On Generalized Signal Waveforms for Satellite Navigation (797942), страница 29
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Autocorrelation Function of BOC8(15,2.5)4.5.6m-PSK Coded Symbols (m-PSK CS)So far, we have analyzed the case of 8-PSK sine-phased and cosine-phased BOC modulationsbut as one can imagine, we can extend the idea to any BCS using more levels.
Next figureshows some examples:Figure 4.33. Example of waveform for a general 8-PSK BCS signalIn addition, we can recognize again here that the BOC case that we studied above is nothingelse than a particular BCS case, as shown next:Figure 4.34. Equivalence between 8-PSK BCS(1,-1) and 8-PSK BOCThis rule applies also for the case of other well-known BCS signals as BPSK. Finally, it isimportant to underline that all the signals we have studied in the preceding chapters areindeed particular cases of the most general MCS definition that we gave at the verybeginning. The only distinction to make is whether the MCS segments are of equal length ornot.122GNSS Signal Structure4.6CBCS Modulation definition and analysis ofperformanceOn June 26th, 2004, the United States of America and the European Union signed theAgreement on the promotion, provision and use of Galileo and GPS satellite-basednavigation systems and related applications [G.W.
Hein et al., 2005]. Among other topics itwas decided to adopt a common baseline signal to be transmitted by both the Galileo E1 OpenService (OS) and the future GPS L1 Civil signal (L1C) on E1/L1. Although the agreementfixed BOC(1,1) as the baseline for both Galileo E1 OS and the GPS future L1C signals, it leftthe door open for a possible optimization of that signal considering the overall frameworkconditions of the agreement.Right after the Agreement was signed, experts on both sides of the Atlantic started to work onpossible solutions that would fulfil the criteria set up in the Agreement.
The solution wouldhave to clearly outperform the agreed BOC(1,1). Finally, in September 2005 a first temptativesolution, known as CBCS(20) was presented by members of the Signal Task Force (STF) ofthe European Commission (EC) [G.W. Hein et al., 2005]. The proposed solution was highlyinteroperable with the baseline BOC(1,1) and offered at the same time the possibility to havesuperior performance to high precision receivers with wider bandwidths.The CBCS modulation (Composite Binary Coded Symbols) is the result of superposingBOC(1,1) and a BCS (Binary Coded Symbol) waveform with the same chip rate, according tothe following expression:GCBCS ( f ) = α GBOC(1,1) ( f ) + β GBCS([s ],1) ( f )(4.120)where α and β indicate the amount of power that is put on BOC(1,1) and on the BCS signalwith respect to the total OS power of the signal.
Thus, α and β fulfil the condition α + β = 1 .For this same reason, we will use in other parts of the thesis β = ρ and α = 1 − ρ instead.Moreover, [s] represents the BCS vector as defined in chapter 4.2. As we saw there, BCS is ageneralization of the BPSK and BOC modulations. In addition, it is important to realize thatthe CBCS definition intrinsically assumes the use of Interplex to multiplex the signals.The flexibility of the CBCS approach lies in the fact that it could be easily converted intoanother CBCS by changing the contribution of the BCS part or even choosing different chiprates.
In fact, a particular case of the CBCS solution is the pure BCS signal which seems topresent the best performance in terms of multipath for selected sequences. Nonetheless, forthe EU developers keeping high interoperability with BOC(1,1) receivers was a mandatoryfrom the very beginning and this forced the design to have an important amount of BOC(1,1)in the definition.123GNSS Signal StructureWe show next graphically the signal generation of CBCS in the time domain. It is importantto note that CBCS is not a binary signal but two binary signals in anti-phase in data and pilot.Figure 4.35.
CBCS representation in the time domainAs we saw in previous chapters, signal waveforms with a very sharp peak were the goal of theoptimization carried out in the past years for both GPS and Galileo. Indeed, as we have shownin chapter 4.1.1, by selecting pTc (t ) with good aperiodic correlation, important improvementsin terms of performance can be obtained, especially regarding multipath. In the course of theoptimization other interesting solutions were found with even different chip rates than thoseof the Agreement.
Nevertheless, the important constraint to be compliant with BOC(1,1)limited the candidates to have a chip rate of 1 MHz, as we have already underlined.Unlike the MBOC signal that we will present in the next chapter, the CBCS modulation wasproposed alone from the European side. Thus, to the signal definition of the equation (4.120)above the extra constraint to use the Interplex modulation scheme was added in the definitionin light with the development of other signals in the Galileo satellites. Indeed, the CBCSmodulation is defined as the superposition of a BOC signal with a BCS using a modified andoptimized Interplex scheme in the navigation payload of the satellite.4.6.1CBCS Time Domain Representation and SpectrumThe CBCS signal features a spread-spectrum signal with 4-level sub-carriers, whereas theBOC or BCS signals feature only binary sub-carriers.
