On Generalized Signal Waveforms for Satellite Navigation (797942), страница 60
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In fact, while Interplex uses exclusively additivemethods to multiplex the signals, CASM employs a combination of angle modulation andadditive methods. In the end, both of these techniques require the addition of an InterModulation (IM) component that is necessary to maintain constant carrier magnitude[A.
R. Pratt and J. I. R. Owen, 2007]. It is therefore important to keep in mind that while inthe next pages we will refer indistinctly to CASM and Interplex since they are very similarfrom the mathematical point of view, they are realized and implemented in two very differentways, with two associated patents. In fact, CASM is described in [P.A. Dafesh, 2002], whileInterplex was presented later by [G.L. Cangiani, 2005].
The slight differences between bothimplementations are also reflected in the performance during the amplification, where CASMis more subject to non desired effects.CASM and Interplex are constant envelope modulations with added sub-carriers that do notdistort the existing ones when the composite signal is passed through a high-power amplifieroperating close to saturation. Moreover, they provide additional control on the power and thespectral separation of the different quadrature multiplexed signals through the use of differentsub-carrier frequencies, a particular sub-carrier code rate and a sub-carrier modulation index.As we have emphasized in the previous chapters, this is especially interesting when a highnumber of signals must be transmitted on the same band.
In addition, the modulation oforthogonal pairs of sub-carrier signals on the I and Q phases is also possible with reduceddistortion and losses.The CASM and Interplex implementations provide a means to multiplex all the signals that isequivalent to the spatially combined transmitter implementation that we described in chapter7.3, where the Linear Modulation was described. In fact, CASM and Interplex have onlyslightly higher modulation losses than the Linear Modulation, but can work in saturationachieving thus in the end a superior efficiency for the same total required power. It is alsoimportant to keep in mind that although using a separate aperture would in principle provide273Signal Multiplex Techniques for GNSSthe cleanest transmission of all the signals, the simplification in the modulator design thatusing an unique constant envelope allows is more than offset by the impact on the satellite ofadding an independent antenna and amplifier.Finally, it is interesting to note that as stated in the CASM patent [P.A.
Dafesh, 2002] theInter-Modulation (IM) signals could be used as additional ranging or communication signals,transmitting thus additional information to that of the data channels. This is indeed the pointwhere some people make another difference between CASM and Interplex. According to this,CASM would use the Inter-Modulation signals as another useful signal to transmit, while theInterplex implementation would allocate such a low power on this component that can be seenas lost power. Finally it is important to underline that the patent of [G.L.
Cangiani, 2005]incorporates CASM but it is actually directed to a multi-beam/multi-antenna invention.7.7.2 CASM, InterplexHexaphaseandModifiedTri-CodeCASM and Interplex can be seen as particular cases of the QPSM modulation or as anevolution of the conventional constant-envelope sub-carrier modulation that we saw inchapter 7.7. It is important to stress again that while Interplex uses exclusively additivemethods to multiplex the signals, CASM employs a combination of angle modulation andadditive methods.
Moreover, CASM can utilize the cross-product inter-modulation (IM) termsas an additional useful signal. These terms can be considered as new ranging communicationsignals in some applications and not only as noise in the most general case. Nevertheless, forour navigation applications these terms will not be desired.This modulation is extremely flexible and efficient, offering additionally the possibility toprovide modes of operation with civilian and military signals together. This makes theapproach of great interest.
In addition, CASM and Interplex provide high efficiency withvalues greater than 90 % and inherent flexibility to fine tune the modulation architecturemaintaining an ability to provide backward compatibility with current signals[G.L. Cangiani, 2005]. Also of great interest is that they may be generated using both squarewave and sine-wave sub-carriers although employing square-wave signals is normallypreferred.As shown in [A.R. Pratt and J.I.R.
Owen, 2005] and [G.L. Cangiani, 2005], the CASM andInterplex techniques are able to support altogether more complex solutions than any of thetechniques studied so far. In fact, if we work with equation (7.71) derived above for thegeneral QPSM case, and assume that there is a single sub-carrier, the expression can berewritten as follows:s (t ) = I 0 (t ) cos[2π f c t + m sc (t )ϕ s (t )] − Q0 (t )sin[2π f c t + m sc (t )ϕ s (t )](7.77)274Signal Multiplex Techniques for GNSSwhere m is the modulation index of the multiplex, sc (t ) the modulating signal and ϕ s (t ) theperiodic sub-carrier.
