NB-IoT NTN Link Budget Analysis

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This example shows how to compute the link budget for narrowband Internet-of-Things (NB-IoT) equipment in non-terrestrial networks (NTN) using the parameter sets described in 3GPP TR 36.763. To improve the radio coverage in NB-IoT systems, the transmitter repeats the same signal over additional periods. This example calculates and reports the minimum number of additional repetitions required for an NB-IoT transmission.

Set Satellite Payload Characteristics

Set the payload characteristics for satellite transmissions. To use the satellite parameter sets provided in TR 36.763 Section 6.2.1 [1], set satelliteParamsSource to one of these values. Alternatively, you can specify satelliteParamsSource as Custom, but you must then manually update the values of the EIRPDensity, RxGByT, and Altitude fields of the satellite structure.

Set 1 GEO
Set 1 LEO-1200
Set 1 LEO-600
Set 2 GEO
Set 2 LEO-1200
Set 2 LEO-600
Set 3 GEO
Set 3 LEO-1200
Set 3 LEO-600
Set 4 LEO-600
Set 5 MEO-10000

By default, this example uses the Set 2 GEO satellite parameters in TR 36.763 Table 6.2-5. This example assumes that the satellite is moving in a circular orbit.

satelliteParamsSource = "Set 2 GEO";
% When you set satelliteParamsSource to Custom, provide these fields.
satellite = struct;
satellite.EIRPDensity = 59;   % dBW/MHz
satellite.RxGByT = 19;        % dB/K
satellite.Altitude = 35786e3; % m

Set User Equipment Payload Characteristics

Set the payload characteristics for user equipment (UE) transmissions. TR 36.763 defines two UE power classes: PC5 and PC3. PC5 has a transmit power of 20 dBm, and PC3 has a transmit power of 23 dBm.

By default, this example uses the UE power class PC3 with a noise figure of 7 dB.

ue = struct;
ue.TxPower = 23;               % dBm
ue.TxGain = 0;                 % dBi
ue.TxCableLoss = 0;            % dB
ue.RxNoiseFigure = 7;          % dB
ue.RxGain = 0;                 % dBi
ue.RxAntennaTemperature = 290; % K
ue.RxAmbientTemperature = 290; % K
ue.Altitude = 0;               % m

Set Link Characteristics

Set the link characteristics by defining the link direction, elevation angle, bandwidth, frequency, and atmospheric losses.

The transmission bandwidths for NB-IoT are:

Downlink — 180 kHz
Uplink — 3.75 kHz, 15 kHz, 45 kHz, 90 kHz, or 180 kHz

By default, this example uses the S-band downlink scenario for a bandwidth of 180 kHz. This example supports a vector of elevation angles to compute the link statistics of IoT devices at different locations within a cell.

% Enable or disable the ITU-R P.618 propagation losses
useP618PropagationLosses = false;           % 0 (false), 1 (true)

% Set the link characteristics
link = struct;
link.Direction = "downlink";    % "uplink", "downlink"
link.ElevationAngle = [10.95 20];         % degrees (Vector of elevation angles)
link.Frequency = 2e9;                     % Hz
link.Bandwidth = 180e3;                   % Hz
link.ShadowMargin = 3;                    % dB
link.AdditionalLosses = 0;                % dB
link.PolarizationLoss = 3;                % dB

if useP618PropagationLosses == 0
    % Set these fields when you set useP618PropagationLosses to false.
    link.ScintillationLosses = 2.2;           % dB
    link.AtmosphericLosses = 0.2;             % dB
else
    % Set these fields when you set useP618PropagationLosses to true. In
    % this case, the example uses digital maps to calculate the
    % attenuation.
    link.P618Configuration = p618Config;
    link.P618Configuration.Latitude = 51.5;                   % degrees
    link.P618Configuration.Longitude = -0.14;                 % degrees
    link.P618Configuration.GasAnnualExceedance = 1;
    link.P618Configuration.CloudAnnualExceedance = 1;
    link.P618Configuration.ScintillationAnnualExceedance = 1;
    link.P618Configuration.TotalAnnualExceedance = 1;
    link.P618Configuration.PolarizationTiltAngle = 0;         % degrees
    link.P618Configuration.AntennaDiameter = 1;               % meters
    link.P618Configuration.AntennaEfficiency = 0.5;
end

Set NB-IoT Data Channel Parameters

To calculate the reference carrier-to-noise ratio (CNR) for an NB-IoT data channel transmission, set these NB-IoT parameters.

