Advanced global navigation satellite system receiver design (797918), страница 11
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The multipath signalhas the effect of shifting the code or carrier discriminator’s zero crossing away fromthe correct timing location, this is depicted in Figure 4-13. The error induced by thepresence of the multipath signal is then calculated from difference in the timing of thenew zero-crossing from the correction timing location. This provides only a worsecase analysis of error due to multipath but does provide an adequate performancemeasure with which we can compare PSK and BOC signals.Atrue time locationtA/2multipath time location tcomposite discriminatortime locationtFigure 4-13, Depiction of discriminator error induced by the presence of multipathThe relative amplitude of the multipath interferer is defined by the coefficient ofreflection, α.
In all analysis presented here we assumed the maximum relativeamplitude of multipath signal to be half amplitude (α = 0.5). A multipath error67PSK and BOC signalsenvelope can then computed over various multipath time delays. The multipath errorenvelope for a PSK-R(1) modulation in shown in Figure 4-14 derived from Mathcadsimulation (see Appendix B for details of the simulation).
The carrier phase of therelative multipath is simulated at a worst-case of 0° and 180°. This results in the twosides of the multipath error envelope.80Wide PSKNarrow PSK8060Multipath induced code error (m)4020PSKm0PSKNm50100150200250300350400450500550204060− 80800met2 , met549.853Relative muiltpath delay (m)Figure 4-14, Multipath error envelopes for wide PSK(TD = TC ) and narrow PSK (TD = TC 2)The multipath induced error only occurs across the range of the PSK discriminatorcharacteristic (TC + TD 2 ) . Reducing the early-late discriminator spacing restricts therange over which the multipath signal can affect the discriminator.
Also, thereduction in discriminator spacing flattens the discriminator, which limits themaximum error induced by the multipath. Therefore, narrow discriminator spacingcan reduce timing jitter and multipath induced errors.When considering PSK and BOC multipath performances it is common in theliterature to make a comparison by setting equal chip widths [Irsigler et al 2004]. Forexample, comparing PSK-R(1) to BOC(1,1) as shown in Figure 4-15 for which wefind agreement with the published results. However, this results in the suggestion that68PSK and BOC signalsBOC modulation provides better multipath error performance over PSK.
This isagain not a fair basis for comparison, for exactly the same reason as given for thetiming jitter performance, clearly the processing rate of BOC(1,1) is twice that ofPSK-R(1).80BOC(1,1)PSK-R(1)8060Multipath induced code error (m)4020µ0m0µ0PSKm50100150200250300350400450500550204060− 80800met549.853Relative multipath delay (m)Figure 4-15, Multipath error envelopes of PSK-R(1) and BOC(1,1) signals(TD= 2 × TS( BOC )= TC( PSK ))In contrast, a fair comparison between PSK and BOC can be made by setting equaldiscriminator spacings and equal processing rates. A comparison between PSK-R(2)and BOC(1,1) provides a fair comparison with both discriminator spacings equal to(the sub-chip width TD = TS( BOC )= TC( PSK )). The multipath error envelopes are shownin Figure 4-16. A clearer view of the relative performance of the two modulations canbe seen by the examining the running average error across the dataset, as shown inFigure 4-17.
It can be seen that on a like-for-like basis BOC modulation outperformsPSK for short-range multipath delays. The lines intersect indicating equal ( PSK ) TD ( PSK ) . However,performance over the range of the PSK discriminator TC+2 across the entire range of delays PSK has a 14.7% lower average multipath error than69PSK and BOC signalsthe equivalent BOC modulation.
The degradation of BOC performance at long-rangemultipath delays is due to the secondary peaks in the BOC correlation.80BOC(1,1)PSK-R(2)8060Multipath induced code error (m)4020µ0m0µ0PSK2m50100150200250300350400450500550204060− 80800met549.853Relative multipath delay (m)Length := 30Figure 4-16, Multipath error envelopes for PSK-R(2) and BOC(1,1) signals(TD= TS( BOC )= TC( PSK ))5048.876Running average error (m)4030RunAvr ( MAG_PSK )RunAvr ( MAG_BOC )2010001002003000met400500550Relative multipath delay (m)Figure 4-17, Running average multipath error of PSK-R(2) and BOC(1,1) signals(TD= TS( BOC )= TC( PSK ))Doubling the processing rate we compare PSK-R(4) with BOC(2,1) modulation asshown in Figure 4-18 and Figure 4-19.
