ti_mo
9.2 KiB
Lab 5 - Wireless Networking Technologies
Analyzing a LEO Satellite Pass
by Timo Niemann
Task1
1.1
See code lab_5.m and create_satellite_sim.m, where the first file defines all parameters for the simulation and the create_satellite_sim function creates and returns the satellite and ground station.
1.2
To calculate the distance to the satellite, the MATLAB access analysis example was used as a basis and modified. The distance is calculated with the aer function, which returns azimuth, elevation, and slant range between the ground station and the satellite. To avoid invalid channel simulations, the signal-based estimation step is skipped when the Doppler shift fshift is non-finite.
The first satellite flyby occurs at around 08:05:30. During the pass, the distance first decreases as the satellite approaches the ground station and then increases again after the closest approach. Around 08:53:30 to 08:54:00, the distance reaches a maximum because the satellite is on the far side of its orbit relative to the ground station. The second pass occurs at around 09:42. Its minimum distance is larger than during the first pass because Earth's rotation changes the relative position of the ground station below the satellite orbit.
1.3
As in the distance plot, the elevation angle reaches its highest value during the first pass. The second pass has a lower maximum elevation because Earth's rotation shifts the ground station relative to the satellite ground track.
Task2
2.1
The normalization calculation is done by firstly extracting the Short Training Field from the generated WLAN Waveform:
tx = wlanWaveformGenerator(txPSDU, cfgEHT);
stf = tx(ind.LSTF(1):ind.LSTF(2), :);
On the extracted STF the mean of the per value absolute potentiation by 2 is calculated to get the power of the STF:
stfPower = mean(abs(stf(:)).^2);
Following wikipedia to convert Watt (P) into dBm (x) following formula is used:
x = 10 \cdot \log_{10}\frac{P}{1\text{mW}}
= 10 \cdot \log_{10}(P \cdot 1000)
To simplify that:
= 10 \cdot (\log_{10}(P) + \log_{10}(1000))
= 10 \cdot \log_{10}(P) + 10 \cdot \log_{10}(1000)
= 10 \cdot \log_{10}(P) + 10 \cdot 3
= 10 \cdot \log_{10}(P) + 30
After this the formula is solved for P, because the MATLAB signal has to be scaled with a linear power value in Watt:
x = 10 \cdot \log_{10}(P) + 30
x - 30 = 10 \cdot \log_{10}(P)
\frac{x - 30}{10} = \log_{10}(P)
10^{\frac{x - 30}{10}} = P
The 10^ is used because it is the inverse function of log10. The division by 10 is needed because the logarithm was multiplied by 10 in the dBm formula. For example, 20 dBm results in:
P = 10^{\frac{20 - 30}{10}} = 10^{-1} = 0.1\text{W}
The waveform itself is scaled by amplitude and not directly by power. Since power is proportional to the squared amplitude, the scaling factor has to use the square root. Therefore the target power in Watt is divided by the measured STF power and the square root is applied:
tx = tx * sqrt(10^((txPower - 30) / 10)) / sqrt(stfPower);
With this calculation the generated waveform is normalized by the STF power and then set to the desired transmit power in dBm.
2.2
To include free space path loss the corresponding field in create_baseline_configuration.m:37 is set.
Following wikipedia's free space path loss in decibels, the formula is:
FSPL(dB) = 20 \cdot \log_{10}(\frac{4\pi d}{\lambda}), where \lambda = \frac{c}{f}
Therefore the wavelength is calculated from the carrier frequency:
lambda = physconst("lightspeed") / carrier_frequency;
The received power is then the transmit power minus the free space path loss:
P_{rx} = P_{tx} - FSPL
This is possible because P_tx and P_rx are dBm values, while FSPL is a dB loss. In the simulation this is implemented as:
pathLoss(numPacketsSimulated) = 20 * log10(4 * pi * packetDistance / lambda);
rxPower(numPacketsSimulated) = txPower - pathLoss(numPacketsSimulated);
2.3
calculatorshub.net - this site provided helpful formulas and verification possibilities.