Modulation scheme
Transport block size ( $N_{bits}$ )
Number of symbols used for transmission ( $N_{symbols}$ )
Number of repetitions ( $N_{Rep}$ )
Number of subframes in downlink ( $N_{SF}$ )
Number of resource units in uplink ( $N_{RU}$ )

This example considers three modulation schemes: binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), and quadrature amplitude modulation (16-QAM). The NB-IoT system uses these modulation schemes for data transmission. The modulation orders of BPSK, QPSK, and 16-QAM are 1, 2, and 4, respectively.

modulation = "QPSK"; % Modulation scheme
nBits = 208;                       % Number of useful bits (transport block size)
nSymbols = 160;                    % Number of symbols used for transmission
nRep = 1;                          % Number of repetitions
nSF = 8;                           % Number of subframes (used in downlink)
nRU = 1;                           % Number of resource units (used in uplink)

Set these NB-IoT waveform parameters.

Number of used data subcarriers ( $N_{DSC}$ )
Number of fast Fourier transform (FFT) bins ( $N_{FFT}$ )
Data symbol duration ( $T_{d}$ )
Cyclic prefix duration ( $T_{CP}$ )
Oversampling factor ( $OSR$ )

nDSC = 72;                         % Number of data subcarriers (6 resource blocks)
nFFT = 128;                        % FFT length
tsamp = 1/1.92e6;                  % Sample time (in s)
td = nFFT*tsamp;                   % Data symbol duration (in s)
nCP = 9;                           % Number of cyclic prefix samples
tCP = nCP*tsamp;                   % Cyclic prefix duration (in s)
osr = 1;                           % Oversampling factor

In the presence of additive white Gaussian noise without any channel coding, the modulation schemes return these results:

BPSK achieves a bit error rate of 1e-6 at an $\frac{E_{b}}{N_{o}}$ of 10.5 dB.
QPSK achieves a bit error rate of 1e-6 at an $\frac{E_{b}}{N_{o}}$ of 10.5 dB.
16-QAM achieves a bit error rate of 1e-6 at an $\frac{E_{b}}{N_{o}}$ of 14.4 dB.

As a result, this example uses an ${(\frac{E_{b}}{N_{o}})}_{ref}$ value of 10.5 dB or 14.4 dB depending on the modulation scheme.

% Reference Eb/No in dB
if modulation == "16-QAM"
    % Modulation scheme is 16-QAM
    ebnoRef = 14.4;
else 
    % Modulation scheme is either BPSK or QPSK
    ebnoRef = 10.5;
end

Compute Reference CNR

To compute the reference CNR in dB, use this equation:

${(\frac{C}{N})}_{ref} = {(\frac{E_{b}}{N_{o}})}_{ref} + 10 \log_{10} (m R_{eff}) + 10 \log_{10} (\frac{N_{DSC}}{N_{FFT}}) + 10 \log_{10} (\frac{T_{d}}{T_{d} + T_{CP}}) - 10 \log_{10} (OSR)$ ,

where:

${(\frac{E_{b}}{N_{o}})}_{ref}$ is the value in dB for the desired bit error rate.
$m$ is the modulation order.
$R_{eff}$ is the effective code rate.

The effective code rate for NB-IoT downlink, as defined in TS 36.213 Section 7.1.7 [3], is

$R_{eff} = \frac{N_{bits} + N_{CRC}}{N_{SF} N_{symbols} m N_{Rep}}$ ,

where:

$N_{bits}$ is the number of useful bits to transmit (transport block size).
$N_{CRC}$ is the number of bits used for check code (24 for NB-IoT).
$N_{SF}$ is the number of allocated subframes.
$N_{symbols}$ is the number of symbols.
$N_{Rep}$ is the number of repetitions.

Similarly, the effective code rate for NB-IoT uplink is

$R_{eff} = \frac{N_{bits} + N_{CRC}}{N_{RU} N_{symbols} m N_{Rep}}$ ,

where $N_{RU}$ is the number of allocated resource units. For 1-tone transmission, $N_{symbols}$ is 96, and for 3-tone transmission, $N_{symbols}$ is 144.

% Modulation order
m = 1;
if modulation == "QPSK"
    m = 2;
elseif modulation == "16-QAM"
    m = 4;
end

% Number of CRC bits
nCRC = 24;

% Calculate the effective code rate and the reference CNR
if link.Direction == "downlink"
    Reff = (nBits + nCRC)/(nSF*nSymbols*m*nRep);
else % "uplink"
    Reff = (nBits + nCRC)/(nRU*nSymbols*m*nRep);
end
cnrRef = ebnoRef + 10*log10(m*Reff) + 10*log10(nDSC/nFFT) + ...
        10*log10(td/(td + tCP)) - 10*log10(osr);

disp("Reference CNR: " + cnrRef + " dB")

Reference CNR: 0.2889 dB

Compute Link Budget

Calculate CNR using the characteristics of the satellite, UE, and link for each elevation angle. To compute CNR, this example uses the satelliteCNRConfig object and the satelliteCNR function.