As we will show in detail in chapter 7,an implementation of the CBCS signals on the Galileo E1 modulation could have beenperformed using other multiplexing schemes such as the FH-Interplex (Faded-Harmonics)[CNES, 2005], as this also relies on the sum of two 4-level spread-spectrum signals.Yet, the analysis of the FH-Interplex scheme for the CBCS put in evidence two importantdrawbacks [G.W. Hein et al., 2005]:124GNSS Signal Structure•The inter-modulation product relative power of the FH-Interplex that results fromapplying CBCS is increased resulting thus in an important loss of efficiency•The quadrature component suffers from important distortions which may induceunacceptable losses on the receiver, as well as an increased spreading of thequadrature signal in adjacent frequency bands.
In the case of Galileo, the degradedsignal would be the PRS what supposed an important drawback.As a solution, a new modulation scheme was developed in [L. Ries et al., 2006] to provide anoptimized implementation of the CBCS signals, without the drawbacks described in thepreceding lines. The resulting modulation is more efficient than the Modified Hexaphase as itreduces significantly the effect and power of the inter-modulation product.As shown in Appendix J, the generic CBCS baseband modulation can be expressedmathematically as follows:⎡ cD (t )(cosθ1 sBOC(1,1) (t ) + cosθ 2 sBCS([s ],1) (t )) + ⎤⎥⎢⎢ 2⎥cP (t )⎢(4.121)(cosθ1 sBOC(1,1) (t ) − cosθ 2 sBCS([s ],1) (t )) +⎥⎥s (t ) = A1 ⎢+2⎢⎥⎢+ j s (t ) ⎛⎜ sin θ1 + sin θ 2 ⎞⎟ + s (t )⎥PRSIM⎢⎣⎥⎦2⎝⎠⎛ sin θ1 − sin θ 2 ⎞(4.122)sIM (t ) = − j cD (t ) cP (t ) sPRS (t ) ⎜⎟2⎝⎠where:•A1 is the amplitude of the modulation envelope, sum of the OS data (D) and pilot (P),PRS and Inter-Modulation product IM.
The maximum possible value of A1 thatrespects the Agreement of 2004 is a function of the percentage of power put on theBCS component of the signal and the spectral relationship between BOC(1,1) andBCS. Moreover, A1 = 2 PT where PT is the total power of the multiplexed signal.•θ1 and θ2 describe the angular distance of points of the 8-PSK modulation as described•in Figure 4.36. This depends on the percentage of power that is placed on BCS.sBOC(1,1) (t ) represents the BOC(1,1) modulation with chip rate of 1.023 MHz•sBCS([ s ],1) (t ) represents the BCS([s],1) modulation with a chip rate of 1.023 MHz and a•BCS vector given by [s].sPRS (t ) is the PRS modulation BOCcos(15,2.5)••sIM (t) is the Inter-Modulation product signalcD (t) and cP (t) are the data and pilot codes respectively. It is important to note thatcD (t) also includes the data bits.The phase points of the resulting constellation are shown in the following figure:125GNSS Signal StructureFigure 4.36.
Modified 8-PSK modulation with constant envelope for the optimized signalThe modulation can be optimized so as to pseudo-randomly time-multiplex the BOC and BCSsub-carriers on the in-phase component. Rearranging the terms of (4.121) to make thispseudo-random time-multiplexing appear yields to the following expression:⎡ cD (t ) + cP (t )⎤cosθ1 sBOC(1,1) (t ) +⎢⎥2⎢⎥cD (t ) − cP (t )⎢cosθ 2 sBCS([s ],1) (t ) + ⎥⎥s (t ) = A1 ⎢+2⎢⎥⎢+ j s (t ) ⎛⎜ sin θ1 + sin θ 2 ⎞⎟ + s (t )⎥PRSIM⎢⎣⎥⎦2⎝⎠(4.123)If we look at the previous equation in detail, we can observe that the BOC(1,1) sub-carrier ofthe OSD (Data) and OSP (Pilot) components is transmitted during the same time-slots as it wason the original Hexaphase modulation with only BOC(1,1).
This will be further analyzed inchapter 7.7. In addition, the BCS sub-carrier of the OSD and OSP components is transmitted intime-slots complementary to those of the BOC sub-carrier (i.e in the time slot when theModified Hexaphase in-phase component was equal to zero and therefore nothing wastransmitted). As a result, the IM product is considerably reduced and 8 phase points appearinstead of only 6.
Also important to note is that the quadrature component (the PRS signal) isleft unaffected by this new scheme, except for its relative amplitude.Figure 4.37. Pseudo-random time multiplexing of BCS and BOC(1,1) in CBCS solution126GNSS Signal StructureAnother important conclusion that we can draw from observing the equation above is that ifone optimizes the data and pilot channel codes with each other, the code structure that resultsfrom applying the multiplexing scheme of (4.123) does not necessarily have to be alsooptimized in the general case.Indeed, we can clearly recognize that the code that actually modulates the BOC(1,1) signalwaveform is the semi-sum of the data and pilot codes. Equally, the semi-difference of the dataand pilot codes modulates the BCS sequence. Moreover, these codes are not binary since theycan take the values +2, 0 and -2 [P.G. Mattos, 2005].
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