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Non vérifiée Valider b270a166 rédigé par Martin Braquet's avatar Martin Braquet Validation de GitHub
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...@@ -18,21 +18,21 @@ A ground station is emitting a plane wave toward a satellite, with an elevation ...@@ -18,21 +18,21 @@ A ground station is emitting a plane wave toward a satellite, with an elevation
\begin{enumerate} \begin{enumerate}
\item (1 point) Calculate the elevation angle in layer 2 ($\alpha_2$ in the figure). \item (1 point) Calculate the elevation angle in layer 2 ($\alpha_2$ in the figure).
\item (2 point) Calculate the reflection coefficient $\Gamma$ and the transmission coefficient T of the electric field at the interface between the to layers. \item (2 point) Calculate the reflection coefficient $\Gamma$ and the transmission coefficient $T$ of the electric field at the interface between the two layers.
\item (1,5 points) If the distance between the satellite and the ground station (Matera) is 40500 km and the frequency 7,8 GHz, calculate the free space losses + total tropospheric losses exceeded during 0.01\% of the time. \item (1,5 points) If the distance between the satellite and the ground station (Matera) is \SI{40500}{km} and the frequency \SI{7.8}{GHz}, calculate the free space losses + total tropospheric losses exceeded during 0.01\% of the time.
\end{enumerate} \end{enumerate}
(CCDF graph available with an attenuation of 9 dB for 0.01\% of the time at the angle and frequency related to this problem) (CCDF graph available with an attenuation of \SI{9}{dB} for 0.01\% of the time at the angle and frequency related to this problem)
\nosolution \nosolution
\section{(4,5 points)} \section{(4,5 points)}
Two parabolic dish antennas are facing each other to establish a horizontal link over a distance of 2 km. The frequency of operation is 5 GHz and the diameter of the dishes is 1 meter. Both antennas have an input impedance of 50 Ohm, while the generator impedance is $(100-j50)$ Ohm on the transmitting side and the receiver impedance is 50 Ohm on the receiving side. The noise figure of the receiver is 3 dB, the bandwidth of the signal is 5 MHz. The transmitting polarization is vertical, while the receiving polarization is circular. 10 milliWatt are available at the generator. Two parabolic dish antennas are facing each other to establish a horizontal link over a distance of \SI{2}{km}. The frequency of operation is \SI{5}{GHz} and the diameter of the dishes is 1 meter. Both antennas have an input impedance of \SI{50}{\ohm}, while the generator impedance is $(100-j50)$ Ohm on the transmitting side and the receiver impedance is \SI{50}{\ohm} on the receiving side. The noise figure of the receiver is \SI{3}{dB}, the bandwidth of the signal is \SI{5}{MHz}. The transmitting polarization is vertical, while the receiving polarization is circular. \SI{10}{mW} are available at the generator.
\begin{enumerate} \begin{enumerate}
\item Assuming in a first instance that the two antennas have the same polarization and that they are impedance matched, what is the signal-to-noise ratio on the receiver? \item Assuming in a first instance that the two antennas have the same polarization and that they are impedance matched, what is the signal-to-noise ratio on the receiver?
\item What does that SNR become with the impedance and polarization mismatches referred to above? \item What does that SNR become with the impedance and polarization mismatches referred to above?
\item With which accuracy (in degrees) do the two antennas need to be pointed at each other to avoid a decrease of the signal by more than 3dB? (do the calculation assuming that one antenna is perfectly pointed and the other is not) \item With which accuracy (in degrees) do the two antennas need to be pointed at each other to avoid a decrease of the signal by more than \SI{3}{dB}? (do the calculation assuming that one antenna is perfectly pointed and the other is not)
\end{enumerate} \end{enumerate}
\nosolution \nosolution
...@@ -40,15 +40,15 @@ Two parabolic dish antennas are facing each other to establish a horizontal link ...@@ -40,15 +40,15 @@ Two parabolic dish antennas are facing each other to establish a horizontal link
\section{(4,5 points)} \section{(4,5 points)}
We consider the downlink of a cellular transmission 3.5 GHz, using a bandwidth of 5 MHz per user. At the base station, the transmit power is 20 W and the antenna gain is 5 dBi. For the considered environment, the path-loss is given in [dB] by: We consider the downlink of a cellular transmission \SI{3.5}{GHz}, using a bandwidth of \SI{5}{MHz} per user. At the base station, the transmit power is 20 W and the antenna gain is \SI{5}{dBi}. For the considered environment, the path-loss is given in [\si{dB}] by:
$$P_L [dB] = 140 + 10 \gamma \log_{10}(d) + S_{dB}$$ \[ P_L [\si{dB}] = 140 + 10 \gamma \log_{10}(d) + S_{\si{dB}} \]
where $d$ is the distance in km from the base station , $\gamma = 3$ is the pass-loss exponent and $S_{dB}$ is the log-normal shadowing: $S_{dB}$ is a zero-mean Gaussian variable with a standard deviation of 6 dB. where $d$ is the distance in km from the base station , $\gamma = 3$ is the pass-loss exponent and $S_\si{dB}$ is the log-normal shadowing: $S_\si{dB}$ is a zero-mean Gaussian variable with a standard deviation of \SI{6}{dB}.
The mobile terminal is characterized by a quasi-omnidirectional antenna of 2 dBi gain and a noise spectral density of $\SI{1.9e-19}{mW/Hz}$. The mobile terminal is characterized by a quasi-omnidirectional antenna of \SI{2}{dBi} gain and a noise spectral density of \SI{1.9e-19}{mW/Hz}.
\begin{enumerate} \begin{enumerate}
\item What should be the cell radius $R$ in order to guarantee that the average received power is at least -100 dBm over the entire cell? \item What should be the cell radius $R$ in order to guarantee that the average received power is at least \SI{-100}{dBm} over the entire cell?
\item What is therefore the average SNR (received power to noise power ratio) at the cell edge (i.e. at a distance $d=R$)? \item What is therefore the average SNR (received power to noise power ratio) at the cell edge (i.e. at a distance $d=R$)?
\item What is the probability that the received power falls bellow -114 dBm at the cell edge? \item What is the probability that the received power falls bellow \SI{-114}{dBm} at the cell edge?
\item Assuming hexagonal cells, at which distance can the network operator re-use the same frequency to maintain a Signal-to-Interference Ratio (SIR) of 18 dB (neglecting thermal noise)? What is in this case the cell pattern (i.e. the number of available frequencies)? \item Assuming hexagonal cells, at which distance can the network operator re-use the same frequency to maintain a Signal-to-Interference Ratio (SIR) of \SI{18}{dB} (neglecting thermal noise)? What is in this case the cell pattern (i.e. the number of available frequencies)?
\item If the channel consists in two multi-paths of equal amplitude, what is the maximum separation in delay that could still guarantee flat-fading transmission? Is this realistic in urban areas? \item If the channel consists in two multi-paths of equal amplitude, what is the maximum separation in delay that could still guarantee flat-fading transmission? Is this realistic in urban areas?
\end{enumerate} \end{enumerate}
Appendix - Cumulative distribution of standard normal variable (zero-mean Gaussian with unit variance)\\ Appendix - Cumulative distribution of standard normal variable (zero-mean Gaussian with unit variance)\\
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