On Generalized Signal Waveforms for Satellite Navigation (797942), страница 32
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Moreover, it is important to note that theBarankin bound is a lower bound on the covariance matrix of the position errors but it doesnot say anything about the probability density function of the position errors.Finally, we must underline that the Barankin bound is more accurate than the Cramér Raolower bound as shown in [R. McAulay and E. Hofstetter, 1971]. In fact, the Barankin boundcan be made tighter than the Cramér-Rao bound provided the correct test points are chosen.Moreover, the Barankin bound can be applied in general to more cases than the Cramér Raobound under the assumption that we have some a priori knowledge on the conditionalprobability of some particular points.
As one can imagine, this information is not alwaysavailable and justifies the common use of the Cramér Rao lower bound instead.4.6.5CBCS Interference PerformanceAnother important aspect in the performance of a signal is the interference that the signalsuffers and causes from and to the rest of signals in the band. The Spectral SeparationCoefficient (SSC), to which we will dedicate the next two chapters, is the key figure to assessthe isolation among signals and gives us thus a good insight into this problem. In the nexttables different SSCs are given for the case that no filter is used at the satellite.
However, itmust be noted that in case of filtering the spectral isolation would even improve. For thecalculations a transmission bandwidth of 40.92 MHz and a receiver bandwidth of 24.00 MHzwere assumed.Table 4.1. Spectral Separation Coefficients of proposed Open Signals on E1/L1.
For theCBCS signal an optimized filter was employed to avoid the third harmonic emissionsSSC [dB-Hz]C/A CodeBOC(1,1)CBCS(20%)C/A Code-61.8008-67.7844-68.1428BOC(1,1)-67.7844-64.7373-CBCS(20%)-68.1428--65.6087As we will see in detail in chapter 5, the self SSC (SSC of one signal with itself) tells us howthe intra-system interference is.
From the table above we can also recognize that CBCS hasbetter spectral isolation with itself than BOC(1,1) given its wider spreading. Moreover, theCBCS modulation has better spectral isolation with the GPS C/A Code than BOC(1,1) whichis logical since part of the power has been moved to higher frequencies. As a conclusion,137GNSS Signal StructureCBCS presented an improvement in the SSC values that lead to an increase of the minimumC/N0 value (in both Galileo OS and GPS L1C) of up to 0.6 dB, resulting thus in an overallsuperior link budget.The interference that we have analyzed so far refers to interference from other GNSS sources.Now we concentrate on the case of non-intentional interference coming from other potentialsources.
We distinguish between narrowband interference and wideband interference.••Narrowband interference: The susceptibility to narrow band interference depends onthe continuous PSD and on the code structure. Since this latter is not modified byCBCS, and because the continuous PSD of CBCS was wider than that of BOC(1,1),the optimized CBCS presented a higher robustness to narrowband interference.Wideband interference: The susceptibility to wide band interference is closely linkedto the spreading of the PSD: the more the PSD is spread, the higher the robustness willbe.
Because CBCS features a PSD which is more spread than that of the BOC(1,1)signal, the CBCS was consequently present a higher robustness than BOC(1,1).For more details on the mathematical model behind, refer to Appendix J. As we will see, alsohere CBCS was superior to BOC(1,1).One final aspect to analyze the performance of a signal is the acquisition. A verystraightforward strategy to acquire CBCS was presented in [G.W. Hein et al., 2005], provingthat false acquisition should not represent a big problem.
In fact, the only degradationobservable with respect to BOC(1,1) would be of less than 1 dB, coming from the correlationlosses due to processing with a pure BOC(1,1) receiver.4.6.6Receiver Options for CBCSAs presented in [G.W. Hein et al., 2005] and [A.R. Pratt et al., 2006] there are several optionsto receive the CBCS signals. As we will see, some solutions are more efficient while othersaim at reducing the receiver complexity as much as possible.
We enumerate them next:•The most straightforward approach is to use a CBCS replica at receiver level for boththe data and the pilot channels. As usual, the pilot signal can be used to support datademodulation of the other signal and help in scenarios with poor C/N0 ratios.•A simplified model would be to use a BOC(1,1) replica only. Indeed, as we haverepeatedly commented in different parts of this thesis, special care was put during theoptimization of the E1 OS signals to achieve a modulation that should be as highlyinteroperable as possible with BOC(1,1). This option results in a slight loss of signalpower (-0.97 dB) but the receiver is then enormously simplified.138GNSS Signal Structure•Another imaginable configuration would be to only process the BCS channelextracting thus the difference data message as we will describe in chapter 7.
