On Generalized Signal Waveforms for Satellite Navigation (797942), страница 47
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Note that the goodness of the approximation will depend on how truethe approximation is that the receiver bandwidth is large enough compared with the main lobe of the signal.208Spectral Separation CoefficientsTable 5.10. Spectral Separation Coefficients in E6. The PSDs are normalized to infinitebandwidth and integrated in an infinite bandwidth. The figures were obtained using theanalytical expressions derived in chapter 5.2RECEPTIONSSC in E6 [dB-Hz]QZSSTx2 BWGalileoBPSK(5)BPSK(5)BOCcos(10,5)∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHzRx BWEMISSIONTx1 BWQZSSBPSK(5)∞ MHz-68.8494-68.8494-86.9112GalileoBPSK(5)∞ MHz-68.8494-68.8494-86.9112BOCcos(10,5)∞ MHz-86.9112-86.9112-73.4870Table 5.11.
Spectral Separation Coefficients in E5. The PSDs are normalized to infinitebandwidth and integrated in an infinite bandwidth. The figures were obtained using theanalytical expressions derived in chapter 5.2RECEPTIONSSC in E5 [dB-Hz]Tx2 BWQZSSGPSGalileoBPSK(10)BPSK(10)AltBOC(15,10)∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHzRx BWEMISSIONTx1 BWQZSSBPSK(10)∞ MHz-71.8597-71.8597-84.0291GPSBPSK(10)∞ MHz-71.8597-71.8597-84.0291GalileoAltBOC(15,10)∞ MHz-84.0291-84.0291-76.2645For E5 and E6 we can see that again the analytical approximation corrected by the efficiencyparameters are a good approximation except for the case of the cosine-phase BOC(10,5) andAltBOC.Now that we have calculated the SSCs of some of the GPS, Galileo and QZSS signals, weanalyze next the particular case of GLONASS. As we thoroughly described in chapter 2.5,GLONASS makes use of FDMA instead of CDMA yet.
Let us see the robustness of theapproach in regards to the Spectral Separation Coefficients. For exemplification, the Self SSCof the GLONASS L1 C/A Code and P-Code for SVNs with indexes from -7 to -1 arepresented in the following tables:209Spectral Separation CoefficientsTable 5.12. L1 GLONASS C/A Code Self SSCs. The PSDs are normalized to the mainlobe of the C/A Code and integrated in a receiver with infinite bandwidthGLONASS C/A Code SSC [dB-Hz]SVN-7-6-5-4-3-2-1-7-57.9700-69.5604-∞-∞-∞-∞-∞-6-69.5604-57.9700-69.5604-∞-∞-∞-∞-5-∞-69.5604-57.9700-69.5604-∞-∞-∞-4-∞-∞-69.5604-57.9700-69.5604-∞-∞-3-∞-∞-∞-69.5604-57.9700-69.5604-∞-2-∞-∞-∞-∞-69.5604-57.9700-69.5604-1-∞-∞-∞-∞-∞-69.5604-57.9700In the same manner, the Self SSCs of the L1 GLONASS P-Code signals for SVNs with indexranging between -7 to -1 are shown next:Table 5.13. L1 GLONASS P-Code Self SSCs.
The PSDs are normalized to the main lobeof the P-Code and integrated in a receiver with infinite bandwidthGLONASS P-Code SSC [dB-Hz]SVN-7-6-5-4-3-2-1-7-67.9700-68.0732-68.3840-68.9060-69.6454-70.6122-71.8202-6-68.0732-67.9700-68.0732-68.3840-68.9060-69.6454-70.6122-5-68.3840-68.0732-67.9700-68.0732-68.3840-68.9060-69.6454-4-68.9060-68.3840-68.0732-67.9700-68.0732-68.3840-68.9060-3-69.6454-68.9060-68.3840-68.0732-67.9700-68.0732-68.3840-2-70.6122-69.6454-68.9060-68.3840-68.0732-67.9700-68.0732-1-71.8202-70.6122-69.6454-68.9060-68.3840-68.0732-67.9700As we can see from the tables above, the FDMA concept that GLONASS employs does notreally bring alone a clear improvement of the spectral isolation among signals. In fact, thefigures are in the same order of magnitude of the Self SSCs of the CDMA signals we haveanalyzed in previous pages.
