Advanced global navigation satellite system receiver design (797918), страница 17
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This results in increased acquisitiontime of the BOC(2,1) BJ simulation at large initial offsets. The effect becomes morepronounced for high rate BOC modulations.Table 5-8 shows the simulated acquisition times for a BOC(6, 1) signal under thesame conditions. For the high rate BOC(6, 1) the BJ is significantly worse over allinitial offsets. This is mostly due to the small difference between the centralcorrelation peak and its adjacent pairs, now only 1/12 compared to 1/4 for BOC(2, 1).This results in a significant increase in threshold level, which in turn increases thecorrection time. Simulating with an initial offset of 1 sub-chip and applying the BJcounters over 2000 correlations without timing correction, we find the number ofthresholds reached is 54 with an equivalent C/N0 = 24 dB-Hz.
This results in acorrection time of 810 ms for a sub-chip correction (for integration time, T = 15 ms).Compared with the SSB technique the acquisition performance of BJ algorithmbecomes worse as the initial offset is increased. Again this is due to a reduction in thecomparison amplitude because the tracking loops do not settle at integer sub-chipoffsets. With larger initial offsets the reduction in comparison amplitude is greaterresulting in increased acquisition time from the nominal correction time.111Receiver theoryTable 5-8, Acquisition times of the BJ and SSB for BOC(6, 1), BL = 1 Hz, C/N0 = 24 dB-HzInitial chipoffsetBJacquisitiontime (ms)JumpsrequiredCorrectiontime (ms)SSBacquisitiontime (ms)BJ / SSB5.4.41/122/123/124/12100923273481475412348101620243032402765276117363.654.425.696.46The effect of distortion on the BJ algorithmObservations of the wide band BOC(15, 2.5)-cosine Galileo PRS signal transmittedfrom the Giove-A satellite have shown an asymmetry in the spectrum [Montenbrucket al 2006].
No significant asymmetry was observed before the amplification by highpower ‘travelling-wave tube’ (TWT) amplifiers. It is assumed that the asymmetry isdue either to the amplitude dependant phase distortion of TWTs or in the final stageRF filters. In [Graf and Günther 2006] a model of the phase distortion of TWTs isshown to result in similar distortion to that of the Giove-A signals. It has been arguedthat this asymmetry is a result of filter designs intended for a slightly narrowerBOC(14,2) modulation. However, a certain amount of asymmetry has been observedin all BOC transmissions from Giove-A. Even observations of the narrow bandBOC(1,1) modulation show an asymmetry which although small may stillcompromise receiver operation under weak signal conditions.Although a certain amount of asymmetry correction may be possible in thetransmitter, distortion may be an inherent problem with BOC transmissions.
Even ifthe distortion is perfectly corrected in transmission, the large bandwidths occupied bymany of the future BOC transmissions may result in significant asymmetry fromconsumer-grade receiver front-end filters.112Receiver theoryThis asymmetry in the spectrum translates into an asymmetric correlation, which hasbeen observed to potentially cause tracking errors in BOC receivers using the BJalgorithm [Falcone 2006].
This is due to the reduction in magnitude differencebetween the central correlation peak and its adjacent peaks. The BJ algorithm reliesof the difference in peak magnitudes in order to determine the correct tracking state.In order to assess the effect on receiver tracking schemes we can model a receivedasymmetry in BOC by introducing a fixed offset between the received code and subcarrier. For example Figure 5-29 shows an correlation of an asymmetric correlationBOC(2×fC, fC) created by introducing a quarter sub-chip offset between the code andsub-carrier.1symmteric BOCasymmteric BOCDiscriminator error (chips)10.5ΛBF2( R , 0)ΛBF3( R , 0)420240.5−11−4R4Code error (sub-chips)Figure 5-29, Symmetric and asymmetric BOC(2×fC, fC) correlations, sub-carrier to code offset=TS / 4An asymmetric correlation function has a significant effect on the integrity of trackingusing the BJ algorithm. The asymmetry reduces the relative difference in peakamplitudes (see Table 5-9), which is vital for the BJ algorithm to correctly identify avalid tracking state.
Therefore, the BJ threshold must be increased to ensure stabletracking.113Receiver theoryTable 5-9, Symmetric and asymmetric BOC(2×fC, fC) peak valuesPeakSymmetric amplitudeAsymmetric amplitude(sub-carrier to code offset =TS / 4)P10.937VE–0.75–0.812VL–0.75–0.687P – VE0.250.125The BJ tracking algorithm requires careful tuning. If a BJ threshold is set too low toaccount for the noise conditions or asymmetry in the signal the BJ algorithm cancause the receiver to jump out of correct lock to an invalid tracking state. An exampleof this is shown in Figure 5-30.
