gaussianAntenna

Add Gaussian antennas

Since R2021a

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Syntax

gaussianAntenna(trx)
gaussianAntenna(trx,Name=Value)
ant = gaussianAntenna(___)

Description

gaussianAntenna(trx) adds a Gaussian antenna to each transmitter or receiver in the vector trx using default parameters. The existing antennas in the transmitters or receivers are overwritten. For more information about antenna gain, see Algorithm.

gaussianAntenna(trx,Name=Value) adds a Gaussian antenna to each transmitter or receiver in the vector trx and specifies options using name-value arguments. For example, DishDiameter=1.7 defines the diameter of the antenna dish.

example

ant = gaussianAntenna(___) adds a Gaussian antenna to the transmitters or receivers and returns them in the vector ant.

Examples

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Open Live Script

Create a satellite scenario object.

startTime = datetime(2020,11,25,0,0,0);
stopTime = startTime + days(1);
sampleTime = 60;                                     % seconds
sc = satelliteScenario(startTime,stopTime,sampleTime)
sc = 
  satelliteScenario with properties:

         StartTime: 25-Nov-2020
          StopTime: 26-Nov-2020
        SampleTime: 60
      AutoSimulate: 1
        Satellites: [1×0 matlabshared.satellitescenario.Satellite]
    GroundStations: [1×0 matlabshared.satellitescenario.GroundStation]
         Platforms: [1×0 matlabshared.satellitescenario.Platform]
           Viewers: [0×0 matlabshared.satellitescenario.Viewer]
          AutoShow: 1

Add a satellite to the scenario.

semiMajorAxis = 10000000;                                                                  % meters
eccentricity = 0;
inclination = 60;                                                                          % degrees
rightAscensionOfAscendingNode = 0;                                                         % degrees
argumentOfPeriapsis = 0;                                                                   % degrees
trueAnomaly = 0;                                                                           % degrees
sat = satellite(sc,semiMajorAxis,eccentricity,inclination,rightAscensionOfAscendingNode, ...
        argumentOfPeriapsis,trueAnomaly,Name="Satellite");

Add gimbals to the satellite. These gimbals enable the satellite receiver antenna to steer to the first ground station, and its transmitter antenna to steer to the second ground station.

gimbalrxSat = gimbal(sat);
gimbaltxSat = gimbal(sat);

Add a receiver to the first gimbal of the satellite.

gainToNoiseTemperatureRatio = 5;                                                        % dB/K
systemLoss = 3;                                                                         % dB
rxSat = receiver(gimbalrxSat,Name="Satellite Receiver",GainToNoiseTemperatureRatio= ...
    gainToNoiseTemperatureRatio,SystemLoss=systemLoss)
rxSat = 
  Receiver with properties:

                           Name:  Satellite Receiver
                             ID:  4
               MountingLocation:  [0; 0; 0] meters
                 MountingAngles:  [0; 0; 0] degrees
                        Antenna:  [1x1 satcom.satellitescenario.GaussianAntenna]
                     SystemLoss:  3 decibels
                PreReceiverLoss:  3 decibels
    GainToNoiseTemperatureRatio:  5 decibels/Kelvin
                   RequiredEbNo:  10 decibels
                 CoordinateAxes:  [1x1 matlabshared.satellitescenario.CoordinateAxes]

Add a transmitter to the second gimbal of the satellite.

frequency = 27e9;                                                                     % Hz
power = 20;                                                                           % dBW
bitRate = 20;                                                                         % Mbps
systemLoss = 3;                                                                       % dB
txSat = transmitter(gimbaltxSat,Name="Satellite Transmitter",Frequency=frequency, ...
    power=power,BitRate=bitRate,SystemLoss=systemLoss)
txSat = 
  Transmitter with properties:

                Name:  Satellite Transmitter
                  ID:  5
    MountingLocation:  [0; 0; 0] meters
      MountingAngles:  [0; 0; 0] degrees
             Antenna:  [1x1 satcom.satellitescenario.GaussianAntenna]
          SystemLoss:  3 decibels
           Frequency:  2.7e+10 Hertz
             BitRate:  20 Mbps
               Power:  20 decibel-watts
               Links:  [1x0 satcom.satellitescenario.Link]
      CoordinateAxes:  [1x1 matlabshared.satellitescenario.CoordinateAxes]

Specify the antenna specifications of the repeater.

dishDiameter = 0.5;                                                                    % meters
apertureEfficiency = 0.5;
gaussianAntenna(txSat,DishDiameter=dishDiameter,ApertureEfficiency=apertureEfficiency);
gaussianAntenna(rxSat,DishDiameter=dishDiameter,ApertureEfficiency=apertureEfficiency);

