On Generalized Signal Waveforms for Satellite Navigation (797942), страница 46
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In the same manner, we have assumed atransmission bandwidth of 40.92 for the PRS for at least one of the secondary lobes to fallinside. As one can imagine, real emissions will considerably differ from the assumptions ofprevious and next pages.203Spectral Separation CoefficientsTable 5.3. Spectral Separation Coefficients in E1/L1. The Power Spectral Densities are normalized to the transmission bandwidth andintegrated in the bandwidth of the receiverRECEPTIONSSC in L1 [dB-Hz]GPSBPSK(1)GPSGalileoEMISSIONTx2 BWBOC(1,1)MBOCGalileoP-CodeM-CodeBOC(1,1)MBOCPRS30.69 MHz 30.69 MHz 30.69 MHz 30.69 MHz 30.69 MHz 40.92 MHz 40.92 MHz 40.92 MHzRx BWTx1 BW24 MHz24 MHz24 MHz24 MHz24 MHz24 MHz24 MHz40.92 MHzBPSK(1)30.69 MHz-61.8008-67.7619-68.0983-69.9070-87.1118-67.7844-68.1539-99.0884BOC(1,1)30.69 MHz-67.7619-64.6921-65.0346-70.1590-82.2681-64.7147-65.0901-94.3047MBOC30.69 MHz-68.0983-65.0346-65.3483-70.3936-81.9455-65.0572-65.4039-94.2558P-Code30.69 MHz-69.9070-70.1590-70.3936-71.2521-79.9042-70.1816-70.4492-86.4481M-Code30.69 MHz-87.1118-82.2681-81.9455-79.9042-71.6920-82.2906-82.0010-86.7214BOC(1,1)40.92 MHz-67.7844-64.7147-65.0572-70.1816-82.2906-64.7373-65.1127-91.6095MBOC40.92 MHz-68.1539-65.0901-65.4039-70.4492-82.0010-65.1127-65.4594-91.3435PRS40.92 MHz-108.6953-103.1826-101.4261-100.5956-88.8814-103.2052-101.4817-68.4503As we can recognize from the table above, MBOC presents better spectral separation with the rest of signals in the band, making thus thecompatibility considerably easier.
For instance, the spectral overlapping of the GPS MBOC with the GPS C/A code is approximately 0.34 dB betterthan that of BOC(1,1) and even 0.37 dB in the case of Galileo. In addition, since the Self SSC of MBOC is around 0.7 dB lower than that ofBOC(1,1) for both GPS and Galileo, resulting in better intrasystem interference figures as the results of chapter 4.7.8 clearly showed.204Spectral Separation CoefficientsTable 5.4.
Spectral Separation Coefficients in E6. The Power Spectral Densities arenormalized to the transmission bandwidth and integrated in the receiver bandwidthRECEPTIONSSC in E6 [dB-Hz]QZSSBPSK(5)Tx2 BWGalileoBPSK(5)40.92MHz 40.92 MHzBOCcos(10,5)40.92 MHzRx BW24 MHz24 MHz40.92 MHzEMISSIONTx1 BWQZSSGalileoBPSK(5)40.92 MHz-68.6289-68.6289-85.7897BPSK(5)40.92 MHz-68.6289-68.6289-85.7897BOCcos(10,5) 40.92 MHz-86.9659-86.9659-71.3410Table 5.5. Spectral Separation Coefficients in E5.
The Power Spectral Densities arenormalized to the transmission bandwidth and integrated in the receiver bandwidthRECEPTIONSSC in E5 [dB-Hz]Tx2 BWQZSSGPSGalileoBPSK(10)BPSK(10)AltBOC(15,10)24 MHz30.69 MHz92.07 MHz24 MHz24 MHz92.07 MHzRx BWEMISSIONTx1 BWQZSSBPSK(10)24 MHz-71.0089-71.1305-74.5742GPSBPSK(10)30.69 MHz-71.1305-71.2521-74.6958AltBOC(15,10) 92.07 MHz-74.5742-74.6851-75.0696GalileoWe repeat now the computation of the SSCs of QZSS, GPS and Galileo signals but this timewithout normalizing at the satellite and thus assuming an infinite transmission bandwidth. Thepurpose of this exercise is to show the difference with respect to the values of the tablescalculated above.
Since analytical expressions have been derived for infinite bandwidth, tocompute the band-limited versions of the SSCs their analytical counterparts could beemployed applying the corresponding corrections from the efficiency parameters. As one canimagine, this would imply an enormous simplification. We see this more in detail in the nexttables.205Spectral Separation CoefficientsTable 5.6.
Spectral Separation Coefficients in E1/L1. The PSDs are normalized to infinite bandwidth and integrated in the receiverbandwidthRECEPTIONGPSGPSGalileoEMISSIONSSC in L1 [dB-Hz]GalileoBPSK(1)BOC(1,1)MBOCP-CodeM-CodeBOC(1,1)MBOCPRSTx2 BW∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHzRx BWTx1 BW24 MHz24 MHz24 MHz24 MHz24 MHz24 MHz24 MHz40.92 MHzBPSK(1)∞ MHz-61.8597-67.8803-68.2823-70.2466-87.9436-67.8803-68.2823-97.5478BOC(1,1)∞ MHz-67.8803-64.8702-65.2781-70.5581-83.1594-64.8702-65.2781-92.7828MBOC∞ MHz-68.2823-65.6573-65.2781-70.8582-82.9023-65.2781-65.6573-92.5493P-Code∞ MHz-70.2466-70.5581-70.8582-71.8723-81.0166-70.5581-70.8582-85.0854M-Code∞ MHz-87.9436-83.1594-82.9023-81.0166-73.2967-83.1594-82.9023-88.3768BOC(1,1)∞ MHz-67.8803-64.8702-65.2781-70.5581-83.1594-64.8702-65.2781-92.7828MBOC∞ MHz-68.2823-65.6573-65.2781-70.8582-82.9023-65.2781-65.6573-92.5493PRS∞ MHz-109.8317 -104.3785-102.6875-102.0126-90.7907-104.3785-102.6875-70.6641If we compare now tables 5.3 and 5.6 we can clearly see that the SSCs normalized to the transmission bandwidth and to infinite bandwidth cansignificantly differ from one another being the difference more significant the more power the signal concentrates at higher frequencies.
