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fixing typos and removing latex cross-references 

git-svn-id: https://svn.code.sf.net/p/gnss-sdr/code/trunk@338 64b25241-fba3-4117-9849-534c7e92360d
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Carles Fernandez 2013-02-02 19:31:20 +00:00
parent 3061c721ef
commit 1510695863
1 changed files with 9 additions and 2 deletions
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docs/doxygen/other/signal_model.dox
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@ -80,7 +80,14 @@ s^{\text{(GPS L1)}}_{T}(t)=e_{L1I}(t) + j e_{L1Q}(t)~,
e_{L1I}(t) =& \sum_{l=-\infty}^{\infty} D_{\text{NAV}}\Big[ [l]_{204600}\Big] \oplus C_{\text{P(Y)}}\Big[ |l|_{L_{\text{P(Y)}}} \Big] p(t - lT_{c,\text{P(Y)}})~,\label{eq:L1CAI}\\
e_{L1Q}(t) =& \sum_{l=-\infty}^{\infty} D_{\text{NAV}}\Big[ [l]_{20460} \Big] \oplus C_{\text{C/A}} \Big[ |l|_{1023} \Big] p(t - lT_{c,\text{C/A}})~,\label{eq:L1CA}
\f}
where \f$\oplus\f$ is the exclusive-or operation (modulo-2 addition), \f$|l|_{L}\f$ means \f$l\f$ modulo \f$L\f$, \f$[l]_{L}\f$ means the integer part of \f$\frac{l}{L}\f$, \f$D_{\text{NAV}}\f$ is the GPS navigation message bit sequence, transmitted at \f$50\f$ bps, \f$T_{c,\text{P(Y)}}=\frac{1}{10.23}\f$ \f$\mu\f$s, \f$T_{c,\text{C/A}}=\frac{1}{1.023}\f$ \f$\mu\f$s, \f$L_{\text{P(Y)}}=6.1871 \cdot 10^{12}\f$, and \f$p(t)\f$ is a rectangular pulse of a chip-period duration centered at \f$t=0\f$ and filtered at the transmitter. According to the chip rate, the binary phase-shift keying modulations in (\ref{eq:L1CAI}) and (\ref{eq:L1CA}) are denoted as BPSK(10) and BPSK(1), respectively. The precision P codes (named Y codes whenever the anti-spoofing mode is activated, encrypting the code and thus denying non-U.S. military users) are sequences of \f$7\f$ days in length. Regarding the modernization plans for GPS, it is worthwhile to mention that there is a new civilian-use signal planned, called L1C and defined at <a href="http://www.gps.gov/technical/icwg/IS-GPS-800B.pdf" target="_blank"><b>Interface Specification IS-GPS-800 Revision B</b></a>, to be broadcast on the same L1 frequency that currently contains the C/A signal. The L1C will be available with first Block III launch, currently scheduled for 2013. The implementation will provide C/A code to ensure backward compatibility.
where \f$\oplus\f$ is the exclusive-or operation (modulo-2 addition), \f$|l|_{L}\f$ means \f$l\f$ modulo \f$L\f$, \f$[l]_{L}\f$ means the integer part of \f$\frac{l}{L}\f$,
\f$D_{\text{NAV}}\f$ is the GPS navigation message bit sequence, transmitted at \f$50\f$ bps, \f$T_{c,\text{P(Y)}}=\frac{1}{10.23}\f$ \f$\mu\f$s, \f$T_{c,\text{C/A}}=\frac{1}{1.023}\f$ \f$\mu\f$s,
\f$L_{\text{P(Y)}}=6.1871 \cdot 10^{12}\f$, and \f$p(t)\f$ is a rectangular pulse of a chip-period duration centered at \f$t=0\f$ and filtered at the transmitter.
According to the chip rate, the binary phase-shift keying modulations in the equations above are denoted as BPSK(10) and BPSK(1), respectively. The precision P codes (named Y codes whenever
the anti-spoofing mode is activated, encrypting the code and thus denying non-U.S. military users) are sequences of \f$7\f$ days in length. Regarding the modernization plans for GPS, it
is worthwhile to mention that there is a new civilian-use signal planned, called L1C and defined at <a href="http://www.gps.gov/technical/icwg/IS-GPS-800B.pdf" target="_blank"><b>Interface Specification IS-GPS-800 Revision B</b></a>,
to be broadcast on the same L1 frequency that currently contains the C/A signal. The L1C will be available with first Block III launch, currently scheduled for 2013. The implementation will
provide C/A code to ensure backward compatibility.
\li <b>GPS L2C</b>. Defined at <a href="http://www.gps.gov/technical/icwg/IS-GPS-200F.pdf" target="_blank"><b>Interface Specification IS-GPS-200 Revision F</b></a>, is only available on Block IIR-M and subsequent satellite blocks. Centered at \f$f_{\text{GPS L2}}=1227.60\f$ MHz, the signal structure is the same than in (\ref{eq:GPSL1}), with the precision code in the In-phase component, just as in (\ref{eq:L1CAI}) but with an optional presence of the navigation message \f$D_{\text{NAV}}\f$. For the Quadrature-phase component, three options are defined:
@ -222,7 +229,7 @@ e_{E5aI}(t)=& \sum_{m=-\infty}^{+\infty}C_{E5aIs}\Big[|m|_{20}\Big] \oplus \sum
Channel A contains the F/NAV type of navigation message, \f$D_{\text{F/NAV}}\f$, intended for the Open Service. The I/NAV message structures for the E5bI and E1B signals use the same page
layout. Only page sequencing is different, with page swapping
between both components in order to allow a fast reception of data by a dual frequency
receiver. The single subcarrier \f$sc_s(t)\f$ and the product subcarrier \f$sc_p(t)\f$ of expressions (\ref{sscs}) and (\ref{sscp}) are defined as:
receiver. The single subcarrier \f$sc_s(t)\f$ and the product subcarrier \f$sc_p(t)\f$ are defined as:
\f{align}{
sc_s(t)=& \frac{\sqrt{2}}{4}\text{sign} \left( \cos \left( 2 \pi f_s t - \frac{\pi}{4}\right) \right)+\\ \nonumber {}&+ \frac{1}{2}\text{sign} \Big( \cos \left( 2 \pi f_s t \right) \Big)+\\
{} &+\frac{\sqrt{2}}{4}\text{sign} \left( \cos \left( 2 \pi f_s t + \frac{\pi}{4}\right) \right)~,