Add two ground stations to the scenario.

gs1 = groundStation(sc,Name="Ground Station 1");
latitude = 52.2294963;                                              % degrees
longitude = 0.1487094;                                              % degrees
gs2 = groundStation(sc,latitude,longitude,Name="Ground Station 2");

Point gimbals of the satellite towards the two ground stations for the simulation duration.

pointAt(gimbaltxSat,gs2);
pointAt(gimbalrxSat,gs1);

Add gimbals to the ground stations. These gimbals enable the ground station antennas to steer towards the satellite.

gimbalgs1 = gimbal(gs1);
gimbalgs2 = gimbal(gs2);

Add a transmitter to ground station gs1.

frequency = 30e9;                                                                          % Hz
power = 40;                                                                                % dBW
bitRate = 20;                                                                              % Mbps
txGs1 = transmitter(gimbalgs1,Name="Ground Station 1 Transmitter",Frequency=frequency, ...
        Power=power,BitRate=bitRate);

Add a receiver to ground station gs2.

requiredEbNo = 14;                                                                     % dB
rxGs2 = receiver(gimbalgs2,Name="Ground Station 2 Receiver",RequiredEbNo=requiredEbNo);

Define the antenna specifications of the ground stations.

dishDiameter = 5;                                % meters
gaussianAntenna(txGs1,DishDiameter=dishDiameter);
gaussianAntenna(rxGs2,DishDiameter=dishDiameter);

Point gimbals of the ground stations towards the satellite for the simulation duration.

pointAt(gimbalgs1,sat);
pointAt(gimbalgs2,sat);

Add link analysis to transmitter txGs1.

lnk = link(txGs1,rxSat,txSat,rxGs2)
lnk = 
  Link with properties:

    Sequence:  [10 4 5 11]
    LineWidth:  2
    LineColor:  [0.3922 0.8314 0.0745]

Determine the times when ground station gs1 can send data to ground station gs2 via the satellite.

linkIntervals(lnk)
ans=4×8 table
                Source                          Target               IntervalNumber         StartTime                EndTime           Duration    StartOrbit    EndOrbit
    ______________________________    ___________________________    ______________    ____________________    ____________________    ________    __________    ________

    "Ground Station 1 Transmitter"    "Ground Station 2 Receiver"          1           25-Nov-2020 00:20:00    25-Nov-2020 00:40:00      1200         NaN          NaN   
    "Ground Station 1 Transmitter"    "Ground Station 2 Receiver"          2           25-Nov-2020 03:19:00    25-Nov-2020 03:36:00      1020         NaN          NaN   
    "Ground Station 1 Transmitter"    "Ground Station 2 Receiver"          3           25-Nov-2020 06:15:00    25-Nov-2020 06:36:00      1260         NaN          NaN   
    "Ground Station 1 Transmitter"    "Ground Station 2 Receiver"          4           25-Nov-2020 22:20:00    25-Nov-2020 22:38:00      1080         NaN          NaN

Visualize the link by using the Satellite Scenario Viewer.

play(sc);

Open Live Script
startTime = datetime(2020,11,25,0,0,0);
stopTime = startTime + days(1);
sampleTime = 60;                                     % seconds
sc = satelliteScenario(startTime,stopTime,sampleTime)
sc = 
  satelliteScenario with properties:

             StartTime: 25-Nov-2020
              StopTime: 26-Nov-2020
            SampleTime: 60
          AutoSimulate: 1
    CentralBodyOptions: [1×1 Aero.satellitescenario.CentralBodyOptions]
            Satellites: [1×0 matlabshared.satellitescenario.Satellite]
        GroundStations: [1×0 matlabshared.satellitescenario.GroundStation]
             Platforms: [1×0 matlabshared.satellitescenario.Platform]
               Viewers: [0×0 matlabshared.satellitescenario.Viewer]
              AutoShow: 1

Define the orbital parameters of the satellite.

semiMajorAxis = 10000000;                                                                  % meters
eccentricity = 0;
inclination = 60;                                                                          % degrees
rightAscensionOfAscendingNode = 0;                                                         % degrees
argumentOfPeriapsis = 0;                                                                   % degrees
trueAnomaly = 0;                                                                           % degrees

Create a satellite object and attach a gimbal to the satellite.

sat = satellite(sc,semiMajorAxis,eccentricity,inclination,rightAscensionOfAscendingNode, ...
    argumentOfPeriapsis,trueAnomaly,Name="Satellite");
gimbalSat = gimbal(sat);
frequency = 27e9;                                                                     % Hz

Define the transmitter parameters. Create a transmitter object and attach it to the gimbal.

