Статья Optimal aligning of the sums of GNSS navigation signals (1141994)
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working papersPhoto courtesy of NASAOptimal Aligning of the Sumsof GNSS Navigation SignalsTwo or more modernized GNSS signals transmitted on the same carrier produce varying amplitudes thatreduce the power amplifier efficiency and results in the need for aligning the group signal amplitude.In this column, two Russian signals experts introduce a new symmetrized signals class that enablessignificant reductions in the loss factor created during this amplitude alignment compared to existingmethods. The authors also propose optimal combinations of three and four signals when exploitingmultiple GNSS systems and offer a design for GLONASS L3 and L5 signals based on this analysis.Vladimir Kharisov VNIIR ProgressAlexander Povalyaev Russian Space SystemsThe theory of optimal alignment ofGNSS navigation signals is evolving.
While current GNSS effortsassume signals to be on only onecarrier frequency, varying amplitudesof more than two signals can greatlyreduce system efficiency. Alignmentof these amplitudes can reduce systemlosses provided that the best signal combination is chosen. This column reviewsapplicable alignment methods and proposes a new methodology for selectingthe optimal signal combination.GNSS current development assumesthe broadcasting of a set of binary navigation signals on one carrier frequency.The sum of two or more signals hasvarying amplitude that reduces thepower amplifier efficiency. This effectresults in the need for aligning the groupsignal amplitude.56 InsideGNSS This article presents the comparison of optimal aligning with otherwell-known alignment methods (suchas alternate binary offset carrier —AltBOC — or interplex modulation) andincludes an overview of signal alignmentmethods.
The discussion will introducea new symmetrized signals class, ensuring significant reductions in the aligningloss factor, is introduced. For instance,use of interplex modulation for threeequipollent binary phase signals resultsin 25 percent power loss, while optimalaligning with symmetrization providesfor only 12.7 percent loss. The use ofoptimal aligning for four signals yieldsa loss of 14.64 percent.The article also describes our methodology for choosing the best signalcombination. As an example, optimalcombinations of three and four signalsj a nu a ry/ febru a ry 2012were discovered. Further, it also proposes design for GLONASS L3 and L5signals based on summarizing the AltBOC signal.IntroductionThe navigation signals emitted by thefirst generation of GLONASS and GPSsatellites were binary signals located ontwo carrier wave quadratures.
One ofthese quadratures was allocated for theopen access signals, Soa(t), and anotherone for the authorized access signals,Saa(t):where θi(t) = ±1,are the binarycode sequences. Meanwhile, if we havearbitrary binary signals, θ1(t) and θ2(t),the amplitude of the composite signal iskept constant:www.insidegnss.comand only the phase of the composite signal changes.This is a particularly important property for the efficientoperation of the power output satellite-signal amplifier.
Efficiency of this amplifier in linear mode, which is necessary forsignal amplification with variable amplitude, suddenly decreases in comparison with the saturation mode where signal amplification with a constant amplitude is possible.In further GNSS development, the necessity of structuralenhancement of the signals transmitted on the same carrierarose. New and more effective modulation types were created.Use of signal division for open- and authorized-access transmissions on pilot and data components was suggested to provideincreased interference immunity of the user equipment (UE).For the purpose of maintaining the operability of earlier UEmodels (“backwards compatibility”), the emission of “legacy”signals must be continued invariably for a long time. This allrequires the emission of more than two binary signals on onecarrier frequency.However, the sum of more than two independent binarycomposite signals has a variable amplitude.
The different meansof alignment of the amplitude leads to different energy lossesand introduces the possibility of mutual interference betweenthe components of the composite signal. Hence, the need aroseto find optimal methods for the sum alignment of binary complex signals. The first task is providing minimum energy losses.The second task is researching the value of possible mutualinterferences and possible power redistribution between thecomponent signals of the sum.An obvious solution to sum alignment task for new signalsconsists of the application of their time-division multiplex.Such decisions are already applied in the current GLONASSsystem and GPS L2C signals. In this case, energy losses onalignment equal zero.
However, the time-division multiplexhas a number of essential faults. Time-division multiplex cannot be applied for augmentation of the legacy signals’ structure,and we cannot augment the signals generated on the basis oftime-division multiplex in the future. For this reason, in thiswork we consider the alignment methods of binary compositesignals other than time-division multiplex.Review of Current Alignment MethodsIn the literature we can find the following methods appliedfor signal alignment in different initial conditions: interplexmodulation and AltBOC modulation (For full citations, seethe Additional Resources section near the end of this article):Interplex modulation was proposed by U. T.
