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- finished task 2

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- fixed perform_access_analysis to use 2.4GHz instead of 2GHz
- finished task 3
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ti_mo
2026-06-24 21:48:12 +02:00
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commit edbc22bcf6
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lab_5/doppler_shift_over_time_x_visibility.svg
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>80</text>
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>Elevation angle over time plot of satellite pass</text>
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lab_5/lab_5.m
+13 -1
View File
@@ -18,6 +18,7 @@ groundStation.Altitude = 37;
calc_task1 = true;
calc_task2 = true;
calc_task3 = true;
if calc_task1
task1;
@@ -28,4 +29,15 @@ if calc_task2
task1;
end
task2;
end
end
if calc_task3
if ~calc_task1
task1;
end
if ~calc_task2
task2;
end
task3;
end
lab_5/leo_satellite_pass.md
+185
View File
@@ -27,3 +27,188 @@ The first satellite flyby occurs at around 08:05:30. During the pass, the distan
![Elevation angle over time sweep](elevation_angle_over_time.svg)
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:
```matlab
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:
```matlab
stfPower = mean(abs(stf(:)).^2);
```
Following [wikipedia](https://en.wikipedia.org/wiki/DBm) 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:
```matlab
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](https://en.wikipedia.org/wiki/Free-space_path_loss)'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:
```matlab
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:
```matlab
pathLoss(numPacketsSimulated) = 20 * log10(4 * pi * packetDistance / lambda);
rxPower(numPacketsSimulated) = txPower - pathLoss(numPacketsSimulated);
```
![Receive power over time sweep](receive_power_over_time.svg)
#### 2.3
[calculatorshub.net](https://calculatorshub.net/telecom-calculators/dbm-to-range-calculator/) - 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:
```matlab
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:
```matlab
maxPathLossReliable = txPower - reliableRxPower;
maxDistanceReliable = lambda / (4 * pi) * 10^(maxPathLossReliable / 20);
```
In MATLAB this is:
```matlab
requiredTxPower = reliableRxPower + pathLoss;
```
![Required transmit power over time sweep](required_transmit_power.svg)
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:
```matlab
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
![receive power over time at groundstation](receive_power_over_time_groundstation.svg)
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
![satellite visibility over time plot](sat_visibility_over_time.svg)
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
![Doppler shift over time plot](doppler_shift_over_time_x_visibility.svg)
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.
lab_5/perform_access_analysis.m
+5 -1
View File
@@ -17,7 +17,7 @@ function res = perform_access_analysis(satSim, queryTime)
res.distanceToSatellite = r;
res.elevationAngleToSatellite = el;
carrierFrequency = 2e9;
carrierFrequency = 2.4e9;
[fshift,~,dopplerInfo] = dopplershift( ...
sat,ue,queryTime,Frequency=carrierFrequency);
res.rangeRate = -1*dopplerInfo.RelativeVelocity;
@@ -26,11 +26,15 @@ function res = perform_access_analysis(satSim, queryTime)
res.satPos = satPos;
res.satVel = satVel;
res.fshift = fshift;
if ~isfinite(fshift)
res.satelliteVisible = false;
return;
end
