical concepts have been proposed to represent a signal waveform in boththe time and frequency domains. The analyzed theory on Multilevel Coded Symbols (MCS)provides a powerful means to mathematically model any of the current navigation signals and,what is of even greater interest, of potential alternative signal schemes that could be proposedin the future.The thesis starts with a complete description of all existing and planned Global, Regional andAugmentation Satellite Navigation Systems. Special attention has been paid to all the aspectsrelated to signal structure with particular focus on the European Galileo system. The evolutionof the Galileo frequency and signal plan was a case of intensive study given its novelty.The main relevant parameters in the signal design of any navigation system have been furtherdiscussed and generally valid formulas have been obtained. A family of generalizedwaveforms has been proposed and investigated in detail.
Furthermore, potential applicationsand the performance of alternative solutions were studied and compared with other wellknown solutions.Given the fact that the number of navigation systems sharing the currently availableRadio-Navigation frequency bands is dramatically increasing, this thesis has discussed therelevant aspects related to the spectral compatibility and interoperability among signals. Toachieve this objective, the Spectral Separation Coefficients were object of profound analysis.Building on generalized theoretical models to describe any chipping waveform, analyticalexpressions have been derived for the case of smooth spectra. In addition, the effect of nonidealities related to the imperfections of the Pseudo Random Noise (PRN) codes and theexistence of data were also modelled in detail.
Simulations have shown that numericalcomputations deliver exactly the same results predicted by the analytical formulas.To conclude, the different signals introduced in this thesis have been briefly analyzedregarding their implementation in the payload. Here, already implemented and newmultiplexing techniques were presented and studied in light of their feasibility toaccommodate optimized signal waveforms in the future. This is a field which is expected toattract attention in coming years.305Conclusions and Recommendations8.2 Recommendations for Future WorkThis thesis has provided the theory and mathematical tools with which any present and futurenavigation signal could be represented.
The present work should serve as fundament forfuture research activities in the field signal design. As this thesis has shown, payloadlimitations practically reduce today the number of palette signals to binary solutions.However, other families of signals could become reality in the coming years.In order to guarantee a peaceful coexistence of all existing, planned and potential futuresignals a correct understanding of compatibility and interoperability is a fundamentalrequirement.
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