Advanced global navigation satellite system receiver design (797918), страница 20
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AnAltBOC(15, 10) signal modulation is intended to combine four PRN code signals in133BOC tracking with double estimation receiverthe Galileo E5 band. Omitting the data modulation for simplicity the AltBOC signalcan be written as follows.uAltBOC (t ) = A1 × [a1 (t − τ ) + a2 (t − τ )]× s (t − τ ) × cos(ωC t + φ ) +A × [a (t − τ ) − a (t − τ )]× ~s (t − τ ) × sin(ω t + φ ) +1126-22CA2 × [a3 (t − τ ) + a4 (t − τ )]× ~s (t − τ ) × cos(ωC t + φ ) −A2 × [a3 (t − τ ) − a4 (t − τ )] × s (t − τ ) × sin(ωC t + φ )The upper and lower sidebands of the AltBOC signal can be individually processed asseparate PSK signals because the code combinations modulate separate upper andlower side bands respectively.
However, to achieve the full potential of this widebandmodulation the full bandwidth must be processed. Tracking the full AltBOCmodulation can be achieved using either the sum of the a1( ) and a2( ) codes or thesum of the a3( ) and a4( ) codes. Correlating the sum of the a3( ) and a4( ) codes theresulting correlations for a coherent DE AltBOC receiver are as follows.TwIII() (()() (()() (1= ∫ u AltBOC (t ) × cos ω0t + φˆ × ~s t − τˆ* × [a3 (t − τˆ ) + a4 (t − τˆ )]dtT0())6-23≈ 2 A × cos φ − φˆ × trc τˆ* − τ × Λ (τˆ − τ ) × dTwIIQ =1u AltBOC (t ) × cos ω0t + φˆ × ~s t − τˆ* × [a~3 (t − τˆ ) + a~4 (t − τˆ )]dt∫T0(wIQI))≈ 2 A × cos φ − φˆ × trc τˆ* − τ × VΛ (τˆ − τ ) × dT1= ∫ u AltBOC (t ) × cos ω0t + φˆ × s t − τˆ* × [a3 (t − τˆ ) + a4 (t − τˆ )]dtT0()())≈ 2 A × cos φ − φˆ × Trs τˆ* − τ × Λ (τˆ − τ ) × dTwQII =() (()1u AltBOC (t ) × sin ω0t + φˆ × ~s t − τˆ* × [a3 (t − τˆ ) + a4 (t − τˆ )]dtT ∫0())≈ 2 A × sin φ − φˆ × trc τˆ* − τ × Λ(τˆ − τ ) × dThese correlations provide equivalent error signals to the DE BOC receiver allowingcontrol of all three loops into lock.
The SLL delay estimate can then be corrected bythe DLL estimate as in Equation 6-15.134BOC tracking with double estimation receiver6.4Simulated performance of DE BOCIn Section 5.4 a comparison of the BOC tracking techniques in the literature is given.From this analysis, a design trade-off is identified between receiver settling time andtiming jitter of the delay estimate. Techniques approximating a PSK singlecorrelation peak provide an unambiguous rapid loop settling time but at the cost ofsignificantly worse receiver timing jitter. Other techniques, such as the BJ algorithmcan provide the full potential of BOC tracking precision but suffer in terms of loopsettling times.The DE BOC receiver is believed to provide the best of both worlds, an unambiguousrapid loop settling time while providing the full timing precision available from theBOC characteristic. The settling time of the DLL loop follows the desirable singlecorrelation peak synonymous with PSK modulation, while the SLL loop simplysettles to the nearest sub-chip offset.
The maximum precision of the BOC modulationis then achieved by correcting the SLL estimate using the DLL estimate as inEquation 6-15.From Section 5.4 the SSB technique has been shown to provide the best acquisitionperformance and the BJ algorithm the best timing precision. Table 6-4 shows theacquisition times of the DE BOC receiver in comparison to the SSB technique and BJalgorithm. We are assuming a BOC(6, 1) signal, a carrier to noise density of C/N0 =24 dB-Hz, equal DLL and SLL loop bandwidths of BDLL = BSLL = 1 Hz and averagingacross 20 acquisitions at each time step. The DE BOC receiver is shown to deliveracquisition speed equivalent to that of the SSB technique.135BOC tracking with double estimation receiverTable 6-4, Acquisition times of the DE BOC receiver, BJ algorithm and the SSB technique forBOC(6, 1), BL = 1 Hz, C/N0 = 24 dB-HzInitial chipoffsetDE BOCacquisitiontime (ms)BJacquisitiontime (ms)SSBacquisitiontime (ms)DE / SSBBJ / SSB1/122/123/124/1227252362077610092327348147542765276117360.990.991.011.053.654.425.696.46Using Mathcad simulations we can evaluate the timing jitter of the DE in the presenceof additive Gaussian noise and give comparisons with the theoretical equations givenin Chapter 4.