Again BOC modulation outperforms PSK atshort range multipath and the performances converge at the width of the PSKdiscriminator. However, the additional secondary peaks in the BOC correlation70PSK and BOC signalsdegrade the overall performance such that the average PSK error is now 39.6% lowerthan the equivalent BOC error.40BOC(2,1)PSK-R(4)4030Multipath induced code error (m)2010µBOC0µPSK50100150200250300350400102030− 40400met366.569Relative multipath delay (m)Figure 4-18, Multipath error envelopes for PSK-R(4) and BOC(2,1) signals (TD= TS )25PSK-R(4)BOC(2,1)24.438Running average error (m)2015RunAvr ( MAG_PSK )RunAvr ( MAG_BOC )10500050100150200250met300350400400Relative multipath delay (m)Figure 4-19, Running average multipath error of PSK-R(4) and BOC(2,1) signals(TD = TS )The carrier phase error induced by multipath signals is closely related to the signal’sfundamental correlation function (see Section 5.2 for a illustrative examples).Therefore, the multipath induced error envelope follows the envelope of correlationfunction, as shown in Figure 4-20 for PSK-R(4) and BOC(2,1).
The running averagecarrier phase error is shown in Figure 4-21. BOC outperforms PSK at multipath71PSK and BOC signalsdelays less than the PSK chip width where the multipath performance converges.Despite this, across all multipath delays the PSK signal significantly outperforms theequivalent BOC signal (63% improvement).0.0150.014Carrier phase error (m)0.010.005σPSK0σM501001502002503000.0050.01− 0.0140.0150met300Relative multipath delay (m)Figure 4-20, Multipath induced carrier phase error envelopes for PSK-R(4) and BOC(2,1) signals0.0250.023Running average error (m)0.020.015RunAvr( MAG_PSK )RunAvr( MAG_BOC )0.010.00500050100150200met250300300Relative multipath delay (m)Figure 4-21, Running average carrier phase multipath error of PSK-R(4) and BOC(2,1) signalsLong range multipath is generally easier to distinguish and mitigate, therefore BOCmodulation potentially offers better performance than PSK for complex multipathmitigating receivers.
However, for receivers which either do not attempt to correct72PSK and BOC signalsfor multipath errors or rely on correlator techniques such as narrow discriminatorspacing, BOC can be considerably worse than the equivalent PSK system.To summarise the discussion given in this chapter we consider the advantages anddisadvantages of BOC modulation. The advantages of implementing a GNSS systemwith BOC modulation rather than the conventional PSK modulation are as follows.
Spectral separation – BOC modulation provides a method of re-usingfrequency allocations in a bandwidth efficient way. This can provide spectralseparation between signals within the same bandwidth allocation and thereforereduce the amount of interference between the signals.
The spectral separationalso enables filters to be employed to isolate individual signals. Interference regulation – BOC sub-carrier phasing can be adjusted to regulatethe amount of interference with neighbouring signals. Reduced timing jitter – BOC modulation results in a small improvement (3dBmaximum) to the code timing jitter in the presence Gaussian noise over theequivalent PSK system.
Increased resilience to short-range multipath – The BOC correlation functionresults in a small reduction in multipath induced code and carrier phase errorsin the presence of short-range multipath.The disadvantages of implementing a GNSS system with BOC modulation rather thanthe conventional PSK modulation are as follows. False locking points – The secondary peaks in the BOC correlation enveloperesult in multiple zero crossings across the discriminator characteristic, onlyone of which corresponds to the correct timing location. It is then possible forthe receiver to be in a stable lock at a false zero crossing causing a gross errorin the receivers timing location.
This research has developed a new solutionwhich we believe to be superior to any currently proposed in the literature.This issue is analysed in depth in Section 5.4 and Chapter 6. Complicating the search process – The nulls in the BOC correlation envelopecomplicate search process requiring additional receiver technology to achieveequivalent PSK performance. This issue is analysed in depth in Section 5.3.73PSK and BOC signals Poor long-range code and carrier multipath performance – Compared on alike-for-like basis PSK would seem to significantly outperforms BOC in thepresence of long-range relative multipath delays.In this chapter we have focused purely on the technical considerations, which must beaddressed when choosing a specific GNSS signal modulation.
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