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fixing typos and removing latex cross-references

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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
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1 changed files with 9 additions and 2 deletions
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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_{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} 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} \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: \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 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 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 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}{ \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)+\\ 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)~, {} &+\frac{\sqrt{2}}{4}\text{sign} \left( \cos \left( 2 \pi f_s t + \frac{\pi}{4}\right) \right)~,