On Generalized Signal Waveforms for Satellite Navigation (797942), страница 63
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In the case of the IM component, the signal presents the spectrum of aBOC(10,10) modulation. In fact, as we have already seen, the Inter-Modulation signal isformed by multiplying the three signals we want to modulate. In this case, s1 (t ) is BPSK(1),s2 (t ) is BPSK(10) and s3 (t ) is BOC(10,5). Since the three signals are binary, the product ofthem will be a sine or cosine-phased BOC( f s , f c ) modulation with fs the highest offset carrierfrequency of the three and with code rate fc the highest of the three.
In this particular case thechipping rate of the P(Y) code and the offset carrier frequency of the M-Code.Moreover, as presented in [P.A. Dafesh et al., 2000], the GPS CASM modulation defines itsangle β 2 as follows:cos(β 2 ) =PQsin (β 2 ) =PIPP(7.129)being thus the only variable to play with the angle β 3 which is renamed as m in this particularcase. Consequently, in line with the derivations of chapter 7.7.2, the power of each particularsignal depends only on m:P1 (m ) = PQ cos 2 (m )P2 (m ) = PI cos 2 (m )(7.130)P3 (m ) = PQ sin 2 (m )PIM (m ) = PI sin 2 (m )so thatP = P1 + P2 + P3 + PIM = PI + PQ(7.131)As a conclusion, the CASM GPS signal can thus be expressed as follows:[]⎧ PI cos(m )s 2 (t ) + PQ sin (m ) s3 (t ) cos(2πf c t ) −⎫⎪⎪s(t ) = 2 ⎨⎬⎪⎩− PQ cos(m )s1 (t ) − PI sin (m ) s1 (t ) s 2 (t ) s3 (t ) sin (2πf c t )⎪⎭[](7.132)As we can see, the desired powers and relationships between the different signals, can be welladjusted by appropriately selecting the values of β 2 and m.
The corresponding diagram of themodulation constellation is shown in the following figure from [E. Rebeyrol et al., 2006].288Signal Multiplex Techniques for GNSSFigure 7.11. GPS CASM modulation constellationAs we can recognize from equation (7.132), the phase rotation of the sub-carrier signal ontothe carrier can be implemented in very different ways. Apart from implementations ofproprietary nature, two main realizations of the CASM modulation have been identified forGPS as identified in [P.A. Dafesh et al., 2000]:•The most straightforward approach is to process the sub-carrier signal in baseband.According to this, the new signal to add in the multiplexing produces a digital rotationof the phase of the carrier as shown in Figure 7.12 below:Figure 7.12. Flexible digital CASM modulator implementation [P.A. Dafesh et al., 2000]•An alternative implementation is to phase modulate the local oscillator as described in[P.A.
Dafesh, 1999b]. This approach is very similar to that followed on the SpaceGround Link Subsystem (SGLS. In this case we would only need an additional biphase modulator to modulate the cross-term. It must be noted that depending on thesub-carrier frequency of the new signal to multiplex one approach or the other will bemore appropriate.289Signal Multiplex Techniques for GNSSIn the previous lines a CASM implementation was applied to multiplex all the GPS baselinesignals except for the new GPS L1C.
However, the original CASM modulation method forGPS pursued the transmission of not only one military signal, but actually two. In fact, theCASM technique proposed by [P.A. Dafesh et al., 1999a] was applicable to the transmissionof Military Acquisition (MA) and Military Tracking (MT) signals in a flexible and efficientmanner. The high efficiency approach presented there for combined aperture, that is C/A,P(Y), MA and MT sent through the same upconverter amplifier chain and antenna, wasshown to be equivalent to that of the separate aperture, where MA and MT would betransmitted with a separate upconverter, amplifier and antenna from that of C/A and P(Y).One final point to discuss is the power efficiency of the resulting multiplex.
As an example,we show the case of the C/A Code, P(Y) Code and M-Code signals and assume that the InterModulation signal is 2 dB lower power than the M-Code and the P(Y) Code as also done in[P.A. Dafesh et al., 2000]. Furthermore, if we recall the filtering losses derived in Table 7.1,the power efficiency of CASM in GPS will be:Table 7.8. Power Efficiency of CASMSignal andCarrier PhasePercentage of Power beforefiltering and combiningFilteringLoss (dB)Transmitted Powerafter filtering (dBW)C/A (Q)39.96 %-0.03-156P(Y) Code (I)21.36 %-0.31-159M-Code (I)23.91 %-0.80-159IM (10,10) (Q)14.78 %-0.71-161Total100 %-152.0As we can see, the total transmitted power is approximately the same as that of the LinearModulation in chapter 7.3.1 (-151.6 dBW). However, here the result of applying CASM toGPS results in a final efficiency of approximately 79.45 %, or 0.99 dB loss in total power dueto the CASM Multiplexing and filtering of the IM signal when only the useful signals areconsidered.
That results in 0.69 dB higher losses than in the case of the Linear Modulation,which had 0.30 dB losses or 93.23 % power efficiency. The efficiency of the CASM approachcan be further improved if the Inter-Modulation signal is tracked reaching then a finalefficiency of approximately 92 %, or 0.36 dB losses. This means only 0.06 dB higher lossesthan in the case of the Linear Modulation.We can conclude that the CASM implementation of GPS presents slightly higher modulationlosses than the Linear Modulation in general. However, the overall power efficiency when allthe contributions are taken into account is significantly greater for CASM than for the LinearModulation since in this case it is not required that the amplifier works at back-off or that aseparate high power amplifier chain is used.290Signal Multiplex Techniques for GNSSIt is important to note that the conclusion from the example above results from a verysimplified approach as it is not possible to complete all the modulation at baseband and havejust one up-conversion to the transmission frequency.