res.satelliteVisible = true;
rng(0)
lightspeed = physconst("lightspeed");
lab_5/receive_power_over_time.svg
+90 -90
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lab_5/task1.m
+35 -15
View File
@@ -4,6 +4,8 @@ satSim = create_satellite_sim(satConfig, groundStation);
sampleTimes = satConfig.startTime:seconds(satConfig.sampleTime):satConfig.stopTime;
distancesToSat = zeros(size(sampleTimes));
elevationAnglesToSat = zeros(size(sampleTimes));
satelitteVisibilities = zeros(size(sampleTimes));
dopplerShifts = zeros(size(sampleTimes));
progressStartText = "Starting ...";
f = waitbar(0, progressStartText, "Name", "Task 1");
@@ -18,6 +20,8 @@ parfor idx = 1:numel(sampleTimes)
res = perform_access_analysis(satSim, sampleTimes(idx));
distancesToSat(idx) = res.distanceToSatellite;
elevationAnglesToSat(idx) = res.elevationAngleToSatellite;
satelitteVisibilities(idx) = res.satelliteVisible;
dopplerShifts(idx) = res.fshift;
send(progressQueue, sprintf("Index %d", idx));
end
@@ -26,20 +30,36 @@ if ishandle(f)
close(f);
end
figure;
plot(sampleTimes, distancesToSat);
grid on;
xlabel("Time [s]");
ylabel("Distance to Satellite [m]");
title("Distance over time plot of satellite pass");
figure;
plot(sampleTimes, elevationAnglesToSat);
grid on;
xlabel("Time [s]");
ylabel("Elevation angle to satellite [degree]");
title("Elevation angle over time plot of satellite pass");
accessAnalysisResults.times = sampleTimes;
accessAnalysisResults.distances = distancesToSat;
accessAnalysisResults.elevationAngles = elevationAnglesToSat;
accessAnalysisResults.elevationAngles = elevationAnglesToSat;
accessAnalysisResults.satelitteVisibilities = satelitteVisibilities;
accessAnalysisResults.dopplerShifts = dopplerShifts;
carrierFrequency = 2.4e9;
timeSeconds = seconds(sampleTimes - sampleTimes(1));
rangeRate = gradient(accessAnalysisResults.distances, timeSeconds);
dopplerShift = -(rangeRate / physconst("lightspeed")) * carrierFrequency;
accessAnalysisResults.geometricDopplerShifts = dopplerShift;
% prevent figure plot when only the other tasks should be calculated
% task2 needs task1
if calc_task1
figure;
plot(sampleTimes, distancesToSat);
grid on;
xtickformat("HH:mm");
xlabel("Time of day [HH:mm]");
ylabel("Distance to Satellite [m]");
title("Distance over time plot of satellite pass");
figure;
plot(sampleTimes, elevationAnglesToSat);
grid on;
xtickformat("HH:mm");
xlabel("Time of day [HH:mm]");
ylabel("Elevation angle to satellite [degree]");
title("Elevation angle over time plot of satellite pass");
end
lab_5/task2.m
+26 -18
View File
@@ -27,15 +27,20 @@ packetTimes = accessAnalysisResults.times(packetIdx);
rxPower = rxPower(packetIdx);
pathLoss = pathLoss(packetIdx);
figure;
plot(packetTimes, rxPower);
grid on;
xlabel("Time");
ylabel("Power [dBm]");
title("Receive power over time plot of satellite pass");
yline(wifiSensitivity, "--", "receive sensitivity -85 dBm");
yline(reliableRxPower, "--", "reliable reception -75 dBm");
if calc_task2
figure;
plot(packetTimes, rxPower);
grid on;
xtickformat("HH:mm");
xlabel("Time of day [HH:mm]");
ylabel("Power [dBm]");
title("Receive power over time plot of satellite pass");
yline(wifiSensitivity, "--", "receive sensitivity -85 dBm");
yline(reliableRxPower, "--", "reliable reception -75 dBm");
end
% this site helped in providing formulas and a calculator to verify
% https://calculatorshub.net/telecom-calculators/dbm-to-range-calculator/
lambda = physconst("lightspeed") / carrier_frequency;
maxPathLossDetectable = txPower - wifiSensitivity;