Here the BJ threshold has been calculated for asymmetric BOC(2,1) signal operating at a carrier to noise of 24 dB-Hz with anequivalent integration time of 15 ms. An asymmetric correlation is created byintroducing a quarter sub-chip offset between the sub-carrier and the code in thereceived signal (see Figure 5-29). It can be seen that noise induced increments of thevery early counter pass the BJ threshold, causing a jump to an invalid tracking state.The tracking estimate remains in error until correction by the very late counterpassing the BJ threshold. The threshold must be increased to a stage where noiseinduced increments of the counters should never cause a jump from the correcttracking state. The increase in threshold results in an increase acquisition andcorrection time.1.5VE count valueVL count valueBJ threshold98tT k−tRC k0100200300400500Counter valuesTiming error (subchips)16CNTE kCNTL k48210− 1.500kLoop iterations5000100200300400k500500Loop iterationsFigure 5-30, Example jump to invalid tracking state, BOC(2,1), C/N0 = 24 dB-Hz, sub-carrier tocode offset =TS / 4114Receiver theoryThe effect of asymmetry is more significant for BOC signals with high ratios of subcarrier frequency to code rate.
The BJ algorithm relies on the ability to determine themagnitude difference between the central and secondary BOC correlation peaks. Asthe ratio of sub-carrier frequency to code rate increases the magnitude differencedecreases. For example, the magnitude difference Galileo BOC(15,2.5) signal is only1/12 compared with 1/2 for BOC(1,1). Therefore, any further reduction due toasymmetry can completely compromise the receiver’s ability to determine a validtracking state. Asymmetry has been observed to compromise the operation of theSeptentrio GETR implementation of the BJ algorithm with the BOC(15,2.5) signalfrom Giove-A.In addition to compromising the receiver’s tracking integrity, asymmetry in thereceived BOC signal causes a bias in the receiver’s delay estimate when operating theBJ algorithm.
The reason for the tracking bias is obvious when examining thecorrelation envelope of an asymmetric signal. An exaggerated asymmetry correlationis depicted in Figure 5-31. The slope of the symmetric correlation is equal on bothsides and has no tracking bias. However, the asymmetric slope is steeper on one side.Therefore, with equally spaced early-late gates the asymmetry causes a bias in thereceiver estimated delay.Early gateEarly gateLate gateLate gateτˆ − τSymmetric (Early – Late = 0)τˆ − τAsymmetric (Early – Late /= 0)Figure 5-31, Depiction of asymmetric tracking bias115Receiver theory5.4.5The effect of multipath on the BJ algorithmThe BJ algorithm relies on the ability to detect whether or not the receiver has settledto a valid tracking state through comparison of the adjacent correlation peaks.
Thecentral BOC correlation peak must be sufficiently greater in amplitude than itsadjacent peaks to enable valid tracking in the presence of noise. In Section 5.4.3 itwas shown that the comparison amplitude between the peaks, required for the BJalgorithm to make a correction, reduces the further the false-lock point is from thecentre of the correlation function. This degrades the performance of the peakdetection and poses a potential integrity risk to the receiver. Inference from multipathsignals can further reduce the comparison amplitude and therefore further degradesthe performance of the BJ algorithm.Figure 5-32 shows the effect of multipath interference on a BOC(2,1) signal. Themultipath is assumed to be of half amplitude relative to the direct signal with an inphase carrier and therefore provides a worst-case scenario.
It is assumed that thereceiver maintains lock on the central peak of the BOC correlation. The comparisonamplitude is the difference between either the prompt, P and very-early, VEcorrelations or the prompt and the very-late, VL correlations. Reducing either ofthese comparison amplitudes will result in an increased chance jump away from thevalid timing location in the presence of noise. The receiver designer must thenincrease the BJ threshold to account for noise induced increments of the VE and VLcounters or risk the integrity of the receiver under strong multipath.0.40.375Comparison amplitude0.3P k − VEkP k − VLk 0.2TH0.1|P|-|VE||P|-|VL|Multipath free value00050100150200250k⋅ mincr , k⋅ mincr , met300350400375.733Multipath delay (m)Figure 5-32, BJ comparison amplitude of BOC(2, 1) correlations against relative multipathdelays (in-phase carrier, central correlation peak tracking)116Receiver theoryThe results show that when the relative delay of the multipath interference is atinteger sub-chip (73 m) intervals the comparison amplitude is halved from thenominal value (no multipath interference present).
At short multipath delayshowever, the comparison amplitude is actually 3/2 times greater than the nominalvalue, actually improving the performance of the BJ peak detection. In this case themultipath is constructive to the BOC correlation at short delay because the multipathis in-phase with the direct carrier signal. Simulating a multipath which is 180° out ofphase with the direct signal results in the opposite effect as shown in Figure 5-33.0.40.375Comparison amplitude0.3P k − VEkP k − VLk 0.2TH0.1|P|-|VE||P|-|VL|Multipath free value00050100150200250k⋅ mincr, k⋅ mincr, met300350400375.733Multipath delay (m)Figure 5-33, BJ comparison amplitude of BOC(2, 1) correlations against relative multipathdelays (180°° out of phase, central correlation peak tracking)Clearly the presence of strong multipath can significantly compromise the ability ofthe BJ algorithm to determine the valid tracking location.
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