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Eb/No at final node of link



    e = ebno(lnk) returns a matrix e of the history of received values for energy per bit to noise power spectral density (Eb/No) in dB at the final node in each possible multihop link in the vector lnk. The rows of the matrix correspond to the link object in lnk and the columns correspond to the time sample.

    e = ebno(lnk,timeIn) returns a column vector of Eb/No e in dB at the final node in each link defined in the vector lnk at the specified datetime timein. Each element of e corresponds to a link in lnk. If no time zone is specified in timeIn, the time zone is assumed to be Coordinated Universal Time(UTC).


    [e,timeOut] = ebno(___) returns the received Eb/No values and the corresponding times in UTC.


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    Create a satellite scenario object.

    startTime = datetime(2021,12,12,10,42,0);
    stopTime = startTime + days(1);
    sampleTime = 5000;                                       % seconds
    sc = satelliteScenario(startTime,stopTime,sampleTime);

    Add a satellite to the scenario.

    semiMajorAxis = 10000000;                               % meters
    eccentricity = 0;
    inclination = 0;                                        % degrees
    rightAscensionOfAscendingNode = 0;                      % degrees
    argumentOfPeriapsis = 0;                                % degrees
    trueAnomaly = 210;                                      % degrees
    sat = satellite(sc,semiMajorAxis,eccentricity, ...
        inclination,rightAscensionOfAscendingNode, ...

    Add a transmitter to the satellite.

    tx = transmitter(sat);

    Add a ground station to the scenario.

    latitude = 0;                             % degrees
    longitude = 30;                           % degrees
    gs = groundStation(sc,latitude,longitude);

    Add a receiver to the ground station.

    rx = receiver(gs,MountingAngles=[0; 180; 0]);

    Add link analysis to the transmitter.

    lnk = link(tx,rx);

    Get the Eb/No history at the receiver and the time samples.

    [e,t] = ebno(lnk)
    e = 1×19
      -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf  -Inf
    t = 1x19 datetime
    Columns 1 through 3
       12-Dec-2021 10:42:00   12-Dec-2021 12:05:20   12-Dec-2021 13:28:40
    Columns 4 through 6
       12-Dec-2021 14:52:00   12-Dec-2021 16:15:20   12-Dec-2021 17:38:40
    Columns 7 through 9
       12-Dec-2021 19:02:00   12-Dec-2021 20:25:20   12-Dec-2021 21:48:40
    Columns 10 through 12
       12-Dec-2021 23:12:00   13-Dec-2021 00:35:20   13-Dec-2021 01:58:40
    Columns 13 through 15
       13-Dec-2021 03:22:00   13-Dec-2021 04:45:20   13-Dec-2021 06:08:40
    Columns 16 through 18
       13-Dec-2021 07:32:00   13-Dec-2021 08:55:20   13-Dec-2021 10:18:40
    Column 19
       13-Dec-2021 10:42:00

    This example demonstrates a simple technique for incorporating random pointing loss at the transmit and receive antennas in a space-to-ground radio link. Caluclate the link margin without pointing loss, and then you add the random sequences of pointing loss to the result.

    Define parameters for pointing error simulation.

    freq = 8;                 % Carrier frequency, GHz
    satAntDiam = 0.4;         % Satellite antenna diameter, m
    satAntEff = 0.43;         % Satellite antenna efficiency, (0,1]
    satAntPtErr = 0.5;        % Satellite antenna std. dev. pointing error, deg
    gsAntDiam = 2.7;          % Ground antenna diameter, m
    gsAntEff = 0.63;          % Ground antenna efficiency, (0,1]
    gsAntPtErr = 0.2;         % Ground antenna std. dev. pointing error, deg
    gsNoiseTemp = 150;        % Ground system noise temperature, Kelvin
    reqEbNo = 13.0;           % Required Eb/No for 8PSK BER=1e-5, decibels

    Create a satellite scenario object.

    startTime = datetime(2020,8,19,22,35,0);              
    stopTime = datetime(2020,8,19,23,15,0);    
    sampleTime = 1;                                       % Seconds
    sc = satelliteScenario(startTime,stopTime,sampleTime);

    Add satellite orbital elements for a sun-synchronous satellite.