power = 20;                                                                           % dBW
bitRate = 20;                                                                         % Mbps
systemLoss = 3;                                                                       % dB
txSat = transmitter(gimbalSat,Name="Satellite Transmitter",Frequency=frequency, ...
    power=power,BitRate=bitRate,SystemLoss=systemLoss)
txSat = 
  Transmitter with properties:

                Name:  Satellite Transmitter
                  ID:  3
    MountingLocation:  [0; 0; 0] meters
      MountingAngles:  [0; 0; 0] degrees
             Antenna:  [1x1 satcom.satellitescenario.GaussianAntenna]
          SystemLoss:  3 decibels
           Frequency:  2.7e+10 Hertz
             BitRate:  20 Mbps
               Power:  20 decibel-watts
               Links:  [1x0 satcom.satellitescenario.Link]
      CoordinateAxes:  [1x1 matlabshared.satellitescenario.CoordinateAxes]

Define the antenna parameters.

rho_a = 0.5; % Aperture efficiency
d = 0.5; 
lambda = 0.01110342; % Wavelength in meters

Calculate the boresight gain and 3dB beamwidth for the gaussian antenna properties.

boresightGain = rho_a * ((pi * d / lambda)^2); % This is in linear scale
beamwidth_3dB = 70 * lambda / d; % in degrees

Convert boresight gain from linear scale to dB. Create a gaussian antenna object and attach it to the transmitter.

boresightGain_dB = 10 * log10(boresightGain);
antenna = gaussianAntenna(txSat,DishDiameter=d,ApertureEfficiency=rho_a);

Define the angle range from -180 to 180 degrees for gain calculation. Calculate the gain pattern and convert the gain to dB.

theta = -180:1:180;
gain = boresightGain * exp(-(4 * log(2) * ((theta/beamwidth_3dB).^2)));
gain_dB = 10 * log10(gain);

Generate a plot visualize the gain pattern of the Gaussian antenna. 

figure;
plot(theta, gain_dB);
xlabel('Angle off the boresight (degrees)');
ylabel('Gain (dB)');
title('Gaussian Antenna Gain Pattern Using Algorithm');
grid on;
axis tight;
ylim([-40, max(gain_dB)+5]); % Adjust y-axis limits for better visualization

Figure contains an axes object. The axes object with title Gaussian Antenna Gain Pattern Using Algorithm, xlabel Angle off the boresight (degrees), ylabel Gain (dB) contains an object of type line.

The X-axis represents the angle off the boresight in degrees, and the Y-axis represents the gain in dB.

Input Arguments

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Transmitter or receiver object to which the Gaussian antenna is added, specified as either a scalar or a vector.

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'DishDiameter'=1.7 sets the dish diameter of the antenna to 1.7 meters upon creation.

This property is read-only.

You can set this property only when calling gaussianAntenna. After you call gaussianAntenna, this property is read-only.

Diameter of the Gaussian antenna dish in meters, specified as a scalar or a vector.

  • If DishDiameter is a scalar, the same value is assigned to all transmitters or receivers in trx.

  • If DishDiameter is a vector, the length of the vector must equal that of trx, and each transmitter or receiver in trx is assigned the corresponding element in the DishDiameter vector.

This property is read-only.

You can set this property only when calling gaussianAntenna. After you call gaussianAntenna, this property is read-only.

Aperture efficiency of the Gaussian antenna, specified as a scalar in the range (0,1].

  • If ApertureEfficiency is a scalar, the same value is assigned to all transmitters or receivers in trx.

  • If ApertureEfficiency is a vector, the length of the vector must equal that of trx, and each transmitter or receiver in trx is assigned the corresponding element in the ApertureEfficiency vector.

Output Arguments

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Gaussian antenna object added to the specified transmitter or receiver, returned as either a scalar or a vector.

Note

When the AutoSimulate property of satellite scenario is false, you can call the gaussianAntenna function only when SimulationStatus is NotStarted. You can use the restart function to reset the SimulationStatus to NotStarted, but doing so erases the simulation data.

Algorithms

The Gaussian antenna approximates a parabolic reflector using a Gaussian curve as

gain(theta) = boresightGain*exp(-(4*log(2)*((theta/3dBbeamwidth)^2)))

Note that log(2) is a natural log, where:

  • boresightGain = rho_a*((pi*d/lambda)^2)

  • 3dBbeamwidth = 70*lambda/d

    (in degrees)

  • theta is the angle between the direction in which the gain is computed and the boresight direction is in degrees.

  • rho_a is the aperture efficiency.

  • d is the dish diameter in meters.

  • lambda is the wavelength in meters.

The gain in dBi is

gain_dBi(theta) = 10*log10(gain(theta)

Version History

Introduced in R2021a

See Also

Objects

Functions

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