Butman for thealignment task solution when the third noncorrelated binarysignal θ3(t) is added to the two previously noncorrelated binarysignals θ1(t), θ2(t) located on different quadratures of the carrier. This third signal sums with the signal located on one ofthe quadratures and, as a result, forms the composite signalSΣ(t). For SΣ(t) alignment, the leveling signal, e(t), is added intoanother quadrature:www.insidegnss.com Here,is the power of the ith component in thecomposite signal.The algorithm for generating the leveling signal, e(t), can besynthesized from the constant condition of amplitude, Sout(t),or, what is the same, from the instantaneous power, |Sout(t)|2.Taking into account that θi(t) takes only the value ±1, we obtain:From Equation (4) the constant condition |Sout(t)|2 can beinferred:Then we find the formula for the leveling signal, e(t):The interplex method α1 = α2 = α3 = 1 for is illustrated withthe fourth part of the vector diagram, shown in Figure 1, whereθ1(t) = θ2(t) and θ3(t) = ±1.
The remaining three parts of the diagram are situated symmetrically. In Figure 1, thick lines showthe sum vector, SΣ(t), for the cases when θ3(t) = ±1. The dottedlines identify the vectors of the leveling signal e(t), also for thecases when θ3(t)=±1. The amplitude of the alignment sum Sout(t),equals two and the directions along axis I and Q take equalparts of time. This fact proves that signal amplitudes at theoutputs of navigation receiver correlators under the action ofsum alignment, Sout(t), will be equal to its input.Based on the noncorrelation of mutual signals, θi(t),we can easily prove noncorrelation of e(t) with any of θi(t),, signals.
For example, for θi(t) we obtain:where the line at the top represents the time integration onthe computing interval of correlation integrals in the receivercorrelator. The noncorrelated quality of the signals, θi(t),FIGURE 1 Summary signal SΣ(t) vectors alignment by interplex modulationfor the case 01=02=1. 03= _|_ 1j a nu a ry/ febru a ry 2012InsideGNSS57working paperswith each other and their noncorrelation with the levelingsignal, e(t), supports the absence of mutual interferences andinterferences that occur due to the input of the leveling signal.The power of the leveling signal, e(t), defines the lossesrelated to alignment. The power is equal to Pe = (α1α3/α2)2. Forthe quantitative characteristic we use the loss coefficient onalignment (LCA), η, which is equal to the power ratio of theleveling signal to the power of the equalized signal.We can easily show that the LCA does not dependon absolute values of α i , but only on relative values,.
For this purpose we should divide thenumerator and the denominator in (8) bythat reduces to (9):Equation (9) for LCA allows us to optimize the compositesignal, SΣ(t), for alignment. Actually, η monotonously reduceswith augmentation, μ2, which identifies the fractional power ofthe signal coincident on the quadrature with the leveling signal,e(t).
Hence, under the given power of the component signals,the signal with the maximum, should be theunique one on its quadrature in the composite signal SΣ(t), i.e.,where k ≠ m ≠ i. The LCA of such a signal isNormalization of μi coefficients in (9) allows us to presentthem as the points on the unit sphere by means of the angles,which assign the latitude B and longitude L.at,.
This allows us to present dependence LCA from αi (8) via B and L. This relationship in the formof level lines is shown in Figure 2.We can specify three fields. In each field one of, αk,is maximal. The maximum value of LCA, η=0.25 at alignmentwith the method of interplex modulation will be at the powerequality of the composite signals,(μ1=μ 2=μ 3),whenand L=π/4. Such a value of LCA cannot be considered acceptable because the power of the aligned and useful componentsignals is equal. That is why both GPS and Galileo systemschose component signals that are not equal in power. From(8) it follows that η=0.177 for GPS, and η=1/9 ≈0.1 for Galileo.This is less than η=0.25 under the condition of equal power.Hereafter, we will provide several options that reduce the losseson the alignment of equal-strength signals if we combine thesesignals on the same or nearby frequencies.AltBOC modulation was developed for the transfer of twoindependent pairs of orthogonal binary signals, located onclose carrier frequencies, via common antenna.
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