Advanced global navigation satellite system receiver design (797918), страница 18
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This problem becomesworse for higher ratios of sub-carrier frequency to code rate such as BOC(15,2.5)where the BJ comparison amplitude is already very small.In Chapter 6 we describe an entirely new approach to tracking BOC signals which isbelieved to be robust to distortions in the received signal.117Receiver theory5.4.6Hardware requirements of BOC tracking techniquesIn order to fully evaluate and compare the BOC tracking techniques presented herewe must also look at the impact to the receiver hardware.
Table 5-10 shows thehardware requirements of the BOC tracking techniques, for achieving incoherentcarrier and code tracking. The MGD discriminator is formed from 4 early and 4 latecorrelations, requiring 16 code multipliers and integrators for incoherent codetracking. An additional 2 multipliers and integrators are required for carrier trackingmaking a total of 18, a significant overhead for each tracking channel. The filteringrequired for the SSB technique is undesirable and can significantly impact the sizeand complexity of the receiver. Hence, the best choice in terms of hardwarerequirements is the BJ algorithm.Table 5-10, Hardware requirements of BOC tracking techniquesReceiver typeMultipliersIntegratorsLocal oscillatorsLow pass filtersSSB2×Carrier,41×Carrier,24×CodeMGD (K=4)2×Carrier,1×Code1818×CodeBJ2×Carrier,8×Code5.4.71×Carrier,01×Code81×Carrier,01×CodeComparison of BOC tracking schemesThe BJ algorithm has been implemented on the Septentrio GETR [De Wilde et al2004].
This receiver was built under contract from ESA to demodulate and evaluatenew Galileo signals. Analysis contained in this chapter shows that although the use ofa peak detection algorithm (bump-jumping) seems a logical engineering approach tosolving BOC tracking ambiguity it is sensitive to noise, signal distortion andmultipath. Therefore, the use of the BJ algorithm is not recommended for highintegrity or safety of life applications.The BJ jumping algorithm provides the receiver designer with a similar trade-off tothe bumpy MGD discriminator, delivering apparent unambiguous BOC tracking withlittle or no sensitivity loss at the cost of acquisition and slip correction time.
The SSB118Receiver theorytechnique provides the best acquisition and slip correction performance at the cost ofa loss in tracking sensitivity. In Chapter 6 we describe a novel technique developedduring this research which is believe to solve the problem of BOC tracking ambiguity.This technique removes the ambiguity in BOC tracking with no tracking sensitivityloss and with no degradation of acquisition or slip correction time.In this chapter we have detailed the current approaches given in the literature for PSKand BOC signals. A comparison of three leading BOC tracking techniques was givenbased on their tracking sensitivity, acquisition time and receiver hardware impact. Adesign trade off has been identified between high precision receivers using the BJalgorithm or bumpy MGD technique and the rapid reliable acquisition of the SSB orsmooth MGD techniques.1196BOC tracking with double estimation receiverThis chapter discusses the implementation and benefits of BOC tracking using thedouble estimator (DE).
This technique was conceived during the course of thisresearch and a patent has recently been filed for protection of the inventors, Dr MSHodgart and PD Blunt. Coherent and incoherent implementations are given alongwith an extension to apply the DE technique to AltBOC signals. Details of oursimulations of the DE technique are given including analysis of noise inducedtracking jitter, acquisition and slip correction times and multipath analysis.Comparison is given to the BOC tracking schemes described in Chapter 5.4 and therelative benefits detailed.6.1The coherent BOC double estimatorOnce again we model the received BOC signal (neglecting additive noise and otherinterfering GNSS signals) as follows.u BOC (t ) = A × cos(ω0t + φ ) × a (t − τ ) × s (t − τ ) × d6-1A is amplitude, cos(ω 0 t + φ) represents the carrier signal after down conversion to anintermediate frequency (IF) ω0 and phase φ, s (t − τ ) is the sub-carrier modulation inthe received signal comprising the sub-carrier modulation function s (t ) at delay τ,a(t − τ ) is the code modulation in the received signal comprising the code modulationa (t ) at delay τ and d ∈ (−1,+1) is a polarity.This technique depends essentially on the fact that sub-carrier is half-periodic over arelatively short sub-chip width TS and that Equation 6-1 is mathematically identical to()u (t ) = A × cos(ω0 t + φ) × s t − τ* × a (t − τ ) × d *6-2120BOC tracking with double estimation receiverwhereτ* = τ + nTS6-3is a multi-valued offset delay which has a number of values each offset from the delayτ by a different integer shift n times the sub-chip width TS .
The equivalent polarityd * = d for even number of shifts and d * = − d for an odd integer shift. It should beunderstood that the actual sub-carrier delay and the code delay for any received signalare still the same τ. The receiver must always estimate this actual non-ambiguousdelay τ in the code function a( ). It is however only necessary for the receiver to seek*to estimate the ambiguous τ in the sub-carrier function s( ) and achieve the same*result as if it were estimating the actual delay τ. Accordingly, the offset delay τ anddelay τ are treated as independent quantities, without regard to Equation 6-3, andtwo independent estimates may be generated.
Only in a final correction stage is it*admitted that an estimate of offset delay τ and delay τ are related as in Equation 6-3,and the value of estimate τ^ used to remove the ambiguities in the value of estimate τ^*.In a BOC transmission the sub-carrier is necessarily locked to the code sequence.Indeed it is usually seen as part of the code sequence. The time delay τ mustobviously be the same in both the code and the sub-carrier. However, there is nothingto stop us multiplying by component multiplicative structures with independent timedelay estimates. The DE technique is a three-loop receiver.