This expression can be further developed as follows:⎧ I 0 (t ) cos(2πf c t ) cos[m sc (t )ϕ s (t )] − I 0 (t )sin[m sc (t )ϕ s (t )]sin (2πf c t )s (t ) = ⎨⎩− Q0 (t )sin (2πf ct ) cos[m sc (t )ϕ s (t )] − Q0 (t )sin[m sc (t )ϕ s (t )]cos(2πf c t )(7.78)⎧{I 0 (t ) cos[m sc (t )ϕ s (t )] − Q0 (t )sin[m sc (t )ϕ s (t )] }cos(2πf ct )s (t ) = ⎨⎩− {I 0 (t )sin[m sc (t )ϕ s (t )] + Q0 (t ) cos[m sc (t )ϕ s (t )] }sin (2πf c t )(7.79)yielding:This can also be expressed in a simplified form as follows:s (t ) = I (t )cos(2 π f c t ) − Q(t )sin (2 π f c t )withI (t ) = I 0 (t )cos[m sc (t )ϕ s (t )] − Q0 (t )sin[m sc (t )ϕ s (t )]Q(t ) = I 0 (t )sin[m sc (t )ϕ s (t )] + Q0 (t )cos[m sc (t )ϕ s (t )](7.80)(7.81)where the in-phase and quadrature components have been isolated. Moreover, if we carefullylook at the equation above, we can recognize that the envelope is constant, as it could not bedifferent since the single sub-carrier case is a particular case of the general QPSM modulationwhere we have shown that this is true.In navigation the in-phase I0 and quadrature Q0 signals are modulated with data andpseudorandom codes as we saw in chapter 4.
The signal modulated with data and code iscalled data channel while the other one has only code and is thus known as data-less or pilotchannel. According to this, we have:I 0 (t ) = 2 PI d I (t )cI (t )Q0 (t ) = 2 PQ d Q (t )cQ (t )(7.82)In addition, the sub-carrier modulating signal s c (t ) can be considered to contain data ds(t) andspreading code cs(t). Moreover, this signal is further modulated by the so-called data and codepartitioning functions αd(t) and βc(t) correspondingly [A.R. Pratt and J.I.R. Owen, 2005],depending on whether the term modulates the data or the code.
We can write thus:sc (t ) = [d s (t )α d (t )][cs (t )β c (t )](7.83)These two partitioning functions are of great importance since they control the type of QPSMmodulation that we will have, as shown in [P.A. Dafesh, 1999 and P.A. Dafesh, 1999b]. If weassume, a square-wave sub-carrier we have then:ϕ s (t ) = sign[sin (2πf st )](7.84)where we have to note that the square-wave works with a frequency fs. In addition, if thesignal sc(t) is binary, we can simplify for this particular case as follows:275Signal Multiplex Techniques for GNSScos[m sc (t )ϕ s (t )] = cos(m )(7.85)sin[m sc (t )ϕ s (t )] = sin (m )sc (t )sign[sin (2πf s t )]If we substitute now in (7.80) we have then:[]⎧ 2 PI cos(m ) d I (t )cI (t ) − 2 PQ sin (m ) dQS (t )cQS (t )sign[sin (2πf s t )] cos(2πf ct )⎪s (t ) = ⎨⎪⎩− 2 PQ cos(m ) dQ (t )cQ (t ) − 2 PI sin (m ) d IS (t )cIS (t ) sign[sin (2πf st )] sin (2πf ct )(7.86)whered IS (t ) = d I (t ) d S (t )α d (t )[]d QS (t ) = d Q (t ) d S (t )α d (t )(7.87)cIS (t ) = cI (t ) cS (t ) β c (t )cQS (t ) = cQ (t ) cS (t ) β c (t )As we have already commented above, depending on the values that the functions α d (t ) andβ c (t ) adopt, we will have the different QPSM options identified by[A.R.
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