p618SiteDiversityOutage

Calculate outage probability due to rain attenuation with site diversity

Syntax

Outage = p618SiteDiversityOutage(cfgsd)

Outage = p618SiteDiversityOutage(cfgsd,Name,Value)

Description

Outage = p618SiteDiversityOutage(cfgsd) returns the outage probability due to rain attenuation with site diversity. The function calculates this value as per the ITU-R P.618-14 recommendation [1].

This function requires a MAT file with digital maps from International Telecommunication Union (ITU) documents. If it is not available on the path, download and uncompress the data file from https://www.mathworks.com/supportfiles/spc/P618/ITURP618v14DigitalMaps.tar.gz to a location on the MATLAB^® path.

Note

If you are using MATLAB in version R2025b or earlier, refer to the Tips section for instructions on how to run the examples by using ITU-R P.618-13.

Outage = p618SiteDiversityOutage(cfgsd,Name,Value) specifies additional options using one or more name-value pair arguments.

Examples

Outage Probability Due to Rain Attenuation with Site Diversity

This example requires a MAT file with digital maps from ITU documents. If the MAT file is not available on the path, execute the following commands to download and extract it.

matFile = exist('iturp618v14Maps.mat','file');
if ~matFile
    if ~exist('ITURP618v14DigitalMaps.tar.gz','file')
        url = 'https://www.mathworks.com/supportfiles/spc/P618/ITURP618v14DigitalMaps.tar.gz';
        websave('ITURP618v14DigitalMaps.tar.gz',url)
        untar('ITURP618v14DigitalMaps.tar.gz')
    else
        untar('ITURP618v14DigitalMaps.tar.gz')
    end
    addpath(cd)
end

This example shows how to calculate outage probability due to rain attenuation with site diversity.

The p618SiteDiversityOutage function applies to unbalanced and balanced systems and computes the joint probability of exceeding attenuation thresholds.

Configure P.618 Site Diversity Parameters

Create a default P.618 site diversity configuration object. Change property values, and then display the object properties.

cfgSD = p618SiteDiversityConfig;
cfgSD.Frequency = 25e9;                 % Signal frequency in Hz   
cfgSD.Latitude = [30 60];               % North direction
cfgSD.Longitude = [120 150];            % East direction
cfgSD.PolarizationTiltAngle = [-90 90];
cfgSD.AttenuationThreshold = [7 7];     % Attenuation threshold on the two links
cfgSD.SiteDistance = 50;                % Separation between the two sites
disp(cfgSD);

  p618SiteDiversityConfig with properties:

                Frequency: 2.5000e+10
           ElevationAngle: [52.4099 52.4852]
                 Latitude: [30 60]
                Longitude: [120 150]
    PolarizationTiltAngle: [-90 90]
             SiteDistance: 50
     AttenuationThreshold: [7 7]

Calculate Outage Probability

Calculate the outage probability due to rain attenuation for the specified site diversity configuration.

outage = p618SiteDiversityOutage(cfgSD, ...
                                RainAnnualExceedances=[0.01 0.01 0.03 0.05 0.1 0.2], ...
                                RainProbability1=0.3, ...
                                RainProbability2=0.4);
disp(outage);

    0.0030

Calculate Outage Probability with Site Diversity Using Name-Value Pair Arguments

This example requires a MAT file with digital maps from ITU documents. If the MAT file is not available on the path, execute the following commands to download and extract it.

matFile = exist('iturp618v14Maps.mat','file');
if ~matFile
    if ~exist('ITURP618v14DigitalMaps.tar.gz','file')
        url = 'https://www.mathworks.com/supportfiles/spc/P618/ITURP618v14DigitalMaps.tar.gz';
        websave('ITURP618v14DigitalMaps.tar.gz',url)
        untar('ITURP618v14DigitalMaps.tar.gz')
    else
        untar('ITURP618v14DigitalMaps.tar.gz')
    end
    addpath(cd)
end

Create a default P.618 site diversity configuration object. Change the signal frequency to 25 GHz.

cfgsd = p618SiteDiversityConfig;
cfgsd.Frequency = 25e9;

Specify the separation between two sites as 50 km and the attenuation threshold on the two links as [9 9] dB.

cfgsd.SiteDistance = 50;
cfgsd.AttenuationThreshold = [9 9];

Calculate the outage probability for the specified site diversity configuration.

outage = p618SiteDiversityOutage(cfgsd,RainAnnualExceedances=[0.01 0.05 0.2], ...
                                RainProbability1=0.3, ...
                                RainProbability2=0.5) 

outage = 
0.0339

Input Arguments

cfgsd — P.618 site diversity configuration

p618SiteDiversityConfig object

P.618 site diversity configuration required for the calculation of the outage probability due to rain attenuation, specified as a p618SiteDiversityConfig object.

Name-Value Arguments

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: 'RainAnnualExceedances',[0.01 0.02 0.03 0.05] specifies the average annual time percentage of excess for the rain attenuation.

