get_SINRdistribution.m

function [ SINR , PDF_SINR ] =  get_SINRdistribution( Pr_dBm_avg , Pi_dBm_avg , std_dev_Pr , std_dev_Pi , noise_dBm , sensingThreshold , step_dB )

    % get_SINRdistribution calculates the PDF of the SNR or SINR at the
    % receiver based on average received power and interference levels, noise
    % and other parameters.
    %
    % This is an auxiliary script used by function model80211p to model the 
    % communication performance of IEEE 802.11p using the analytical models described in:
    % 
    %    Miguel Sepulcre, Manuel Gonzalez-Martín, Javier Gozalvez, Rafael Molina-Masegosa, Baldomero Coll-Perales, 
    %    "Analytical Models of the Performance of IEEE 802.11p Vehicle to Vehicle Communications", 
    %    IEEE Transactions on Vehicular Technology, November 2021. DOI: 10.1109/TVT.2021.3124708
    %    Final version available at: https://ieeexplore.ieee.org/document/9599363
    %    Post-print version available at: https://arxiv.org/abs/2104.07923
    %
    % Input parameters:
    %   Pr_dBm_avg: average received power from the transmitting vehicle in dBm
    %   Pi_dBm_avg: average received power from the interfering vehicle in dBm
    %   std_dev_Pr: standard deviation of the shadowing experienced by the signal generated by the transmitting vehicle in dB
    %   std_dev_Pi: standard deviation of the shadowing experienced by the signal generated by the interfering vehicle in dB
    %   noise_dBm: background noise in dBm
    %   sensingThreshold: sensing threshold in dBm
    %   step_dB: discrete steps to compute the PDF of the SNR and SINR (dB)
    %
    % Output metrics:
    %   SINR: Signal-to-Interference and Noise Ratio levels for different distances. It is a matrix where each row represent the SINR levels for a given Tx-Rx distance
    %   PDF_SINR: Probability Density Function of the SINR levels for different distances. It is a matrix where each row represent the PDF for a given Tx-Rx distance

    x = -200:step_dB:200;    % Wide range of values in dB to build the PDFs

    distrib_Pr = normpdf(x,Pr_dBm_avg,std_dev_Pr);        % PDF of the received signal   
    ind = find( x < sensingThreshold);              
    distrib_Pr(ind) = 0;                                  % Remove values below the sensing threshold
    distrib_Pr = distrib_Pr / sum(distrib_Pr) / step_dB;  % Normalize so that the integral between -inf and +inf is equal to 1
    
    if Pi_dBm_avg == -inf     
        % If there is no interference:
        distrib_Pi_noise = zeros(1,length(x));
        distrib_Pi_noise( round( (noise_dBm-x(1))/step_dB ) +1 ) = 1 / step_dB;
    else
        % If there is interference, compute the PDF of the SINR:
        aux = length( find(x <= noise_dBm) );   % Remove values below noise, since Pi+noise will never be lower than noise
        noise = 10^(noise_dBm/10);              % Noise power in linear units
        distrib_Pi_noise = 10.^(x(aux+1:end)/10)./((10.^(x(aux+1:end)/10)-noise)*std_dev_Pi*sqrt(2*pi)) .* exp( -(10*log10(10.^(x(aux+1:end)/10)-noise)-Pi_dBm_avg).^2/(2*std_dev_Pi^2) ); 
        distrib_Pi_noise = [ zeros(1,aux) distrib_Pi_noise];                        % Null probability for values below the noise
        distrib_Pi_noise = distrib_Pi_noise / sum(distrib_Pi_noise) / step_dB;   	% Normalize so that the integral between -inf and +inf is equal to 1
    end

    % Calculate PDF of SINR through the cross-correlation of the PDF of the received power and the PDF of the interference+noise: 
    PDF_SINR = xcorr(distrib_Pr,distrib_Pi_noise);
    PDF_SINR = PDF_SINR / sum(PDF_SINR) / step_dB;    % Normalize so that the integral between -inf and +inf is equal to 1 

    % Adapt the range of the x axes to the values provided by the xcorr function:
    SINR = min(x)*2:step_dB:max(x)*2;


end