To calculate the CNR in dB, use this equation, described in TR 38.821 Section 6.1.3.1 [2]:

$CNR = EIRP + \frac{G}{T} - k - {PL}_{FS} - {PL}_{A} - {PL}_{SM} - {PL}_{SL} - {PL}_{AD} - B$ ,

where:

$EIRP$ is the effective isotropic radiated power in dBW.
$\frac{G}{T}$ is the antenna-gain-to-noise temperature in dB/K.
$k$ is the Boltzmann constant with the value of -228.6 dBW/K/Hz.
${PL}_{FS}$ is the free space path loss (FSPL) in dB.
${PL}_{A}$ is the atmospheric path loss due to gases and shadowing margin in dB.
${PL}_{SM}$ is the shadowing margin in dB.
${PL}_{SL}$ is the scintillation loss in dB.
${PL}_{AD}$ is the additional loss in dB.
$B$ is the channel bandwidth in dBHz.

To calculate antenna-gain-to-noise-temperature, use this equation:

$\frac{G}{T} = G_{R} - N_{f} - 10 \log_{10} (T_{0} + (T_{a} - T_{0}) 10^{- 0.1 N_{f}})$ ,

where:

$G_{R}$ is the receive antenna gain in dBi.
$N_{f}$ is the noise figure in dB.
$T_{0}$ is the ambient temperature in degrees Kelvin.
$T_{a}$ is the antenna temperature in degrees Kelvin.

The receive antenna gain depends on the type of antenna used, and accounts for polarization loss.

To compute the effective isotropic radiated power in dBW, use this equation:

$EIRP = P_{T} - L_{C} + G_{T}$ ,

where:

$P_{T}$ is the transmit antenna power in dBW.
$L_{C}$ is the cable loss in dB.
$G_{T}$ is the transmit antenna gain in dBi.

% Get the satellite parameters based on satelliteParamsSource
if satelliteParamsSource ~= "Custom"
    satellite = getSatelliteParams(satelliteParamsSource);
end

% Calculate EIRP when the satellite is a transmitter (dB)
% To get a value in decibels from density: 
% Value in dB = Value in dB/MHz + 10*log10[BW in MHz]
satellite.EIRP = satellite.EIRPDensity + 10*log10(link.Bandwidth/1e6);

% Calculate EIRP when the UE is a transmitter (dB)
% To get a value in decibels from dBm: dB = dBm - 30
ue.EIRP = (ue.TxPower-30) + ue.TxGain - ue.TxCableLoss;

% Calculate the gain-to-noise temperature or the figure of merit for the UE
% as a receiver.
ue.RxGByT = ue.RxGain - ue.RxNoiseFigure ...
    - 10*log10(ue.RxAmbientTemperature + ...
    (ue.RxAntennaTemperature-ue.RxAmbientTemperature)*10^(-0.1*ue.RxNoiseFigure));

% Set the transmitter and the receiver based on the link direction
if link.Direction == "uplink"
    tx = ue;
    rx = satellite;
else
    tx = satellite;
    rx = ue;
end

% Range of elevation angles
elevAngles = link.ElevationAngle(:);
numElevAngles = numel(elevAngles);

% Calculate the distance from the satellite to the UE for all elevation
% angles
d = slantRangeCircularOrbit(elevAngles,satellite.Altitude,ue.Altitude); % m

% Get the total atmospheric losses for each elevation angle
totalAtmosphericLoss = zeros(numElevAngles,1);
if useP618PropagationLosses == 1
    % Download and extract the digital maps, if not available on the path
    maps = exist("maps.mat","file");
    p836 = exist("p836.mat","file");
    p837 = exist("p837.mat","file");
    p840 = exist("p840.mat","file");
    matFiles = [maps p836 p837 p840];
    if ~all(matFiles)
        if ~exist("ITURDigitalMaps.tar.gz","file")
            url = "https://www.mathworks.com/supportfiles/spc/P618/ITURDigitalMaps.tar.gz";
            websave("ITURDigitalMaps.tar.gz",url);
            untar("ITURDigitalMaps.tar.gz")
        else
            untar("ITURDigitalMaps.tar.gz")
        end
    end
    link.P618Configuration.Frequency = link.Frequency;
    elevAnglesToConsider = elevAngles;
    if any(elevAngles < 5)
        warning("The prediction method for scintillation losses is valid for elevation " + ... 
            "angle greater than 5 degree. For elevation angle less than 5 degree, the " + ... 
            "nearest valid value of 5 degree will be used in the computation.")
        elevAnglesToConsider(elevAngles < 5) = 5;
    end
    for index = 1:numElevAngles
        link.P618Configuration.ElevationAngle = elevAnglesToConsider(index);
        pl = p618PropagationLosses(link.P618Configuration);
        totalAtmosphericLoss(index) = pl.At;
    end
else
    totalAtmosphericLoss(:) = link.AtmosphericLosses + link.ScintillationLosses;
end

