On Generalized Signal Waveforms for Satellite Navigation (797942), страница 30
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As shown in [F. Soualle et al., 2005] thedata and pilot codes were optimized without accounting for the modulation scheme. Theconsequence of this is that unless the receiver applies a coherent processing of the incomingsignal, the codes will show a slight degradation.Another very important aspect from the CBCS modulation is the power distribution, since thisdetermines in the end the multipath rejection potential of the solutions. As shown inAppendix J, the following expressions for the data and pilot channels can be derived:⎡ cos 2 (θ1 ) + cos 2 (θ 2 ) cos(θ1 ) cos(θ 2 ) ⎤POS D = A12 ⎢+r⎥42⎣⎦22⎡ cos (θ1 ) + cos (θ 2 ) cos(θ1 ) cos(θ 2 ) ⎤POS P = A12 ⎢−r⎥42⎣⎦(4.124)(4.125)where the parameter r represents the correlation between BOC(1,1) and the BCS signal:1(4.126)r = ∫ sBOC (1,1) (t ) sBCS([s ],1) (t )dtTc TcThis parameter is of great importance as we will see when we describe the MBOC modulationin the next chapter.
In fact, the BCS sequence of the CBCS was selected among other reasonsbecause its value of r is zero. However, the cross-correlation of the CBCS signal with aBOC(1,1) alone receiver is not zero any more and presents a so-called tracking bias. Indeed,this was the main drawback of the CBCS solution with respect to the finally selected MBOC.We show in the next figure the cross-correlation of the CBCS signal with BOC(1,1):Figure 4.38. Cross-correlation between CBCS and a BOC(1,1) receiver127GNSS Signal StructureIndeed, this asymmetry leads to the mentioned tracking bias, as can be seen in the next figure:Figure 4.39. CBCS and local BOC(1,1) discriminator functionWe will talk a little bit more on this bias at the end of this chapter.
Nevertheless, it isimportant to mention here that although there are solutions to eliminate the tracking bias thatresults from the non-zero correlation between CBCS and BOC(1,1), the need to have a signalthat would not present such a disadvantage was the main reason that lead to moving to thefinally selected CBOC solution. CBOC is a particular implementation of MBOC where theInterplex multiplex is part of the definition as shown in chapter 4.6. Furthermore, CBOC canalso be seen as a particular case of CBCS where the selected BCS is BOC(6,1).
For moredetails on MBOC and its implementations, refer to chapter 4.7A figure of great interest to analyze the impact of the CBCS modulation on a BOC(1,1)receiver is given by the cross-correlation that a receiver would suffer if it would only track theBOC(1,1) component of the CBCS signal.As shown in [G.W. Hein et al., 2005], the delta correlation losses with respect to the baselineBOC(1,1) are the difference between the cross-correlation measured when the input is CBCSand the result of the auto-correlation when the input is a BOC(1,1) signal.
Figure 4.40 belowshows in detail the scheme assumed to measure the correlation losses.Figure 4.40. Model to measure the delta correlations between CBCS and BOC(1,1)128GNSS Signal StructureThe driving idea behind this model is to measure the real delta correlation losses that areceiver would experience if instead of the baseline BOC(1,1), the CBCS were emitted. Itmust be noted that while CBCS will of course not correlate 100 % with a BOC(1,1) replica asBOC(1,1) would do, resulting thus in losses, the more efficient CBCS modulation that resultsfrom reducing the IM product allows for higher receiver powers at user level for the sametransmitted power from the satellite.
Both figures go in opposite directions and must beconsidered together. Indeed, as shown in [G.W. Hein et al., 2005], the delta correlation lossesare shown to be:⎡ A (cos θ1 + r cos θ 2 ) ⎤⎛ A1ΔL = ⎢ 1⎥ = ⎜⎜cos θ 0⎣ A0⎦⎝ A02⎞⎟⎟⎠2⎛ cos θ1⎜⎜⎝ cos θ 0⎞⎟⎟⎠2⎛cos θ 2⎜⎜1 + rcos θ1⎝⎞⎟⎟⎠2(4.127)When we express it in dB, the three contributions to the delta correlation losses can be clearlyseparated as follows:ΔLTotal = ΔLEnvelope Power + ΔLBOC(1,1) Power Share + ΔLMismatch Loss(4.128)where⎛A ⎞ΔLEnvelope Power = 20 log10 ⎜⎜ 1 ⎟⎟⎝ A0 ⎠⎛ cosθ1 ⎞⎟⎟ΔLBOC(1,1) Power Share = 20 log10 ⎜⎜cosθ0 ⎠⎝⎛cosθ 2 ⎞⎟ΔLMismatch Loss = 20 log10 ⎜⎜1 + rcosθ1 ⎟⎠⎝(4.129)(4.130)(4.131)ΔLEnvelope Power accounts for the fact that the amplitude of the baseline interplex modulationand that of the optimized signal differ slightly.
