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CV2XMode4_Step2.m
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function [ deltaCOL , CBR ] = CV2XMode4_Step2( beta , lambda , Pt , S , distance, Psen , step_dB , noise , coding , deltaPRO )
% CV2XMode4_Step2 is a script that calculates the probability of collision
% considering only Step 2 of C-V2X or LTE-V Mode 4 and the Channel Busy Ratio
% based on the models described in the following paper:
%
% Manuel Gonzalez-Martín, Miguel Sepulcre, Rafael Molina-Masegosa, Javier Gozalvez,
% "Analytical Models of the Performance of C-V2X Mode 4 Vehicular Communications",
% arXiv:1807.06508 [cs.NI], Submitted on 17 July 2018, https://arxiv.org/abs/1807.06508
%
% CV2XMode4_Step2 is called from the main script, CV2XMode4.
%
% Input parameters:
% lambda: packet transmission frequency in Hz. .
% Pt: transmission power in dBm.
% S: number of sub-channels. 4.
% distance: distance between tramsmitter and receiver in meters. It can be a vector with multiple distances.
% Psen: sensing threshold in dBm.
% step_dB: discrete steps to compute the PDF of the SNR and SINR in dB.
% noise: noise corresponding to the DATA field of each message. Assumes a noise figure of 9dB and 10MHz channel (background noise of -95dBm). The total number of RBs in 10MHz is 50.
% coding: ID of the coding used to identify the BLER curve
% deltaPRO: probability of packet loss due to propagation effects for different Tx-Rx distances
%
% Output metrics:
% deltaCOL: probability of packet loss due to packet collisions for different Tx-Rx distances (between 0 and 1)
% CBR: Channel Busy Ratio (between 0 and 1)
%
% The equations that are identified with a number between brackets in this script are the ones
% that also appear in the paper so that they can be easily identified.
N = S * 1000/lambda; % Total number of resources in 1000ms. Equation (28)
Nc = 0.2*N; % Number of candidate resources (always 20% of N as specified in 3GPP standards)
d_aux = -1500:1500; % Take into account interfering vehicles up to 1500 meters distance, since the interference generated at that thistance is almost null.
[PL, std_dev] = get_PL_SH(d_aux); % Calculates the pathloss and shadowing for a given set of interfering distances following the Winner+ B1 propagation model.
PSR = 0.5 * (1 + erf( (Pt - PL - Psen)./(std_dev*sqrt(2)) ) ); % PSR for all distances in d_aux. Equation (11)
Spsr = beta * sum(PSR) ; % Equation(29.1)
Ne = Spsr/2 + sum(max( 1 - (1:(Spsr/2))/(N-Spsr/2) , 0 )); % Number of excluded resources. Equation (29)
Na = N - Ne; % Number of assignable resources.
CBR = Ne / N; % Channel busy ratio. Equation (34)
Lint_max = round(1000*beta)/beta; % Distance to the farthest interfering vehicle. Up to 1000m distances considered to speed up the calculations.
distance_int_to_rx = [-Lint_max : 1/beta : Lint_max]; % Distances from all the interfering vehicles to the receiving vehicle.
distance_int_to_rx ( (length(distance_int_to_rx)+1)/2) = []; % Remove from the list the position of the receiving vehicle.
R_PSR = xcorr(PSR); % Autocorrelation of the PSR function. Equation (30.2)
R_PSR = R_PSR(2*max(d_aux)+1:end); % Remove left part of the function
R0 = R_PSR(1); % Equation (40)
Ce = ( R_PSR / R0 ) * (beta*Ne*R0/Spsr - Ne*Ne/N) + Ne*Ne/N; % Common excluded resources. Equation (30)
Ca = N - 2*Ne + Ce; % Common available resources. Equation (27)
Cc = Ca * (Nc/Na)^2; % Common candidate resources. Equation (26)
% Calculate probability of collision for Step 2 for each Tx-Rx distance:
for d=1:length(distance)
[PL_E_R(d), std_dev_E_R(d)] = get_PL_SH(distance(d)); % Calculate the pathloss and shadowing for a given Tx-Rx distance following the Winner+ B1 propagation model.
distance_int_to_tx(d,:) = distance_int_to_rx + distance(d); % Distances from all the interfering vehicles to the transmitting vehicle.
% Calculate probability of collision for each interfering vehicle:
for i = 1:length(distance_int_to_rx)
[PL_I_R , std_dev_I_R] = get_PL_SH(distance_int_to_rx(i)); % Pathloss and shadowing for interf and rx
[PL_I_E , std_dev_I_E] = get_PL_SH(distance_int_to_tx(d,i)); % Pathloss and shadowing for interf and tx
Pi_dB = Pt - PL_I_R; % Average received interference
if deltaPRO(d) == 1
p_int(d,i) = 0; % If the proability of packet loss due to propagation is 1
else
[SINR, PDF_SINR] = get_SINRdistribution( Pt-PL_E_R(d) , Pi_dB , std_dev_E_R(d) , std_dev_I_R , noise , Psen , step_dB); % PDF of the SINR experienced by the receiving vehicle
p_SINR(d,i) = get_BLER ( SINR , PDF_SINR , coding , step_dB ); % Probability that the receiver receives a packet with error due to low SINR. Equation (17)
p_int(d,i) = ( p_SINR(d,i) - deltaPRO(d) ) / ( 1 - deltaPRO(d) ); % Probability that the interference generated on the receiver provokes that the packet transmitted by vt cannot be correctly received at vr. Equation (18)
end
tau = lambda;
pSsensing_I_E = 0.5 * (1 + erf(( Pt - PL_I_E - Psen )/(2^0.5*std_dev_I_E))); % PSR for interfering and transmitting vehicles
p_s(i) = 1-(1-1/tau)*pSsensing_I_E; % Probability that transmitter and interferer do not take into account their respective transmissions before selecting a new resource. Equation (24)
p_sim_2(i) = p_s(i) * Cc( round( abs(distance_int_to_tx(d,i)) ) + 1 ) / (Nc*Nc) ; % Equation (23)
end
p_col = p_sim_2 .* p_int(d,:); % Equation (15)
deltaCOL(d) = 1 - prod(1 - p_col); % Probability of packet loss due to collision when only Step 2 is executed. Equation (14)
end
return