In fact, it istrivial to recognize that the SSC that results from normalizing to the transmission bandwidth and integrating in the receiver bandwidth (Table 5.3)can be easily obtained from the sum of the non-normalized SSC integrated in infinite bandwidth (Table 5.6) minus the efficiency factors of thesignals. For example, SSC BPSK ,Tx (− 61.8008) = SSC BPSK ,∞ (− 61.8597 ) − 2ε BPSK ,Tx (− 0.0294) . Equally for the SSC between the C/A Code and∞ ,∞1 ,Tx2BOC(1,1) we have SSC TxBPSK , BOC (1,1) (− 67.7619 ) = SSC BPSK , BOC (1,1) (− 67.8803) − ε BPSK ,Tx1 (− 0.0294 ) − ε BPSK ,Tx2 (− 0.0890 ) . We can express this as follows:12SSC Ts1x,,sT2x = SSC ∞s1,,∞s2 − ε s1 − ε s2(5.39)206Spectral Separation CoefficientsTable 5.7.
Spectral Separation Coefficients in E6. The PSDs are normalized to infinitebandwidth and integrated in the receiver bandwidthRECEPTIONSSC in E6 [dB-Hz]QZSSTx2 BWGalileoBPSK(5)BPSK(5)BOCcos(10,5)∞ MHz∞ MHz∞ MHz24 MHz24 MHz40.92 MHzRx BWEMISSIONTx1 BWQZSSGalileoBPSK(5)∞ MHz-68.8510-68.8510-87.0217BPSK(5)∞ MHz-68.8510-68.8510-87.0217BOCcos(10,5)∞ MHz-88.1979-88.1979-73.5827Table 5.8. Spectral Separation Coefficients in E5. The PSDs are normalized to infinitebandwidth and integrated in the receiver bandwidthRECEPTIONSSC in E5 [dB-Hz]Tx2 BWQZSSGPSGalileoBPSK(10)BPSK(10)AltBOC(15,10)∞ MHz∞ MHz∞ MHz24 MHz24 MHz92.07 MHzRx BWEMISSIONTx1 BWQZSSBPSK(10)∞ MHz-71.8723-71.8723-83.6088GPSBPSK(10)∞ MHz-71.8723-71.8723-83.6088GalileoAltBOC(15,10)∞ MHz-86.0782-86.0782-75.4304We can still go one step further and not only work with non-normalized Power SpectralDensities as we did in the previous tables, but also integrate in an infinite bandwidth atreceiver level.
This is of enormous interest because if we find out that there are no significantdifferences in the obtained values, we could apply the analytical expressions derived in thischapter to easily calculate the values also for the band-limited case. As we saw, the analyticalvalues are only valid for the infinite bandwidth case, but as we will see, this is a very goodapproximation for most of the signals.207Spectral Separation CoefficientsTable 5.9. Spectral Separation Coefficients in E1/L1. The PSDs are normalized to infinite bandwidth and integrated in an infinitebandwidth.
The numbers were obtained using the analytical expressions derived in chapter 5.2RECEPTIONGPSGPSGalileoEMISSIONSSC in L1 [dB-Hz]GalileoBPSK(1)BOC(1,1)MBOCP-CodeM-CodeBOC(1,1)MBOCPRSTx2 BW∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHzRx BWTx1 BW∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHz∞ MHzBPSK(1)∞ MHz-61.8597-67.8803-68.2821-70.2460-87.8803-67.8803-68.2821-97.4229BOC(1,1)∞ MHz-67.8803-64.8700-65.2779-70.5563-83.1091-64.8700-65.2779-92.6514MBOC∞ MHz-68.2821-65.2779-65.6566-70.8559-82.8373-65.2779-65.6566-92.4166P-Code∞ MHz-70.2460-70.5563-70.8559-71.8597-80.8906-70.5563-70.8559-84.9924M-Code∞ MHz-87.8803-83.1091-82.8373-80.8906-73.1091-83.1091-82.8373-88.2146BOC(1,1)∞ MHz-67.8803-64.8700-65.2779-70.5563-83.1091-64.8700-65.2779-92.6514MBOC∞ MHz-68.2821-65.2779-65.6566-70.8559-82.8373-65.2779-65.6566-92.4166PRS∞ MHz-97.4229-92.6514-92.4166-84.9924-88.2146-92.6514-92.4166-70.5939If we compare now tables 5.6 and 5.9, we can clearly see that the derived SSCs are practically identical for most of the cases of interest, in particularfor the Self SSCs.
While for the case of the Self C/A Code SSC similar results to those obtained with the analytical expressions are achieved usingthe infinite bandwidth approximation and integrating in 24.00 MHz, for the Self SSC of the PRS the difference is lower than 0.1 dB. For the rest ofcombinations, the differences are normally not higher than 0.25 dB except for the particular case of the PRS. Since this signal concentrates animportant amount of power at higher frequencies due to its high sub-carrier frequency and cosine phasing, considerable differences are observedhere. This corresponds to the worst case and thus, unless very accurate figures are required, the derived analytical expressions corrected by theefficiency parameters seem to be accurate enough for most of the purposes.
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