Additionally, the term ΔLBOC(1,1) Power Sharerepresents the losses of power of the BOC(1,1) signal since part of it goes now to the BCScomponent and finally the third term ΔLMismatch Loss of the correlation losses is a function of thecorrelation between the chosen BCS([s],1) and BOC(1,1) and gives an idea of how similar toBOC(1,1) the CBCS signal is. If we look at the correlation term more in detail,ΔLMismatch Loss = 1 + rcosθ 2cosθ1(4.132)we can see that this contribution to the correlation losses can be eliminated by two means.The first one is doing θ 2 = π what corresponds to the case of pure BOC(1,1).
The other2possibility and of much more interest is to have r = 0 what leads to a CBCS solution withzero mismatch correlation losses. For reasons of implementation due to symmetry, specialattention was paid to the solutions with r = 0 .Now that we have shown the mathematical background behind the CBCS modulation, we areready to introduce the signal that for some time was the most interesting candidate of Galileoto substitute BOC(1,1) until CBOC came: namely CBCS. CBOC is the Europeanimplementation of MBOC as will be shown in chapter 4.7.3.129GNSS Signal Structure4.6.2CBCS([1,-1,1,-1,1,-1,1,-1,1,1], 1, 20 %)After signing the Agreement of 2004 and as a result of long months of hard work, a BCSsequence was found to be an interesting candidate for the Galileo E1 OS signal.
The selectedBCS sequence was compatible to a very high degree with pure BOC(1,1) receivers[G.W. Hein et al., 2005] while it offered at the same time an important potential to improvethe positioning performance and to mitigate multipath. Moreover, the selected signal wascompliant with the Agreement of 2004 and did not require important changes in the satellitepayload.
The BCS sequence was [s] = [1, -1, 1, -1, 1, -1, 1, -1, 1, 1] and the amount of poweron the BCS sequence with respect to the total OS power was selected to be 20 % at user levelwhat would corresponds to approximately 26 % at generation in the satellite. For simplicity,the signal was thus baptized with the name CBCS([1, -1, 1, -1, 1, -1, 1, -1, 1, 1], 1, 20 %) orCBCS(20) for short. The selected BCS sequence can be seen as a quasi BOC(5,1). Indeed, interms of performance it was very similar to a BOC(5,1) but had a more favourable spectraldistribution since it did not overlap the M-Code as much as the last one.As we have said above, the CBCS modulation had a minimum impact on the payload, whatmade the solution a serious alternative.
In addition a number of advantages can be identified:••••Compared with the original Interplex using only BOC(1,1), the CBCS modulation ismore efficient, reducing the IM product power by more than 3 dB.As a result, the optimized modulation offered an additional margin of 0.26 dB on thelink budget, for the same transmitted power at satellite level.The modulation is fully compatible with a flexible signal generator implementationbased on modulation tables with a high number of bits of quantization.Finally, in spite of having two additional phase points closer to each other, the CBCSmodulation is less sensitive to payload phase noise than the original modulation.The following figure shows in detail how the Galileo and GPS Signal Plan would have lookedlike if the CBCS signal had been selected instead of MBOC.Figure 4.41.
Power Spectral Density of Galileo and GPS signals in E1/L1130GNSS Signal StructureIn the next figure we show in detail the power distribution of the spectra of the differentcomponents of the CBCS modulation:Figure 4.42. Power Spectral Distribution of BOC(1,1) and BCS within CBCSAn important number of constraints were introduced during the search of the best potentialsignal candidate for the Galileo E1 OS to substitute BOC(1,1). Finally among all the solutionsthat passed the selected criteria, the best candidate was chosen. One of the most importantperformance merit figures for the final selection was the multipath performance for a givenbandwidth (12 MHz) since this was considered to be the most important source of error due toits unpredictable properties.
Furthermore 12 MHz was thought to be a reasonable bandwidthfor future receivers even in the field of mass market.Figure 4.43. Ranking of CBCS solutions in terms of multipath mitigation potential131GNSS Signal StructureAs we can recognize in the previous figure, CBCS(20) occupies the first place in the ranking,followed by CBOC(6) and CBOC(5). It is interesting to note that other solutions were alsofound at that time, with performance figures close to those of the CBCS signal.
The figureabove shows the ranking of the different solutions and the multipath performance of each ofthem. We can clearly recognize that CBOC(6) performed in second place for 12 MHz. This isindeed the signal finally selected as baseline for Galileo E1 OS and GPS L1C since it presentsa better performance over a wider range of receiver bandwidths. We will come back on thispoint in the next chapter. We can also read from the previous figure that CBOC(5) was aninteresting option, but its major drawback was that the coefficient r, as defined in (4.126), isnot zero and thus the delta correlation losses of this solution would increase very rapidly aswe would increase the power on the BOC(5,1) component.
As a result, the percentage of thenon-BOC(1,1) component was very limited, and consequently the growth potential in terms ofmultipath mitigation.4.6.3CBCS Power Spectral DensityUsing the theory developed above for BCS signals and thoroughly explained in chapter 4.3we will derive here a compact simplified expression for the CBCS signal. As we have seen,the selected BCS sequence was s = [+ 1, − 1, + 1, − 1, + 1, − 1, + 1, − 1, + 1, + 1] .
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