On Generalized Signal Waveforms for Satellite Navigation (797942), страница 53
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Forcomparison the ideal smooth spectrum SSC is shown in red242Spectral Separation Coefficients with data and non ideal codesAs we can see, the value of the Self SSC at Doppler shifts multiple of 1 kHz is not alwaysequal since it depends on the particular two codes of the example. Nevertheless, the differenceis negligible and proves that the high Self SSC value of the C/A Code is actually due to thelow data rate and not to the C/A Code structure. In fact, as we can see in the next figure thereis no significant difference to note if we use the approach of quasi ideal codes as defined inchapter 6.2.1:Figure 6.34. C/A Code Self SSC with quasi ideal codes as a function of Doppler. Forcomparison the ideal smooth spectrum SSC is also shown in redAs we can see, the maxima of the SSC (located every multiple of 1 kHz) are constant in thiscase.
To generalize our results, we calculate in the next figure the Self SSC of BOC(1,1) as afunction of the Doppler offset, when two codes are considered and when ideal code propertiesare assumed. It must be noted that the spectra of the codes were normalized to 24 MHz andnot to 40.92 MHz as done in chapter 5. Moreover the SSC were integrated in 24 MHz. If thecorrect normalization to the transmission bandwidth were done, the result would be a shift ofthe curves but from a qualitative point of view there would be no difference.Figure 6.35. BOC(1,1) Self SSC between SVN 1 and SVN 2 as a function of Doppler243Spectral Separation Coefficients with data and non ideal codesIt is interesting to see now, that if we repeat the previous computation for quasi ideal codes,the SSC presents the following smooth structure:Figure 6.36.
BOC(1,1) Self SSC with quasi ideal codes as a function of DopplerAs we can clearly recognize, the variation of the self SSC of BOC(1,1) with data on tophardly varies within the Doppler range that we have studied, showing that the smoothspectrum approach is a good approximation when the data rate is high enough. Indeed, for theC/A code, even with quasi ideal codes, the low data rate was responsible for the importantvariation of the SSC over the Doppler range. To conclude it is important to mention thatsimilar conclusions can be drawn for the case of MBOC.6.2.3Final comments on the SSCsAs we know from [J.W. Betz, 2000b] and [J.W. Betz and K.R.
Kolodziejski, 2000], theeffective C N 0 of a desired signal subject to interference is shown to be:CN0=effCd ∫βr2−βrGd ( f ) df2βr⎤⎡2N⎥⎢0 ∫ β r G d ( f ) df +−2⎥⎢ interfering⎥⎢ N intra∞⎢+ ∑ C i ,k ∫−∞ Gi ,k ( f )Gd ( f − f Doppler ,k )df + ⎥k =1⎥⎢interfering⎥⎢ N inter∞⎢ + ∑ C i ,l ∫−∞ Gi ,l ( f )Gd ( f − f Doppler ,l )df ⎥l =1⎦⎥⎣⎢(6.39)where• βr is the two-sided bandwidth of the front-end filter,• N 0 is the Power Spectral Density of the thermal noise,•Cd and Gd ( f ) are respectively the power and the PSD of the desired signals,•normalized to the transmission bandwidth of the satellite,Ci , k and Gi,k ( f ) are respectively the power and the PSD of the interfering signals,normalized equally to the transmission bandwidth.
These interfering signals can be244Spectral Separation Coefficients with data and non ideal codesfrom the same system or from another system in the band. In the case ofCi , k and Gi ,k ( f ) , the interference comes from the same system as that of the desiredinterferingrefers to the number of interfering signals from the samesignal. Moreover N intra•system that can be seen in the receiver.Finally, Ci ,l and Gi ,l ( f ) are respectively the power and the PSD of interfering signalsinterferingfrom another GNSS interfering system, being N interthe number of interferingsignals from another GNSS system that can be seen in the receiver.As we can clearly recognize in the expression above, the impact of the interference onto theCis directly related to the Spectral Separation Coefficient (SSC), as defined at theN 0 effbeginning of this chapter. Moreover, the expressions above refer to acquisition and datademodulation.
Thus we can say that the SSC as defined in this chapter is an acquisitionSpectral Separation Coefficient, or SSCacq for short.The SSC indicates the degree of degradation that a desired signal suffers during acquisitiondue to the interference of other signals present in the band, no matter whether this comes fromthe same system or from another system.Similarly to the acquisition SSC, it is equally possible to propose an effective C N 0efffor thetracking performance [F. Soualle et al., 2007]. This equivalent figure is computed byestimating the equivalent new noise level N 0 eff that leads to the same jitter that would beobtained in the presence of an equivalent pure thermal noise level.