maxDistanceDetectable = lambda / (4 * pi) * 10^(maxPathLossDetectable / 20);
@@ -45,12 +50,15 @@ maxDistanceReliable = lambda / (4 * pi) * 10^(maxPathLossReliable / 20);
requiredTxPower = reliableRxPower + pathLoss;
figure;
plot(packetTimes, requiredTxPower);
grid on;
xlabel("Time");
ylabel("Power [dBm]");
title("Required transmit power for -75 dBm receive power");
if calc_task2
figure;
plot(packetTimes, requiredTxPower);
grid on;
xtickformat("HH:mm");
xlabel("Time of day [HH:mm]");
ylabel("Power [dBm]");
title("Required transmit power for -75 dBm receive power");
end
amplifiedTxPower = txPower + amplifierGain;
requiredAntennaGain = max(requiredTxPower - amplifiedTxPower, 0);
@@ -58,7 +66,7 @@ requiredAntennaGain = max(requiredTxPower - amplifiedTxPower, 0);
validRequiredTxPower = requiredTxPower(isfinite(requiredTxPower));
validRequiredAntennaGain = requiredAntennaGain(isfinite(requiredAntennaGain));
fprintf("Maximum detectable distance at %.0f dBm TX power: %.2f km\n", txPower, maxDistanceDetectable / 1e3);
fprintf("Maximum reliable distance at %.0f dBm TX power: %.2f km\n", txPower, maxDistanceReliable / 1e3);
fprintf("Required TX power for -75 dBm reception: %.2f dBm to %.2f dBm\n", min(validRequiredTxPower), max(validRequiredTxPower));
fprintf("Required antenna gain with %.0f dB amplifier: %.2f dB to %.2f dB\n", amplifierGain, min(validRequiredAntennaGain), max(validRequiredAntennaGain));
fprintf("Maximum detectable distance at %.0fdBm TX power: %.2fkm\n", txPower, maxDistanceDetectable / 1e3);
fprintf("Maximum reliable distance at %.0fdBm TX power: %.2fkm\n", txPower, maxDistanceReliable / 1e3);
fprintf("Required TX power for -75dBm reception: %.2fdBm to %.2fdBm\n", min(validRequiredTxPower), max(validRequiredTxPower));
fprintf("Required antenna gain with %.0fdB amplifier: %.2fdB to %.2fdB\n", amplifierGain, min(validRequiredAntennaGain), max(validRequiredAntennaGain));
lab_5/task3.m
+47
View File
@@ -0,0 +1,47 @@
rxPowerStation = txPower - pathLoss;
figure;
plot(packetTimes, rxPowerStation);
grid on;
xtickformat("HH:mm");
xlabel("Time of day [HH:mm]");
ylabel("Power [dBm]");
yline(wifiSensitivity, "--", "receive sensitivity -85 dBm");
yline(reliableRxPower, "--", "reliable reception -75 dBm");
title("Receive power over time at ground station plot of satellite pass");
satelliteVisibilities = double(accessAnalysisResults.satelitteVisibilities);
figure;
hold on;
plot(sampleTimes, satelliteVisibilities, "Color", [0.1 0.45 0.2]);
grid on;
xtickformat("HH:mm");
xlabel("Time of day [HH:mm]");
ylabel("Visibility of satellite [bool]");
ylim([-0.05 1.05]);
yticks([0 1]);
yticklabels(["not visible", "visible"]);
title("Satellite visibility over time");
dopplerShiftKHz = accessAnalysisResults.dopplerShifts / 1e3;
dopplerShiftKHz(~isfinite(dopplerShiftKHz)) = NaN;
geometricDopplerShiftKHz = accessAnalysisResults.geometricDopplerShifts / 1e3;
satelliteVisibilities = logical(accessAnalysisResults.satelitteVisibilities);
dopplerVisibleOnly = dopplerShiftKHz;
dopplerVisibleOnly(~satelliteVisibilities | ~isfinite(dopplerVisibleOnly)) = NaN;
figure;
hold on;
plot(sampleTimes, geometricDopplerShiftKHz, "Color", [0.1 0.6 0.2], "DisplayName", "geometric Doppler shift");
plot(sampleTimes, dopplerVisibleOnly, "Color", [0 0.4470 0.7410], "DisplayName", "visible dopplershift() output", "LineWidth", 2);
grid on;
xtickformat("HH:mm");
xlabel("Time of day [HH:mm]");
ylabel("Doppler shift [kHz]");
yline(0, "--", "0 Hz", "HandleVisibility", "off");
legend("Location", "best");
title("Doppler shift over time x satellite visibility");