As a result of distributed signalfiltering, in reality there are differences in the signal trajectory between the phase plane plots,what has a significant effect on the requirement for HPA back-off. Ideally, a desirable featurewould be that all transients lie along the unit circle.
However, this does not happen in realimplementations in any case.7.7.8Interplex Modulation for Galileo: BOC(1,1) +BOCcos(15,2.5)If we apply the Interplex Modulation to the Galileo signals baseline of 2004 as described inchapter 2.4.2, the general expression of the Power Spectral Density is shown to adopt thefollowing expression:( f ) = POS D GOS D ( f ) + POS P GOS P ( f ) + PPRS GPRS ( f ) + PIM GIM ( f )GsGalileoBB(7.133)where the power spectral densities of the OS and PRS signals were derived in chapter 4.3.2.Moreover, the IM signal will have the same spectrum as the PRS BOCcos(15,2.5) as shown by[E.
Rebeyrol et al., 2006] . It must be noted that these expressions are only valid for the caseof having BOC(1,1) as open signal, since as we have repeatedly mentioned in this chapter, thestandard Interplex equations are not valid when we consider the CBOC implementation ofMBOC, as this is not binary.As stated in [Galileo SIS ICD, 2008], the total power of the Galileo E1 signals should beequally divided between the in-phase and quadrature components. Furthermore, the power ofthe data and pilot channels should be equal.
Using (7.102), this leads to the followingrelationship:P1 = P cos 2 (β 2 )cos 2 (β 3 )⎫⎪⎬ ⇒ β 2 = −β3 = mP2 = P3 = P sin 2 (β 2 )cos 2 (β 3 ) = P cos 2 (β 2 )sin 2 (β 3 )⎪⎭(7.134)For the Galileo Interplex modulation with BOC(1,1) and BOCcos(15,2.5), that is the oldbaseline of 2004, the modulation index m adopts the value m = 0.1959π and the expressionof the transmitted signal is shown to be [E. Rebeyrol et al., 2006]:⎧⎪ [sin (m ) cos(m ) sBOC(1,1) (t ) − sin (m ) cos(m ) sBOC(1,1) (t )]cos(2πf ct ) +s (t ) = 2 PT ⎨22⎪⎩+ cos (m ) sBOCcos (15, 2.5 ) (t ) + sin (m ) sBOCcos (15, 2.5 ) (t ) sBOC(1,1) (t ) sBOC(1,1) (t ) sin (2πf ct )(7.135)where• P is the total power of the signal,[]291Signal Multiplex Techniques for GNSS•sBOCcos (15, 2.5 ) (t ) represents the cosine-phased BOCcos(15,2.5) signal waveform of the•Public Regulated Service (PRS),sBOC(1,1) (t ) is the BOC(1,1) modulation that was used for the data and pilot Open•Service in the baseline of 2004, andsBOCcos (15, 2.5 ) (t ) sBOC(1,1) (t ) sBOC(1,1) (t ) is the Inter-Modulation term that keeps the constantenvelope of the multiplexed signal.According to this:P1 = P cos 4 (m )P2 = P3 = P cos 2 (m )sin 2 (m )(7.136)PIM (m ) = P sin 4 (m )Equation (7.135) can be further simplified if we employ the general notation of equations(7.111) and (7.113) as shown next:π⎛⎞s(t ) = 2 P cos⎜ 2 π f c t − s1 (t ) + m s1 (t ) s 2 (t ) − m s1 (t ) s3 (t )⎟2⎝⎠(7.137)The resulting diagram of the modulation constellation is shown in the next figure:Figure 7.13.
Galileo Interplex phase constellation for the Galileo baseline of 2004[E. Rebeyrol et al., 2006]7.7.9Modified Interplex and Modified CASMAs a result of the changes proposed in [G.W. Hein et al., 2005], slight modifications had to bemade to the multiplex schemes presented above in order to be able to transmit the CBOCsignal for the Galileo E1 OS service. As we have seen in detail in chapter 4.6.4, the CBOCmodulation was selected due to its great multipath mitigation potential and spectralcompatibility with the rest of signals in the band, among other characteristics of interest. Thedata and pilot channels are in anti-phase and the difference or additive components are notbinary.
Indeed, CBOC in particular and CBCS in general, are formed by adding BOC(1,1)292Signal Multiplex Techniques for GNSSwith a new sub-carrier, sBOC(6,1)(t) for CBOC and sBCS(t) in general, of relative amplitude μ .This means that the Inter-Modulation component does not obey to the equations that we sawin the previous lines for Interplex and CASM. However, the Interplex and CASM analyticalexpressions can be easily modified to account for the new signal waveform. In fact, thecomposite multiplexed signal should present for CBOC the following form:[][]sE1 (t ) = α sE1OS (t ) − sE1OS (t ) cos(2 π f E1 t ) − β sE1PRS (t ) − γ sE1IM (t ) sin (2 π f E1 t )DP(7.138)being[]E1OSE1OSE1(t ) cDE1OS (t ) sBOCsE1OS (t ) = d OS(1,1) (t ) + μ sBOC (6,1) (t )D[]E1OSE1OSsE1OS (t ) = cPE1OS (t ) sBOC(1,1) (t ) − μ sBOC (6,1) (t )P(7.139)E1E1E1(t ) cPRS(t ) sPRS(t )sE1PRS (t ) = d PRSAs we can clearly recognize from the equations above, this modulation scheme is generallymore efficient.
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