Double estimator. A new receiver principle for tracking BOC signals (797924)
Текст из файла
Double EstimatorA New ReceiverPrinciple for TrackingBOC SignalsThe United States and Europe have selectedthe binary offset carrier (BOC) modulationfor navigation signals in the next-generationGNSS. However, BOC’s multi-peakedcorrelation function is beginning to berecognized as creating a problem that stillneeds to be definitively solved: false lockor the tracking of secondary rather than theprimary peak in the derived cross-correlationfunction. But now researchers have come upwith a radically different approach of twodimensional correlation, which combines twoindependent estimates of the input signal’stime delay to create a single joint estimatethat fully exploits the capabilities of BOCwithout running into problems of false lock.M.
Stephen Hodgart and Paul D. BluntUniversity of SurreyMartin UnwinSurrey Satellite Technology Ltd.Copyright iStockphoto.com/narvikkF26 InsideGNSS or the current civilian GPS C/A code transmission withwhich people are most familiar, each GNSS satellitetransmits an individual periodic code employing theprinciple of code division multiple access (CDMA). Thecode itself is modulated onto a carrier using a phase shift keyingor PSK(fC) technique where fC is a code rate. The aim of signalprocessing design, then, is to estimate the relative delay in eachincoming satellite signal, in order to compute the location ofthe receiver.Time and technology move on.
Based on a 2004 agreementbetween the European Union and the United States, the newEuropean Galileo and the up-graded American GPS will makesubstantial use of the different modulation called Binary OffsetCarrier (BOC).Essentially, BOC multiplies a subcarrier as well as a code,onto the carrier. Standard nomenclature is BOC(fS , fC) where fSis a subcarrier frequency and fC is a code rate. “Sine BOC” and“Cosine BOC” may be identified, depending on the phasing ofthe subcarrier to the code boundaries.
We adopt here nomenclature “BOCs” and “BOCc,” respectively.John Betz, of the MITRE Corporation, introduced the concept of BOC in 1999. Two papers by him, cited in the AdditionalResources section near the end of this article, discuss the BOCmodulation in greater detail.Figure 1 illustrates BOCs(2f, f) where a “square sine” havinga frequency twice the code rate is identified.
A chip width TC =1/fC and a sub-chip width TS= 1/(2fS) may be defined here.As a consequence of the subcarrier modulation, the spectrum of this new BOC signal is split into two sidebands locatedabove and below the nominal carrier frequency. Although theCDMA principle still applies, the BOC design now admits anelement of frequency division multiple access (FDMA).
Thismanifests itself in the multiple sharing of heritage PSK andBOC signals of different subcarrier rates, many of which aresharing the same carrier frequency. (A clear summary of alladopted modulations and processes is given in an article in thesp ring 2008 8www.insidegnss.comSeptember/October 2007 issue of InsideGNSS, “The MBOC Modulation.”)BOC offers some advantages compared to PSK modulation as used by thepresent-generation GPS. However, a significant problem appears in its practicalreception, as attested by many engineering papers and recent practical tests. Seefor example the papers by P. D. Blunt etalia and A. Simsky et alia listed in Additional Resources.Essentially, the problem arises fromthe multi-peaked correlation functioncharacteristic of BOC and the potentialfor a receiver encountering “false lock”or “false node tracking” on a secondaryrather than the primary peak.
In thisarticle, we will present a new receiverprinciple that we believe overcomes thisproblem in a radical manner. Simulations and early practical tests have provided substantial corroboration that thenew solution works.We will explain here in much greater detail — and offer a more system-www.insidegnss.com Repeatsubcarrier modulationTSs(t–τ)delay τ× a(t–τ)Repeatcode modulationtBOC modulation=b(t–τ)TCRepeatcontinueperiod T PFIGURE 1Schematic construction of BOCs(2f, f) modulation where 2f = fS and f = fCatic development — than the succinctaccount published in the article by M.S.Hodgart and P.
D. Blunt cited in Additional Resources.BOC: A MathematicalDescriptionThe BOC input into any receiver can bedescribed mathematically as in Equation 1sp ring 2008where A is an amplitude, ω0 is an intermediate frequency, ϕ is a phase shifton the carrier (which is generally timevarying from Doppler shift), and b( )is the BOC modulation. Delay τ is thekey parameter measured by the receiver(and is also time varying).
Parameter d(-1, +1) denotes either data or an arbi-InsideGNSS27double estimatorinput code × subcarrierb(t–τ) = a(t–τ) × s(t–τ)1Treferenceb(t–τ)∫ ( )dttrue τ()subcarrier × input codeb(t–τ) = a(t–τ) × s(t–τ)BOCcorrelation(τ–τ)1Tenvelope Λ( )correlationreferences(t–τ*) × a(t–τ)double trial τ* and τtrial τFIGURE 3possiblefalse τ’Basic principle of a double estimatorf u nc t ion a ndfalse-node tracking, we shouldFIGURE 2 Standard cross correlation for BOCs(2f, f)note that negatrary sign value. In Equation 1, the timetive peaks are just as much a problem asdependence between phase ϕ and delaypositive ones.τ is left implicit.