CDMA provides the capability to introduce an additionalisolation among signals of the same family and other family by means of well selected codeswhile GLONASS uses the same code for all the satellites. The final superiority .of CDMAconsidering also the effect of the codes would be thus in the order of 20 dB or even more.To have an idea of how GLONASS interferes with other systems in the vicinity, the next tablepresents the SSC between Galileo E6 and GLONASS L3 (option 2) for the differentGLONASS SVNs. For more details on the signal definition, refer to chapter 2.5.3. As we sawthere, this option has BPSK(8) for the I channel and BPSK(2) for the quadrature channel.
Inaddition, for completeness not only the SSC between the GLONASS L3 signals and the210Spectral Separation Coefficientswhole Galileo AltBOC modulation are shown, but also separately between GLONASS andE5a on the one side and between GLONASS and E5b on the other side. In this case, theassumption is that the receiver will correlate each of the main lobes of the AltBOC signal witha BPSK(10) replica. As we mentioned already in chapter 4.3.2.4, AltBOC signals can beprocessed as BPSK signals if only the main lobes are used.
For the simulations, theGLONASS PSDs were normalized to the main lobe while the Galileo signals werenormalized to a transmission bandwidth of 92.07 MHz, that 90 x 1.023 MHz. In addition, theassumed receiver bandwidth was of 92.07 MHz for the AltBOC receiver while for the E5aand E5b receivers a bandwidth of 40.92 MHz was assumed.Table 5.14. SSC between Galileo E5 and GLONASS L3SSC [dB-Hz] between Galileo E5 and GLONASS L3PhaseL3 IL3 QSVNAltBOC receiverL3 IL3 QE5a receiverL3 IL3 QE5b receiver-7-81.4014-86.2399-95.3234-138.3102-78.5145-83.7132-6-80.7037-84.4147-96.6860-∞-77.7527-81.8166-5-80.0278-82.8656-98.1793-∞-77.0261-80.1968-4-79.3815-81.5332-99.8186-∞-76.3387-78.7953-3-78.7700-80.3744-101.6237-∞-75.6925-77.5702-2-78.1961-79.3582-103.6194-∞-75.0887-76.4908-1-77.6614-78.4619-105.8386-∞-74.5273-75.53480-77.1666-77.6685-108.3247-∞-74.0081-74.6854+1-76.7116-76.9651-111.1382-∞-73.5306-73.9297+2-76.2961-76.3416-114.3651-∞-73.0940-73.2577+3-75.9195-75.7903-118.1350-∞-72.6975-72.6616+4-75.5811-75.3050-122.6559-∞-72.3403-72.1349+5-75.2802-74.8807-128.2930-∞-72.0217-71.6728+6-75.0162-74.5135-135.7847-∞-71.7409-71.2710+7-74.7883-74.2001-147.0266-∞-71.4972-70.9264+8-74.5960-73.9381-170.6288-∞-71.2900-70.6362As we can recognize, an important overlapping can be observed between the Galileo signalsand GLONASS L3 for some particular combinations, making thus the compatibility of bothsystems more difficult.
The final decision on the GLONASS final signal selection is still openand subject to discussion.To conclude it is important to recall the definition of SSC that we presented at the beginningof this chapter. As we saw there, the SSC can be seen as the mean power of thecrosscorrelation function between the desired and the interfering signals.
We have repeatedly211Spectral Separation Coefficientsseen in the preceding lines that in reality the signal coming from the satellite is filtered toavoid interference with other services around. This was reflected by the efficiency parameterε. But on the side of the replica generation at receiver level the issue is not so unambiguous.While in our previous tables it was assumed that the Power Spectral Density of the desiredsignal was also normalized to the transmission bandwidth of the receiver, we could have alsoassumed that the replica signal at receiver level is generated with no significant filteringeffects.