A signal is detectable when the receive power has at least a sensitivity of -85 dBm:
P_{rx} \geq -85dBm
The simulated receive power is below this threshold during the whole satellite pass. With the normal 20dBm WiFi transmit power, the received signal is therefore not detectable by a typical WiFi node.
To calculate the maximum reachable distance for detectability, the free space path loss formula is used in the opposite direction. With a transmit power of 20 dBm, the maximum allowed path loss is:
FSPL_{max} = P_{tx} - P_{rx}
FSPL_{detectable} = 20dBm - (-85dBm) = 105dB
The free space path loss formula is then solved for the distance d:
FSPL = 20 \cdot \log_{10}(\frac{4\pi d}{\lambda})
\frac{FSPL}{20} = \log_{10}(\frac{4\pi d}{\lambda})
10^{\frac{FSPL}{20}} = \frac{4\pi d}{\lambda}
d = \frac{\lambda}{4\pi} \cdot 10^{\frac{FSPL}{20}}
This is why the code calculates:
maxPathLossDetectable = txPower - wifiSensitivity;
maxDistanceDetectable = lambda / (4 * pi) * 10^(maxPathLossDetectable / 20);
The calculation results in a maximum detectable distance of 1.77km with 20dBm transmit power. This is much smaller than the satellite distance during the pass, so a normal WiFi transmit power is not sufficient for this link.
2.4
To calculate the required transmit power for reliable reception, the receive power formula is solved for P_tx instead:
P_{rx} = P_{tx} - FSPL
P_{tx} = P_{rx} + FSPL
For reliable WiFi reception the target receive power is -75 dBm. Therefore the required transmit power is:
P_{tx,required} = -75dBm + FSPL
With normal 20dBm transmit power, this reliable reception threshold would only allow a maximum distance of 0.56km:
maxPathLossReliable = txPower - reliableRxPower;
maxDistanceReliable = lambda / (4 * pi) * 10^(maxPathLossReliable / 20);
In MATLAB this is:
requiredTxPower = reliableRxPower + pathLoss;
For the simulated satellite pass, the required transmit power for -75dBm receive power is between 80.99dBm and 107.54dBm. This is far above the normal 20dBm WiFi transmit power.
2.5
The transmit amplifier can add 30 dB gain. Together with the original 20 dBm transmit power, the amplified transmit power is:
P_{tx,amplified} = 20dBm + 30dB = 50dBm
If the required transmit power is still higher than this value, the missing difference has to be provided as antenna gain:
G_{antenna} = P_{tx,required} - P_{tx,amplified}
Negative antenna gain is not needed, therefore the value is limited to zero:
amplifiedTxPower = txPower + amplifierGain;
requiredAntennaGain = max(requiredTxPower - amplifiedTxPower, 0);
With the 30dB amplifier, the remaining required antenna gain is between 30.99dB and 57.54dB.
Task3
3.1
Using the previously set transmit power of 20 dBm, the graph is identical to the receive power plot from task 2.2, because the receiver is the ground station. The received power remains below both the -85 dBm detection threshold and the -75 dBm reliable reception threshold. Therefore, WiFi packet reception is not possible during the simulated pass with normal WiFi transmit power.
3.2
The visibility was extracted from the access analysis. MATLAB's dopplershift function returns no finite value when the satellite is not visible to the ground station. The plot shows that the satellite is visible from about 08:00 to 08:12 and again from about 09:37 to 09:48. The ground station therefore has a total satellite visibility of about 23 minutes during the two-hour simulation.
3.3
The blue line shows the Doppler shift returned by MATLAB's dopplershift function during visible satellite periods. The green line shows a geometric Doppler estimate calculated from the change rate of the satellite distance, the carrier frequency, and the speed of light. The Doppler shift changes sign around the closest approach, because the satellite changes from approaching the ground station to moving away from it.
In this scenario, Doppler shift can support localization because it constrains the relative radial motion between satellite and ground station. However, Doppler alone is not sufficient for unique localization: the satellite orbit, time, and additional measurements such as range or elevation are still required.
Special Thanks
This lab was solved with contribution of GPT 5.5.