On Generalized Signal Waveforms for Satellite Navigation (797942), страница 54
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Pratt and J.I.R. Owen, 2005],alternative multiplexing methods to those discussed in this chapter could be used. In fact,separate antenna and amplifier chains (that is separate aperture) which allow for signalcombination in the far field of the satellite antenna system could be employed.
In addition,different signals could be multiplexed on the carrier frequency on several different antennabeams as suggested in [G.L. Cangiani, 2005]. Nevertheless, the extra complexity that thespacecraft payload would have to deal with would be of consideration and the antenna designwould suffer from poor efficiency and important cost and weight drawbacks. Moreover, themore challenging problem of transmitting these signals would be the development of ageneral modulation approach with a single modulator, up-converter, power amplifier chainand antenna aperture [P.A.
Dafesh et al., 2006].7.2 Multiplexing SchemesThe first multiplexing technique used in navigation (GPS) was employed to send theC/A Code and the P(Y) Code providing two bi-phase signals on the same carrier frequency inphase quadrature (QPSK). Demultiplexing was relatively simple. However, the need to havemore navigation signals has made this multiplexing scheme obsolete for future modernizedimplementations. In fact, the possible solution of adding another signal slightly offset infrequency would give rise to a non-constant envelope with the consequent distortion afterpassing through the High Power Amplifier (HPA).
The following multiplexing techniques248Signal Multiplex Techniques for GNSSwill be studied in the next pages:•••••Linear Modulation (Spatial Combining)o Tri-code Hexaphase ModulationMajority signal votingHard LimitingQuadrature Product Sub-carrier Modulation (QPSM)o Interplex and CASMo Modified Interplex ModulationIntervotingIn spite of the important advances realized in the past years, the research field on signalmultiplex is still subject to active studies as shown in [T. Fan et al, 2005]. Out of all themultiplex techniques presented above, the Linear Modulation and the Tri-code HexaphaseModulation have maximum efficiencies limited to roughly seventy-one percent[P.A.
Dafesh et al., 2006], what is an important disadvantage. Moreover, they are limited tomultiplexing only binary signals. The rest of multiplex techniques offer a superiorperformance as we will see in next chapters. The efficiency is defined as the sum of theeffective transmitted power Puseful plus any band limiting losses, divided by the totaltransmitted power Ptotal .Pη = useful(7.1)PtotalWe describe next all the techniques in detail.7.3Linear Modulation (Spatial Combining)The Linear Modulation, also known as additive or spatial modulation, basically consists in theaddition of a new ranging signal to either the I or Q phases of a carrier where already at leastother two signals are present.
A well documented case in navigation is that of the GPS IIRModernization or GPS IIR-M [P.A. Dafesh et al., 1999a] and [P.A. Dafesh et al., 2000]. Infact, GPS investigated at some point during its modernization the possibility of adding theM-Code in phase with the C/A Code or the P(Y) Code using this technique as shown by[J. W. Betz, 1999] and [S. H. Raghavan et al., 1997].Let as suppose that we want to linearly add a new binary signal s N (t ) to a basebandwaveform modulated with other two binary signals s OI (t ) and s OQ (t ) , where the subindex Nrefers to the new signal, O indicates the old signals that were already on the carrier inquadrature (QPSK) and I and Q are the respective phase.
The In-phase and Quadraturecomponents of the new multiplexed signal may be represented bys (t ) = I (t ) cos(2 π f c t ) − Q(t )sin (2 π f c t )(7.2)249Signal Multiplex Techniques for GNSSwhere the In-phase and quadrature components of the carrier, that is I (t ) and Q(t ) , aredefined as follows:and,I (t ) = 2 POI s OI (t ) + 2 PN s N (t )(7.3)Q(t ) = 2 POQ sOQ (t )(7.4)As we can recognize, the new signal has been added in-phase without loss of generality. If wedefine now the total power of the signal asPT = POI + POQ + PN(7.5)it can be shown that the envelope of the composite signal will adopt the following form:A(t ) = 2 PT + 4 POI PN sOI (t )s N (t )(7.6)which is not constant due to the presence of a time-varying component in addition to theconstant 2 PT . This is in principle negative because the result is AM-to-AM and AM-to-PMdistortions when the signal is filtered through a nonlinear High Power Amplifier (HPA)unless we work in the linear region, far away from saturation.