The corresponding SSC would adopt the following form:κ id = ∫βr / 2−βr / 2Gi ( f )Gd ( f ) H RX ( f ) df2(5.40)where we can recognize that only the interfering signal is normalized this time. The ideabehind this SSC notation is in fact that the receiver generates the desired replica signaldigitally while the interfering incoming signal will present in reality filtered values.
To see theeffect of considering the desired signal without normalization, some SSCs are calculated inthe next table for comparison.Table 5.15. Spectral Separation Coefficients of some signals of interest when the PowerSpectral Density of the replica signal is normalized to the TX Bandwidth and when it isnot (Infinite Bandwidth). All the indicated bandwidths are assumed to be in MHzSSC[dB-Hz]Des.
SignalBPSK(1)BOC(1,1)MBOCTx2 BW30.69∞30.69∞30.69∞Int. SignalRx BWTx1 BW242424242424BPSK(1)30.69-61.8008 -61.8303-67.7619-67.8509-68.0983-68.2528BOC(1,1)30.69-67.7619 -67.7913-64.6921-64.7812-65.0346-65.1891MBOC30.69-68.0983 -68.1278-65.0346-65.1236-65.3483-65.5028As we can see, slight differences can be observed depending on the notation that is followed.These differences are more notable the more energy is concentrated on higher frequenciesbeing even higher than 1 dB in the case of the SSC between GPS M-Code and Galileo PRS.212Spectral Separation Coefficients with data and non ideal codes6.
Spectral Separation Coefficients with dataand non ideal codesSo far we have derived expressions for the Spectral Separation Coefficients between twosignals when ideal codes are assumed. In this chapter we will derive expressions for the casewhen the data is also considered and we will study the effect of non-ideal codes on theresulting spectra.As we have seen above, the analytical expressions for the spectral separation coefficients(SSC) and power spectral densities (PSD) that we have derived above are valid under theassumption that the chip waveform is modulated by ideal random codes which behave likenoise and that we integrate for a infinite period of time. This implies that H ID ( f ) → δ ( f ) .If we recall now (5.9) again,∞Ψks ≈ T ∫ Gk ( f ) ⊗ Gs ( f ) H ID ( f ) df−∞∞2f =0≈ ∫ Gk ( f )Gs ( f )df−∞(6.1)we can clearly see that depending on the integration in the receiver and the properties of thecodes, the results could differ much from those expected from assuming ideal random codes.Experimental results on the goodness of the Galileo and GPS codes have been presented in[S.
Wallner et al., 2006a].The question that arises now is how true the assumptions on ideal random codes are for realreceiver implementations and the effect that non-idealities in the codes have on the finalpower spectral density and, correspondingly, on the SSC values. We concentrate first on theeffect of the data bits and the non ideality of the codes on the spectra of the signals to studylater the effect of having limited integration times versus infinite integrations as assumed inchapter 5.6.1Analytical expressions when data is presentUntil now the effect of the data bits has not been considered yet, but as we know well, GPSand Galileo will both have data channels.
This will affect on the shape of the spectrum.As we know from theory, when the chip waveform of a signal is modulated with a non-idealPRN code, and ideal random data is placed on top of the signal, the power spectral density ofthe resulting modulated signal is obtained by replacing every spike of the code by a sinc ofbandwidth equal to the bit data rate. Indeed, this is equivalent to the convolution of the datasinc with the non continuous line-like spectrum of the non-ideal primary code.213Spectral Separation Coefficients with data and non ideal codesFor the case of the GPS C/A code, the BPSK(1) waveform is modulated by a Gold code oflength 1023 and the bit data rate is of 50 symbols per second (sps) resulting thus in therepetition of 20 code sequences within every data bit.
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