Furthermore, we candistinguish between the coherent and non-coherent DLL cases. As we saw in chapter 4, thetracking error of the EMLP discriminator with only noise is shown to be (4.188):ββr⎤⎡⎛ 1⎞ r22⎥()()BL ⎜1 − BLTI ⎟ ∫ 2β r Gd ( f )sin 2 (π f δ )df ⎢Gfffcosdπδ∫− β2r d⎥⎢⎝ 2⎠ −22σ EMLP =22⎥⎢1 +βrβr⎤Cd ⎡⎢ Cd T ⎡2π 2 G ( f )cos(π f δ )df ⎤ ⎥⎢2π ∫ − 2β r f Gd ( f )sin (π f δ )df ⎥⎥ ⎥⎢ N I ⎢ ∫− β r dN0 ⎣022⎦⎣⎦ ⎦⎣(6.40)If we further develop this idea, it can be shown that an equivalent figure to the SSC is presentin the expressions of the degradation of the tracking performance of the desired signal.Moreover, since this figure is very similar in its form to the SSCacq but applies only fortracking, we will call it tracking SSC.
The tracking SSC is shown to adopt the following form[F. Soualle et al., 2007]:k dTracking=,i∫βr2−βr2∫Gi ( f )Gd ( f )sin 2 (π f δ )dfβr2−βrGd ( f )sin (π f δ )df(6.41)22245Spectral Separation Coefficients with data and non ideal codesIf we recall now the expression of the acquisition SSC for comparison:kAcquisitiond,i=∫βr2−βr2∫Gi ( f )Gd ( f )dfβr2−βrGd ( f )df(6.42)2We can recognize that except for the squared sine function multiplying the power spectraldensity, both figures are nearly identical. We show them now in the next figure as a functionof the spacing:Figure 6.37. Variation of the Acquisition SSC and Tracking SSC with the spacingSimilar figures can be equally derived for MBOC as shown in the following figureFigure 6.38. Acquisition SSC and Tracking SSC as a function of the spacingTo conclude, it is important to mention that the squared sine function that we have seen in thelines above converges to 1 f 2 when the spacing tends to zero according to (4.153).
This isindeed deeply related to the ideas that were gathered in chapter 4.7 on MBOC where wementioned that a signal whose spectrum envelope decays with 1 f 2 would be optimum interms of tracking performance. As we saw, MBOC follows this pattern too.246Signal Multiplex Techniques for GNSS7. Signal Multiplex Techniques for GNSS7.1IntroductionAs we have seen in chapter 2, all the existing and planned Global Satellite NavigationSystems will be transmitting more than two services in each transmission band.•••••In E1/L1o GPS plans to transmit at least four signals: The old C/A Code and P(Y) Code,the modernized military M-Code and the new L1 Civil signal (L1C).o Similarly, Galileo will provide on E1 the Public Regulated Service (PRS) andthe E1 OS data and pilot signals.o GLONASS transmits the C/A Code and P-Code, and plans new CDMA signalso and Compass plans to provide two additional signals with services that are stillto be specified.In L2o GPS will be transmitting the L2 Civil Signal (L2C) together with theP(Y) Code and M-Code,o and GLONASS transmits the C/A Code and P-Code.In E5/L5o GPS L5 will provide data and pilot signals, whileo Galileo plans to transmit four signals using the Alt-BOC modulation,o GLONASS plans to transmit new open CDMA signals in the L5 band,o and Compass plans to provide two additional signals with services that are stillto be specified.In E6o Galileo plans to transmit the Public Regulated Service (PRS) and aCommercial Service (CS) with improved characteristics with respect to thefree Open Service (OS),o and Compass plans to provide two additional signals with services that are stillto be specified.Finally in L3o GLONASS will also transmit one civil signal (C/A Code) and the militaryP-Code.The availability of spectrum allocations is a limited resource as we have seen in previouschapters and thus the existing bands have to be reused.
As new services are demanded, newsignals are also required to fulfil needs that did not exist previously. Moreover it is highlydesirable and of greatest importance that the new navigation signals that are introduced do not247Signal Multiplex Techniques for GNSScause significant distortion on other signals sharing the frequency. In other words, they haveto be compatible with the already existing ones. Additional constraints are that we cantransmit the new signals through the same High Power Amplifier (HPA), to be able toaccommodate new data messages and new Pseudo Random Noise (PRN) code families, tohave spectral isolation with the rest of signals in the band and to be capable of providingflexibility to control the distribution of power between the signals in and outside of theallocated band.If we take a look at all these constraints, we can clearly recognize the importance ofdeveloping good signal multiplex techniques based on a high efficiency constant-envelope.Multiplexing aims at providing a multiplicity of signals that must coexist on the same carrierwithout mutual interference [A.R.
Pratt and J.I.R. Owen, 2005]. Moreover, we cannot ignorethat there are clear constraints to fulfil at payload level and that the multiplex technique musttherefore be carefully selected to avoid undesirable sources of degradation. In this chapter wewill study the characteristics of current and future multiplexing techniques and the recentlyproposed modifications for GPS and Galileo in order to be capable of accommodating theoptimized MBOC signal modulation.Finally, it is interesting to note that, as shown in [A.R.
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