The actual modulationmay be written as in Equation 2,VE-VL or “Bump Jumping”There is only one previously knownfix to the problem of BOC receptionwhich expresses explicitly the productthat preserves signal-to-noise optimalof the code a( ) with periodicity TP andity. It has been implemented in somesubcarrier s( ) with periodicity 2TS. Natpractical receiver designs and adoptsurally the time delay is the same in thea commonsense approach of so-calledtwo factors.“bump-jumping” (B-J).
The idea is thatThe presence of additive noise and ofadditional very-early (VE) and very-latemany other simultaneous transmissions(VL) gates monitor the amplitude of adjausing different codes is ignored in thiscent peaks in ( ). (See the Additionalsimplified representation, which alsoResources citation of the article by P.ignores secondary codes, the conceptFine and W. Wilson for a useful discusof “interplexing,” and “AltBOC” of thesion of this technique.) If a comparisonEuropean proposals.with amplitude on the prompt gate (P)The fundamental principle of theindicates a higher amplitude on eitherheritage PSK GNSS receiver systems isVE or VL, then a condition of false lockto cross-correlate each input signal withis judged to exist and the receiver musta matching reference code and then lookmake the appropriate jump of either +TSfor a peak in the resulting Λ-function byor –TS, hopefully in the direction of theeffectively varying a trial delay .correct peak.Applying the same principle of crossThis method is open to the objectioncorrelation on BOC, however, creates athat the receiver is essentially “blind.” Itstandard multi-peaked function ( )must be in a false lock condition beforeand the well-known difficulty created byit knows that it is in this condition.the secondary peaks onto which a corFurther, it can only move one sub-chiprelating receiver (using a discriminatorstep at a time, and evaluation of relativefrom early and late gates with feedbackamplitudes takes time.through a loop) may easily — but incorMore practical difficulties, whichrectly — lock.naive computer simulations will fail toFigure 2 is a schematic representationreplicate, are the effects of front-end filof the problem in the theoretical case oftering, multipath, and, above all, groupinfinite input receiver bandwidth, anddelay distortion from whatever cause.ignoring the matter of carrier demodAll of these effects tend to degrade theulation.
In addressing the correlationessential requirement that the amplitude28 InsideGNSS ∫ ( )dttwo dimensionalcorrelationχ(τ*–τ, τ–τ)sp ring 2008of the nearest secondary peaks shouldbe significantly less than the amplitudeof the main peak. Otherwise, in theunavoidable presence of additive noisecausing random fluctuations in the relative amplitudes of different peaks, a miscorrection is a real possibility.Actual failures of the VE-VL principle have been recorded with what issupposed to be the “easiest” variant,BOCs(1,1). Other more subtle difficulties may become manifest with higherrate ratios of BOC modulations.New ProposalOur proposed system does not generate the usual ( ) function, because itenvisages the multiplicative componentsin the correlating waveform as two independent entities.Figure 3 shows that, with our proposed approach, the reference cross-correlating function is still the product of amatching code function and a subcarrier, but now independent trial delaysand are assigned to the code and subcarrier components, respectively.The resulting correlation χ( ) is atwo-dimensional function of these twodifferent trial values.
In the dimension, a single peak (alternate positiveand negative) is centered on = . In thedimension, the multi-valued peaks(positive and negative) are located at= + nTS, where n is an integer.Figure 4 depicts the familiar ( )function alongside the new χ( ) function.The former is now seen as a one-dimensional cut across the latter in the specialcase where = . An infinite front-endbandwidth is assumed in these computer-generated plots.www.insidegnss.comstandard 1D(τ – τ)generalised 2D χ(τ* – τ, τ – τ)cross section�(0,τ – τ)τ – TCττ + TCττ* = ττ*Projection of the new correlation forBOCs(2f, f)FIGURE 5Old one-dimensional correlation generalizes to new two-dimensional correlation forBOCs(2f, f)FIGURE 4Figure 5 shows that in the dimen-sion for = 0 we are still looking at thefamiliar Λ-correlation associated withheritage PSK.
Its width is the same ±TC,as if only code modulation were present.However, in Figure 6 in the dimension for = 0, a continuous function ofperiodicity 2TS, now appears, as if onlya subcarrier modulation were present.These particular plots are for BOCs(2f, f).www.insidegnss.com It may be shown that BOCc(2f, f) has thesame general characteristic.2D Correlation Function?Acquisition in a receiver now has quitea different objective. There need only bea search for the nearest peak (positive ornegative) of the χ ( ) function, from whatever are the identical initial trial valuesto and .
Характеристики
Тип файла PDF
PDF-формат наиболее широко используется для просмотра любого типа файлов на любом устройстве. В него можно сохранить документ, таблицы, презентацию, текст, чертежи, вычисления, графики и всё остальное, что можно показать на экране любого устройства. Именно его лучше всего использовать для печати.
Например, если Вам нужно распечатать чертёж из автокада, Вы сохраните чертёж на флешку, но будет ли автокад в пункте печати? А если будет, то нужная версия с нужными библиотеками? Именно для этого и нужен формат PDF - в нём точно будет показано верно вне зависимости от того, в какой программе создали PDF-файл и есть ли нужная программа для его просмотра.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