The innermost delaylocked loop (DLL) tracks the code phase of the received signal. The middle subcarrier locked loop (SLL) tracks the sub-carrier phase of the received signal. Thethird loop tracks the carrier frequency and / or phase of the received signal. Thegeneral schematic of the coherent DE receiver is shown in Figure 6-1.121BOC tracking with double estimation receiverwIII∫••wIQI∫^^cos(ω0t + φ (t))uBOC(t)•^s(t − τ *)~^sin(ω0t + φ (t))••PROCESSINGa(t − τ )~^s(t − τ *)CarrierSIGNAL^a(t − τ )sub-CarrierCode∫∫wIIQwQIIeτeτ∗eφFigure 6-1, General schematic of a coherent DE BOC receiverThe DE BOC receiver requires three local oscillators, which generate continuouscarrier, sub-carrier and code waveforms respectively. The carrier oscillator generates()()in-phase replica carrier cos ω0t + φˆ and an orthogonal replica carrier sin ω0t + φˆ ,where φˆ is the estimate of the received carrier phase φ .
The sub-carrier oscillator()generates in-phase replica sub-carrier s t − τˆ* and an orthogonal replica carrier()~s t − τˆ* , where τˆ* is the SLL estimate of the time delay τ . The code oscillatorgenerates in-phase replica code a(t − τˆ ) and an orthogonal replica code a~(t − τˆ ) ,where τˆ is the DLL estimate of the time delay τ .We define an orthogonal sub-carrier as the difference between early and late timeshifts of the sub-carrier, which can be written as follows.~s t − τˆ* = s t − τˆ* + TDS − s t − τˆ* − TDS 2 2 ()6-4TDS is the total separation between ‘early’ and ‘late’ sub-carrier waveforms, boundedby 0 < TDS ≤ TS .122BOC tracking with double estimation receiverAfter mixing and integration over time T the resulting correlations can be written asfollows.TwIII =() (1u BOC (t ) × cos ω0t + φˆ × s t − τˆ* × a (t − τˆ )dt∫T0()6-5) ( )(t ) × cos(ω t + φˆ )× s (t − τˆ )× a~(t − τˆ )dt≈ A × cos φ − φˆ × trc τˆ* − τ × Λ(τˆ − τ ) × dTwIIQ =1u BOCT ∫0*0(wIQI) ( )( ) ( )≈ A × cos(φ − φˆ )× Trs (τˆ − τ )× Λ (τˆ − τ ) × d1= ∫ u (t ) × sin (ω t + φˆ )× s (t − τˆ )× a (t − τˆ )dtT≈ A × sin (φ − φˆ )× trc(τˆ − τ )× Λ(τˆ − τ ) × d≈ A × cos φ − φˆ × trc τˆ* − τ × VΛ (τˆ − τ ) × dT1= ∫ u BOC (t ) × cos ω0t + φˆ × ~s t − τˆ* × a (t − τˆ )dtT0*TwQII*0BOC0*The single peaked Λ( ) function and the tracking VΛ( ) function are the same asdefined for the PSK GNSS receiver in Equation 5-8 and Equation 5-18 respectively.()The trc( ) function is a continuous triangular cosine waveform where trc τˆ* − τ → ±1as τˆ* → τ + n × TS .
The Trs( ) function is a continuous trapezium shaped sine()waveform where Trs τˆ* − τ → 0 as τˆ* → τ + n × TS , shown in Figure 6-2. The Trs( )function is identical to the result of early minus late correlations of the trc( ) functionas follows.T T Trs τˆ* − τ = trcτˆ* − τ − DS − trcτˆ* − τ + DS 2 2 ()6-6123BOC tracking with double estimation receiver^Trs(τ* - τ )+1^τ* - τ−TS−2TSTS2TSTDSFigure 6-2, Trapezoidal sine functionThe easiest way to visualise the effect of realising independent sub-carrier and codedelay estimates in the DE BOC correlations is assume perfect carrier demodulation,φ = φˆ . Figure 6-3, Figure 6-4 and Figure 6-5 show the wIII, wIIQ and wIQI correlationsrespectively against code error, τˆ − τ and sub-carrier error τˆ* − τ assuming φ = φˆ .These plots are derived from Mathcad simulations of a BOC(2×fC, fC) signal andprovide a graphical perspective to the correlations given in Equation 6-5.1100-1-2-14-1-2-10*1τˆ − τ (sub-chips)2200τˆ* − τ (sub-chips)-212-4τˆ − τ (sub-chips)Figure 6-3, wIII correlation with independent sub-carrier and code delay estimates124BOC tracking with double estimation receiver1.510.5164202460.5011.5-1-54τˆ − τ (sub-chips)200τˆ − τ (sub-chips)-25τˆ* − τ (sub-chips)-4Figure 6-4, wIIQ correlation with independent sub-carrier and code delay estimates TDC = TC1100-1-2-14-1200-2-10*1τˆ − τ (sub-chips)2τˆ* − τ (sub-chips)-212-4τˆ − τ (sub-chips)Figure 6-5, wIQI correlation with independent sub-carrier and code delay estimates TDS = TSA number of discriminators used to remove the amplitude dependence requiregeneration of signals individually multiplied by early and late replica code sequences.Equivalent early and late code correlations may be generated as125BOC tracking with double estimation receiverwIIEwIILT1T = ∫ u BOC (t ) × cos ω0t + φˆ × s t − τˆ* × a t − τˆ ± DC dt2 T0() ()6-7T ≈ A × cos φ − φˆ × trc τˆ* − τ × Λτˆ − τ m DC × d2 () ()where the equivalent early minus late correlation iswIIQ = wIIE − wIIL6-8In order to achieve convergence of the DE triple loop system three error signals mustbe generated from the correlations in Equation 6-5.
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