In all cases we simulate a ‘spacing-limited’ receiver. Figure 6-10shows the theoretical and simulated timing jitter for PSK and DE BOC receiversacross carrier to noise densities from 30 to 50 dB-Hz. We find strong agreement withthe theoretically derived equations, proving that the precision of DE BOC trackingdelivers the full potential accuracy of BOC modulation.PSK-R(1)3.5PSK simulatedPSK theory3.305receiver tracking jitter∆ PSKT= C42.5Timing jitter (m)BL = 1 Hz3ΣCM2ΣCT1.510.50.32830303540CNdB455050Carrier to noise density (dB-Hz)136BOC tracking with double estimation receiverDE BOC(2,1)1.4BOC(2,1) simulatedBOC(2,1) theory1.328receiver tracking jitter1.2∆ BOCT= C = TS4Timing Jitter1BL = 1 HzΣSLLM 0.8ΣSLLHT0.60.40.20.1383035304045CNdB5049Carrier to noise density (dB-Hz)DE BOC(6,1)0.4BOC(6,1) simulatedBOC(6,1) theory0.383receiver tracking jitterBL = 1 Hz∆ BOC =TC= TS12Timing Jitter0.3ΣSLLM0.2ΣSLLT0.10.0433030354045CNdB5049Carrier to noise density (dB-Hz)Figure 6-10, Simulations of PSK and DE BOC timing jitter with comparison to theoryAnother key performance measure of particular interest is that of the multipathperformance of the DE BOC receiver.
As shown in Section 4.5 the simplest methodof evaluating the multipath error performance is to consider the effect of a singleinterfering multipath signal with various relative time delays. This provides only aworse case analysis of error due to multipath but does provide an adequateperformance measure with which we can compare BOC tracking schemes.
The resultof this analysis is a multipath error envelope which for conventional receivers isdependant on the correlation function and the type of discriminator implemented for137BOC tracking with double estimation receivercode tracking. Therefore, to provide a fair comparative basis on which to evaluatemultipath error envelopes it is important to set equal discriminator spacing.Figure 6-11 shows the multipath error envelopes of a conventional BOC receiver andthe DE BOC receiver for a BOC(2,1) signal.
The DE BOC error envelope iscomputed by analyzing the error of the corrected SLL delay estimate with multipathinterference. The relative performance of each scheme can be seen by computing therunning average error across the dataset, shown in Figure 6-12. The pattern of the DEBOC multipath envelope broadly follows that of the conventional receiver but doesshow a small improvement (8.2%) across the whole dataset.Double estimator BOCConventional BOC2520Ranging error (m)10σNSm0σCONVm501001502002503003504001020− 250met366.569Multipath delay (m)Figure 6-11, Multipath error envelope of a conventional and DE BOC receiver,BOC(2,1)∆ BOC = TS138BOC tracking with double estimation receiver25Conventional BOCDouble estimator BOC22.959Running average error (m)2015RunAvr ( RA_CONV )RunAvr ( RA_TRIP )10500501001500200250300350met400366.569Multipath delay (m)Figure 6-12, Running average multipath error of a conventional and DE BOC receiverBOC(2,1)6.5∆ BOC = TSThe effect of asymmetryIn contrast to the BJ algorithm, asymmetry in the received signal is not believed topose a severe problem for the DE BOC receiver.
This is because a DE BOC receiverdoes not rely on peak discrimination and tracks the sub-carrier of the incoming signalindependently of the code. The DE BOC receiver has no false-lock conditionsbecause sub-chip offsets are automatically accounted for in the corrected delayestimate. Therefore, asymmetry has no significant effect on the integrity oracquisition performance of the DE BOC receiver.Figure 6-13 shows an example acquisition of the DE BOC receiver with a distortedsignal created by introducing a quarter sub-chip offset between the sub-carrier and thecode in the received signal. The received code delay is set to –1/4 of a sub-chip.Therefore, the SLL estimate is biased from the correct delay.
However, the effect ofthe sub-carrier is removed from the DLL loop which therefore converges to thecorrect timing location. The SLL bias can be calibrated and corrected by using theDLL estimate, which is assumed to be correct. The bias in the BJ algorithm can only139BOC tracking with double estimation receiverbe resolved if the receiver has the capability of receiving other signals from the samesatellite or through a complex calibration campaign.32.5282tT k − tRS ktT k − tRC ktT k − τ B k1− 140100200300400500− 0.38410k500SLL error (sub-chips)DLL error (sub-chips)Corrected error-1/4 sub-chipFigure 6-13, Example acquisition of the DE BOC receiver with asymmetric correlation,BOC(2,1), C/N0 = 24dB-Hz, sub-carrier to code offset =TS /4The DE BOC receiver can very accurately measure the sub-carrier to code offset, inorder to correct for asymmetry in the received signal.
This is achieved simply byaveraging the difference between SLL and DLL estimates to remove timing jitter. Anexample of receiver calibration for asymmetric signals is shown in Section 9.2.Although calibration of the receiver tracking bias for the BJ algorithm is possible, it iscertainly more complicated to achieve than calibration of the DE BOC receiver. Thiscombined with the risk to BJ receiver integrity proves the DE BOC receiver to be thepreferred choice, particularly for BOC transmissions with high ratios of sub-carrierfrequency to code rate.Further detailed work is continuing at SSTL in order to demonstrate the advantagesDE BOC receiver with the significantly distorted BOC(15,2.5) signal from Giove-A.6.6Integrity of the DE BOC receiverThe DE BOC receiver provides two independent estimates of the incoming signaldelay.
These estimates can be used to improve the integrity of the receiver’s tracking.This is of particular interest in the use of BOC receivers for safety critical140BOC tracking with double estimation receiverapplications, where an incorrect tracking state due to a signal dropout or slip in BOCreceiver tracking could have catastrophic results.The receiver estimated signal to noise ratio is used to indicate when a receiver has lostlock on the incoming signal. An example of a signal drop out from an SNR of 15dBis shown in Figure 6-14. The raw SNR values are filtered in the receiver to avoiddropping the signal while tracking in weak signal conditions.
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