However,the BCS signal was not optimized for this application, more due to the high data ratethan to the low amount of power that was put on the BCS modulation, which wasabout -6.97 dB lower. Nevertheless, there could be other interesting benefits in termsof improved performance to multipath given the wider bandwidth BCS.•Another possibility would be to form composite codes from the sum and thedifference of the data and pilot codes.
By doing so, we could dispread the BOC(1,1)and BCS channels with the BOC(1,1) and BCS signal waveforms correspondingly.Thisoptioncouldalsosupportdata-aidingasidentifiedin[A.R. Pratt and J.I.R. Owen, 2005] but it would not be absolutely necessary.4.6.7Drawbacks of the CBCS solutionAfter describing all the positive aspects of the CBCS modulation, it is time to describe nowthe two main drawbacks of CBCS with respect to other solutions that were not selected at thattime. These are basically the cross-correlation bias and the need of filtering to achieve spectralcompatibility with the rest of signals in the band.
We concentrate on them now:4.6.7.1CBCS Cross-Correlation BiasThe selected CBCS solution presented a non-symmetric correlation function when aBOC(1,1) receiver correlates with the incoming CBCS signal as we saw in Figures 4.38 and4.39. As a result, a constant bias appears that is a function only of the percentage of power puton the BCS signal with respect to the OS signal, the received power of the desired signal andthe receiver bandwidth.
In principle this bias could be corrected if manufacturers wouldcalibrate it as another bias in the receiver processing. Additionally, this bias could be avoidedwith an appropriate correlation at the receiver [A.R. Pratt et al., 2006] and future receiverscould consider it as a variable that could be updated at any moment in case future changes inthe signal structure would occur.
Nevertheless if due to imperfections not all the satelliteswould be similar, this would introduce a non-negligible complexity that handicapped CBCS.Different solutions were proposed to avoid the tracking bias, being one of the more interestingthe so-called flipping CBCS or CBCS*. This consisted of a BOC(1,1) plus a BCS sequencethat alternates its sign from chip to chip. The CBCS* signal would adopt the following form:⎡ cD (t )⎤cosθ1sBOC(1,1) (t ) + (−1) m cosθ 2 sBCS([s ],1) (t ) + ⎥⎢⎢ 2⎥cP (t )⎢m(4.146)cosθ1sBOC(1,1) (t ) − (−1) cosθ 2 sBCS([s ],1) (t ) + ⎥⎥s (t ) = A1 ⎢+2⎢⎥⎢+ j s (t ) ⎛⎜ sin θ1 + sin θ 2 ⎞⎟ + s (t )⎥PRSIM⎢⎣⎥⎦2⎝⎠[][]139GNSS Signal Structure⎛ sin θ1 − sin θ 2 ⎞(4.147)sIM (t ) = − j cD (t ) cP (t ) sPRS (t ) ⎜⎟2⎝⎠where we can recognize that compared to (4.121) the alternating term (−1) m was introduced toaccount for the alternation of the BCS sequence from one chip to the other chip.
As a result,the cross-correlation between CBCS* and BOC(1,1) would be in average zero as desired. Thedisadvantage of this approach would be on the other hand that the real length of the BCSwould duplicate to all effects due to the phase-alternation.4.6.7.2CBCS Satellite Transmission FilterA second and actually the major drawback of the CBCS solution was the need to introduce afilter in the satellite to get sufficient isolation of the third harmonic of the BCS signal with theGalileo PRS signal. As we mentioned above, the selected BCS sequence is qualitatively verysimilar to a BOC(5,1) which, as we know from theory, has got harmonics at odd multiples ofthe sub-carrier frequency of 5 MHz.
Thus, the third harmonic would fall directly on the PRSat 15 MHz. As suggested in [G.W. Hein et al., 2005] different measures might have beenimplemented in the satellite payload without inducing a loss of power at user level. A carefulselection of the technique guarantees that the main power stays more or less around 5 MHzoffset from the centre frequency so that the resulting waveform does not show any significantimpact in the multipath error considerations and subsequent performance of the final signal.Whilst this is true, it is also true that from the moment a filter would have been introduced,the multipath mitigation performance would have been limited saturating for widerbandwidths what was a very undesirable property. Similar arguments have also been usedagainst SRRC signals as we will show at the end of this chapter.
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