    sat = satellite(sc,7*1e6,0.0002178,97.8356,359.1795,135.7406,224.3991);
    satTx = transmitter(sat,Frequency=freq*1e9,BitRate=60,Power=3);    
    satAnt = gaussianAntenna(satTx,DishDiameter=satAntDiam, ...
    gs = groundStation(sc,Latitude=69.649208,Longitude=18.955324, ...
    gsGim = gimbal(gs,MountingAngles=[0;180;0], ...
    waveLen = physconst("lightspeed")/(freq*1e9);         
    pkG = 10*log10(gsAntEff*((pi*gsAntDiam)/waveLen)^2);                % Peak antenna gain, dBi
    gsRx = receiver(gsGim,MountingLocation=[0;0;1], ...
        GainToNoiseTemperatureRatio=pkG-10*log10(gsNoiseTemp), ...
    lnk = link(satTx,gsRx);
    [e, time] = ebno(lnk);         

    Generate a random sequence of pointing losses for transmit and receiver antennas.

    satAntPtErrRad = deg2rad(satAntPtErr);
    satRanAngle = (satAntPtErrRad)*randn(1,length(time));           % Random pointing angle error, radians
    satRanAngle = filter(ones(1,10)/sqrt(10),1,satRanAngle);        % Model control loop filtering
    satBeamWidth = (waveLen/(satAntDiam*sqrt(satAntEff)));          % 3 dB beamwidth, radians
    satPeakGain = 10*log10(satAntEff*((pi*satAntDiam)/waveLen)^2);  % Peak gain, dBi
    satRanAntGain = 10*log10(satAntEff*(((pi.*satAntDiam)./ ...
        waveLen).^2).*exp(-2.76*((satRanAngle./satBeamWidth).^2))); % Antenna gain at off-boresight angle, dBi,
                                                                    % from Satellite Communications, Gagliardi
    satRanPtLoss = satPeakGain - satRanAntGain;                     % Random pointing loss, dB
    gsAntPtErrRad = deg2rad(gsAntPtErr);
    gsRanAngle = (gsAntPtErrRad)*randn(1,length(time));             % Random pointing angle error, radians
    gsRanAngle = filter(ones(1,10)/sqrt(10),1,gsRanAngle);          % Model control loop filtering
    gsBeamWidth = waveLen/(gsAntDiam*sqrt(gsAntEff));               % 3 dB beamwidth, radians
    gsPeakGain = 10*log10(gsAntEff*((pi*gsAntDiam)/waveLen)^2);     % Peak gain, dBi
    gsRanAntGain = 10*log10(gsAntEff*(((pi.*gsAntDiam)./ ...
        waveLen).^2).*exp(-2.76*((gsRanAngle./gsBeamWidth).^2)));   % Antenna gain at off-boresight angle, dBi,
                                                                    % from Satellite Communications, Gagliardi
    gsRanPtLoss = gsPeakGain - gsRanAntGain;                        % Random pointing loss, dB   

    Compute composite pointing losses.

    totRanPtLoss = satRanPtLoss + gsRanPtLoss; 

    Compute the link margin.

    margin = e-totRanPtLoss-gsRx.RequiredEbNo;
    title("Link Margin vs. Time");
    ylim([-3 16]);
    ylabel("Link Margin (dB)");
    grid on;

    Figure contains an axes object. The axes object with title Link Margin vs. Time contains an object of type line.

    Input Arguments

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    Link analysis object, specified as a Link object vector or scalar.

    Time at which the output is calculated, specified as a datetime scalar. If no time zone is specified in timeIn, the time zone is assumed to be UTC.

    Output Arguments

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    Energy per bit to noise power spectral density (Eb/No), returned as a scalar, vector, or matrix. If timeIn is not specified, e is a row vector or a matrix.

    Time samples of the output Eb/No, returned as a scalar or vector. If time history of Eb/No is returned, timeOut is a row vector.


    When the AutoSimulate property of the satellite scenario is true, the Eb/No history from StartTime to StopTime is returned. When the property is false, the Eb/No history from StartTime to SimulationTime is returned.


    The Eb/No in dB is calculated as

    EbNo = txPower + txAntennaGain - txSystemLoss - pathloss + rxAntGaintoNoiseTempRatio - 10*log10(K) - rxSystemLoss - 10*log10(bitRate) - 60


    • txPower is the transmitter power in dBW.

    • txAntennaGain is the transmitter antenna gain in dB.

    • txSystemLoss is the transmitter system loss in dB.

    • pathloss is the path loss in dB.

    • rxAntGaintoNoiseTempRatio is the receiver antenna gain to noise temperature ratio.

    • K is the Boltzmann constant.

    • rxSystemLoss is the receiver system loss in dB.

    • bitRate is the bit rate in Mbps.

    Version History

    Introduced in R2021a