% Define the configuration parameters
config = satelliteCNRConfig;
config.TransmitterPower = tx.EIRP;
config.TransmitterAntennaGain = 0;
config.Frequency = link.Frequency/1e9;          % GHz
config.GainToNoiseTemperatureRatio = rx.RxGByT;
config.Bandwidth = link.Bandwidth/1e6;          % MHz

% Compute the CNR and the free space path loss for each elevation angle
cnr = zeros(numElevAngles,1);
pathLoss = cnr;
for index = 1:numElevAngles
    config.Distance = d(index)/1e3;                                         % km
    config.MiscellaneousLoss = totalAtmosphericLoss(index) + ...
         link.PolarizationLoss + link.ShadowMargin + link.AdditionalLosses;
    [cnr(index),cnrInfo] = satelliteCNR(config);
    pathLoss(index) = cnrInfo.FSPL;
end

% Report the results in a table
table(elevAngles,cnr,pathLoss,VariableNames=["Elevation Angle (degrees)", "CNR (dB)", "FSPL (dB)"])

ans=2×3 table
    Elevation Angle (degrees)    CNR (dB)    FSPL (dB)
    _________________________    ________    _________

              10.95               -8.538      190.61  
                 20              -8.3363      190.41

% Plot CNR as a function of the elevation angle
plot(elevAngles,cnr,"*")
title("CNR As a Function of Elevation Angle")
xlabel("Elevation Angle (degrees)")
ylabel("CNR (dB)")
ylim([min(cnr)-0.2 max(cnr)+0.2])
xlim([min(elevAngles)-1 max(elevAngles)+1])
grid on

Figure contains an axes object. The axes object with title CNR As a Function of Elevation Angle, xlabel Elevation Angle (degrees), ylabel CNR (dB) contains a line object which displays its values using only markers.

Compute Link Margin and NB-IoT Repetitions

The link margin (in dB) is the difference between the calculated CNR and the reference CNR. The link is closed when the link margin is zero or positive.

To calculate the link margin, use this equation:

$LinkMargin = \frac{C}{N} - {(\frac{C}{N})}_{ref}$ .

% Compute link margin
linkMargin = cnr - cnrRef;

The minimum number of additional NB-IoT repetitions ( $N_{Rep_Add}$ ) required for link closure is $⌈ N_{Rep} (10^{\frac{- LinkMargin}{10}} - 1) ⌉$ , where $⌈ ⌉$ represents the ceil function. The overall repetitions required for link closure is the sum of $N_{Rep_Add}$ and $N_{Rep}$ .

% Minimum number of additional repetitions required for link closure
minRepetitions = 10.^(-linkMargin./10);
idx = linkMargin >= 0;
additionalRepetitions = minRepetitions;
additionalRepetitions(idx) = 0;
% When the link margin is negative, improve the CNR by adding repetitions.
% Calculate the required number of additional repetitions.
additionalRepetitions(~idx) = ceil(nRep*(additionalRepetitions(~idx)-1));

% Report the results in a table with this format.
% Elevation Angle | Link Margin | Min. Additional Repetitions Required
table(elevAngles,linkMargin,additionalRepetitions, ...
    VariableNames=["Elevation Angle (degrees)", ...
    "Link Margin (dB)", "NRep_Add"])

ans=2×3 table
    Elevation Angle (degrees)    Link Margin (dB)    NRep_Add
    _________________________    ________________    ________

              10.95                  -8.8269            7    
                 20                  -8.6252            7

Further Exploration

In this example, you calculated the link budget as a variation of the elevation angle. Consider exploring the example using these variations.

Observe the link margin by varying the satellite parameter sets for different orbits.
Add ITU-R P.618 propagation losses by setting useP618PropagationLosses to true.
Analyze the CNR and the minimum number of additional repetitions for NB-IoT under different conditions by varying the link direction, the bandwidth, and the elevation angles.
Check the link characteristics of enhanced machine-type communications by using the relevant transmission bandwidth. For the downlink transmission, use a 1080 kHz bandwidth. For the uplink transmission, use bandwidths up to 1080 kHz with all permissible smaller resource allocations. The smaller resource allocations for an uplink transmission up to 1080 kHz include 360 kHz, 180 kHz, 90 kHz, 45 kHz, and 30 kHz.