If this were the case, theoperating point of the amplifier would be backed off from its saturation point to the linearregion of the amplifier, making in principle this multiplexing approach a suitable alternative.However, such a back-off is not of interest most of the times due to the high powerinefficiency that results. Indeed, as early GPS modernization studies have clearly shown, theback-off functioning of an amplifier working in the linear region can result in several dB ofpower losses. We will show this in the next section with a particular example of the LinearModulation, namely the Tri-code Hexaphase Modulation.Last but not the least, it is important to mention that a Linear modulation is equivalent tospatially combining the signals to multiplex, where a separate amplifier chain and antennaaperture are used to modulate the existing signals and the new signals.
This so-called separateaperture implementation results in a significant loss of overall power efficiency since asecond power amplifier would be required for the new signals to be modulated.7.3.1Tri-code Hexaphase ModulationThe tri-code Hexaphase modulation is a particular implementation of the Linear Modulationdescribed above. Let us assume as an example that the GPS M-Code and P(Y) Code wouldhave the same power level, being this half of that of the C/A Code. [P.A. Dafesh et al., 2000]have shown that as a result of applying the Linear Modulation, the envelope of themultiplexed signal would not be constant. This is shown in the following figure, where theconstellation diagram is depicted.250Signal Multiplex Techniques for GNSSFigure 7.1. Constellation diagram for the Linear ModulationAs we can clearly see, the plot presents two distinct amplitudes since the constellation pointslie on two different constant circles. This results in an hexaphase modulation as the name wellindicates.
In this particular example, the new M-Code was added to the P(Y) Code in-phase(vertical axis in the figure) following the mathematical scheme of (7.3).Let us assume now a GPS transmission bandwidth of 30.69 MHz. This results in a filteringloss of approximately 0.03 dB for the C/A Code, 0.31 dB for the P(Y) Code and 0.80 dB forthe M-Code. If we further assume same transmission powers as [P.A. Dafesh et al., 2000], thepower efficiency of the linear modulation applied to GPS would adopt a value ofapproximately 93.23 %.
This is indeed very close to the figure of the 92.80 % derived by[P.A. Dafesh et al., 2000] under similar assumptions.Table 7.1. Power Efficiency of Linear ModulationSignal andCarrier PhasePercentage of Power beforefiltering and combiningFilteringLoss (dB)Transmitted Powerafter filtering (dBW)C/A (Q)46.88 %-0.03-155P(Y) Code (I)25.06 %-0.31-158M-Code (I)28.06 %-0.80-158Total100 %-151.6This means a 0.30 dB power loss in the total signal power due to filtering and the Linearmodulation.
Although this might seem a good number in principle, the fact is that the overallpower efficiency is in reality significantly reduced due to the amplifier back-off operation(unless we employ a separate power amplifier and work with a separate aperture) required toamplify the linearly modulated signals without causing AM-AM or AM-PM distortions. Infact, the 93.23 % power efficiency obtained in the previous analysis does not include themodulator inefficiency that amplifiers present in real world.251Signal Multiplex Techniques for GNSSIn order to avoid the disadvantages of this modulation, constant envelope solutions have beenproposed to at least reduce the degradation effects that result from the High Power Amplifieras shown in the patent of [P.A. Dafesh et al., 2006]. We describe them in following chapters.7.4Majority Signal Voting7.4.1History of Majority VotingThe majority combining technique dates back to those days when communication engineersrelied on increased power levels and redundancy to improve the reliability of acommunication link.
The basic form of redundancy consisted in transmitting each datasymbol an odd number of times, demodulating each symbol individually and deciding infavour of the symbol value that occurred more frequently [R. S. Orr and B. Veytsman, 2002].In fact, this is the simplest implementation of the majority vote multiplex as we will discuss inthe next chapters. It is important to note however that while the majority voting that we willdescribe in the following chapters is realized at the transmitter, the combination that wereferred to in the previous lines is carried out at the receiver.The type of redundancy that we have mentioned has long been introduced in most of thedigital circuits today. As a good example of it the Triple Modular Redundancy (TMR) is astandard design practice in systems where stringent availability and tolerance are required.Other systems with even higher requirements such as manned space missions use accordinglya higher level of redundancy.As shown by [R.
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