RainAnnualExceedances — Average annual time percentage of excess for rain attenuation

nonnegative vector

Average annual time percentage of excess for the rain attenuation, specified as the comma-separated pair consisting of 'RainAnnualExceedances' and a nonnegative vector. The values in this vector must be less than the probability of rain at the two sites.

If the local data is not available as an input, the function uses [0.01 0.02 0.03 0.05 0.1 0.2 0.3 0.5 1 2 3 5] as the default vector.

To understand how annual exceedance ranges map to availability ranges, see Correlation Between Annual Exceedance and Availability.

Data Types: double | single

RainAttenuations1 — Rain attenuations at site 1

nonnegative vector

Rain attenuations (in dB) at site 1, specified as the comma-separated pair consisting of 'RainAttenuations1' and a nonnegative vector. This value specifies the rain attenuation exceeded for the percentages given in the RainAnnualExceedances name-value pair argument. The dimension of this value must match that of the RainAnnualExceedances.

If the local data is not available as an input, the function uses the method as defined in section 2.2.1.1 of the ITU-R P.618 [1] recommendation to calculate the rain attenuations for site 1.

Note

If you do not specify RainAttenuations1, then RainAnnualExceedances must be in the range from 0.01% to 5%.

Data Types: double | single

RainAttenuations2 — Rain attenuations at site 2

nonnegative vector

Rain attenuations (in dB) at site 2, specified as the comma-separated pair consisting of 'RainAttenuations2' and a nonnegative vector. This value specifies the rain attenuation exceeded for the percentages given in the RainAnnualExceedances name-value pair argument. The dimension of this value must match that of the RainAnnualExceedances.

If the local data is not available as an input, the function uses the method as defined in section 2.2.1.1 of the ITU-R P.618 recommendation to calculate the rain attenuations for site 2.

Note

If you do not specify RainAttenuations2, then RainAnnualExceedances must be in the range from 0.01% to 5%.

Data Types: double | single

RainProbability1 — Probability of rain for site 1

nonnegative scalar

Probability of (in %) rain for site 1, specified as the comma-separated pair consisting of 'RainProbability1' and a nonnegative scalar.

If the local measured rainfall rate data is not available as an input, the function uses the digital maps as defined in ITU-R P.837 Annex 1 [2] to calculate the rain probability for the sites.

Data Types: double | single

RainProbability2 — Probability of rain for site 2

nonnegative scalar

Probability of (in %) rain for site 2, specified as the comma-separated pair consisting of 'RainProbability2' and a nonnegative scalar.

If the local measured rainfall rate data is not available as an input, the function uses the digital maps as defined in ITU-R P.837 Annex 1 [2] to calculate the rain probability for the sites.

Data Types: double | single

Output Arguments

Outage — Outage probability due to rain attenuation with site diversity

nonnegative scalar

Outage probability due to rain attenuation with site diversity, returned as a nonnegative scalar. This argument predicts the joint probability (P_r(A₁≥ a₁, A₂ ≥ a₂)), where the attenuation on the path of the site 1 must exceed a₁ and the attenuation on the path of the site 2 must exceed a₂.

More About

Correlation Between Annual Exceedance and Availability

Availability is the average annual time percentage the link must stay closed. This equation gives the correlation between availability and annual exceedance.

Annual Exceedance (%) = 100 (%) − Availability (%)

The fraction of time during which a preselected threshold is exceeded in an average year is referred to as the annual time percentage of excess, and represents the exceedance or outage of the propagation parameter in consideration.

This table shows how the exceedance property ranges map to the availability ranges.

Attenuation Type	Annual Exceedance	Availability
Gas	[0.01, 99]	[1, 99.99]
Cloud	[0.01, 99]	[1, 99.99]
Rain	[0.001, 5]	[95, 99.999]
Scintillation	[0.01, 50]	[50, 99.99]
Total	[0.001, 50]	[50, 99.999]

Tips

For MATLAB version R2025b or earlier, the p618SiteDiversityOutage object uses ITU-R P.618-13 for its calculations instead of ITU-R P.618-14.

Use this code to download and unzip the MAT files containing digital maps from the ITU-R P.618-13 documents. The code also adds the extracted files to your MATLAB 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
    addpath(cd);
end

To run the examples, replace the corresponding code fragment that downloads and unzips the latest digital maps from ITU-R P.618-14 in each example with this to ensure compatibility with ITU-R P.618-13.

References

[1] International Telecommunication Union, ITU-R Recommendation P.618 (08/2023).

[2] International Telecommunication Union, ITU-R Recommendation P.837 (06/2017).

[3] International Telecommunication Union, ITU-R Recommendation P.1511 (08/2024).

[4] International Telecommunication Union, ITU-R Recommendation P.840 (08/2023).

[5] International Telecommunication Union, ITU-R Recommendation P.453 (08/2019).

[6] International Telecommunication Union, ITU-R Recommendation P.839 (09/2013).

[7] International Telecommunication Union, ITU-R Recommendation P.838 (03/2005).

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Supports only MEX code generation.

Version History

Introduced in R2021a

R2026a: Support for ITU-R P.618-14

The p618SiteDiversityOutage feature now uses ITU-R P.618-14 for its calculations.