References

[1] 3rd Generation Partnership Project (3GPP). Study on Narrow-Band Internet of Things (NB-IoT)/Enhanced Machine Type Communication (eMTC) Support for Non-Terrestrial Networks (NTN). 3GPP TR 36.763. 3GPP, accessed 23 September 2021. https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3747.

[2] 3rd Generation Partnership Project (3GPP). Solutions for NR to Support Non-Terrestrial Networks (NTN). 3GPP TR 38.821. 3GPP, accessed 8 May 2021. https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3525.

[3] 3rd Generation Partnership Project (3GPP). Evolved Universal Terrestrial Radio Access (E-UTRA) Physical Layer Procedures. 3GPP TS 36.213. 3GPP, accessed 21 May 2021. https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=2427.

[4] International Telecommunication Union Radiocommunication Sector (ITU-R). Propagation Data Required for the Design Systems in the Land Mobile-Satellite Service. Recommendation ITU-R P.618-11 (08/2019). https://www.itu.int/rec/R-REC-P.681/en.

Local Function

getSatelliteParams — Gets the satellite parameters defined for the selected satelliteParamsSource in Section 6.2.1 of the 3GPP TR 36.763 specification.

function satellite = getSatelliteParams(satelliteParamsSource)
    
    if satelliteParamsSource == "Set 1 GEO"
        % Table 6.2-4, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 59;    % dBW/MHz
        satellite.RxGByT = 19;         % dB/K
        satellite.Altitude = 35786e3;  % m
    elseif satelliteParamsSource == "Set 1 LEO-1200"
        % Table 6.2-4, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 40;    % dBW/MHz
        satellite.RxGByT = 1.1;        % dB/K
        satellite.Altitude = 1200e3;   % m
    elseif satelliteParamsSource == "Set 1 LEO-600"
        % Table 6.2-4, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 34;    % dBW/MHz
        satellite.RxGByT = 1.1;        % dB/K
        satellite.Altitude = 600e3;    % m
    elseif satelliteParamsSource == "Set 2 GEO"
        % Table 6.2-5, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 53.5;  % dBW/MHz
        satellite.RxGByT = 14;         % dB/K
        satellite.Altitude = 35786e3;  % m
    elseif satelliteParamsSource == "Set 2 LEO-1200"
        % Table 6.2-5, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 34;    % dBW/MHz
        satellite.RxGByT = -4.9;       % dB/K
        satellite.Altitude = 1200e3;   % m
    elseif satelliteParamsSource == "Set 2 LEO-600"
        % Table 6.2-5, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 28;    % dBW/MHz
        satellite.RxGByT = -4.9;       % dB/K
        satellite.Altitude = 600e3;    % m
    elseif satelliteParamsSource == "Set 3 GEO"
        % Table 6.2-6, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 59.8;  % dBW/MHz
        satellite.RxGByT = 16.7;       % dB/K
        satellite.Altitude = 35786e3;  % m
    elseif satelliteParamsSource == "Set 3 LEO-1200"
        % Table 6.2-6, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 33.7;  % dBW/MHz
        satellite.RxGByT = -12.8;      % dB/K
        satellite.Altitude = 1200e3;   % m
    elseif satelliteParamsSource == "Set 3 LEO-600"
        % Table 6.2-6, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 28.3;  % dBW/MHz
        satellite.RxGByT = -12.8;      % dB/K
        satellite.Altitude = 600e3;    % m
    elseif satelliteParamsSource == "Set 4 LEO-600"
        % Table 6.2-7, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 21.45; % dBW/MHz
        satellite.RxGByT = -18.6;      % dB/K
        satellite.Altitude = 600e3;    % m
    else % "Set 5 MEO-10000"
        % Table 6.2-8, TR 36.763
        satellite = struct;
        satellite.EIRPDensity = 45.4;  % dBW/MHz
        satellite.RxGByT = 3.8;        % dB/K
        satellite.Altitude = 10000e3;  % m
    end

end

NB-IoT NTN Link Budget Analysis

Set Satellite Payload Characteristics

Set User Equipment Payload Characteristics

Set Link Characteristics

Set NB-IoT Data Channel Parameters

Compute Reference CNR

Compute Link Budget

Compute Link Margin and NB-IoT Repetitions

Further Exploration

References

Local Function

See Also

Functions

Objects