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Figure_10_11_12_SINR_BER.m
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Figure_10_11_12_SINR_BER.m
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% =========================================================================
% (c) 2018 Ronald Nissel, https://www.linkedin.com/in/ronaldnissel/
% =========================================================================
% This script simulates the Bit Error Ratio (BER) of pruned DFT spread
% FBMC, SC-FDMA, OFDM and FBMC.
% The Bit Error Probability (BEP) is also calculated if "CalculateTheory"
% is set to true.
% Allows to reproduce Figure 10 11 12 of "Pruned DFT Spread FBMC: Low PAPR,
% Low Latency, High Spectral Efficiency", R. Nissel and M. Rupp, IEEE
% Transactions on Communications
clear; close all;
addpath('./Theory');
%% Parameters
% Simulation
M_SNR_dB = [0:5:30]; % Signal-to-Noise Ratio in dB
NrRepetitions = 30; % Number of Monte Carlo repetitions
CalculateTheory = false; % If set to true, calculate the BEP and the SINR. Set to "false" because the theoretical calculations require large matrix multiplications, increasing the simulation/calculation time significantly.
% FBMC and OFDM Parameters
NrSubcarriers = 256; % Number of subcarriers
QAM_ModulationOrder = 16; % Modulation order, 4, 16, 64,...
SubcarrierSpacing = 15e3; % Subcarrier spacing (15kHz, same as LTE)
CarrierFrequency = 2.5e9; % Carrier Frequency
K_FBMC = 30; % Number of FBMC symbols in time
K_OFDMnoCP = 15; % Number of OFDM symbols in time (no CP)
K_OFDM = 14; % Number of OFDM symbols in time (same as in LTE)
CP_Length = 1/SubcarrierSpacing/14; % LTE CP Length in seconds
CP_Length_FBMC_DFT = 0; % CP in the frequency domain for the DFT spreading aproach. Multiple of two: 0, 2, 4... Can usually be set to zero
SamplingRate = 15e3*14*12*2; % Sampling rate, should approximatly match the power-delay profile of the channel. "*14" due to the CP
% Channel
PowerDelayProfile = 'TDL-A_300ns'; % Power delay profile, either string or vector: 'Flat', 'AWGN', 'PedestrianA', 'PedestrianB', 'VehicularA', 'VehicularB', 'ExtendedPedestrianA', 'ExtendedPedestrianB', or 'TDL-A_xxns','TDL-B_xxns','TDL-C_xxns' (with xx the RMS delay spread in ns, e.g. 'TDL-A_30ns'), or [1 0 0.2] (Self-defined power delay profile which depends on the sampling rate)
Velocity_kmh = 200; % Velocity in km/h
% #########################################################################
% % In the paper:
% M_SNR_dB = [0:1.5:30];
% SamplingRate = 15e3*14*12*8;
% NrRepetitions = 1000;
% CalculateTheory = true;
% #########################################################################
% ######################### For Figure 10 #################################
% CalculateTheory = true;
% #########################################################################
% ######################### For Figure 11 #################################
% Velocity_kmh = 0;
% #########################################################################
%% FBMC Object
FBMC = Modulation.FBMC(...
NrSubcarriers,... % Number of subcarriers
K_FBMC,... % Number of FBMC symbols
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
0,... % Intermediate frequency first subcarrier (Hz)
false,... % Transmit real valued signal
'Hermite-OQAM',... % Prototype filter (Hermite, PHYDYAS, RRC) and OQAM or QAM,
4, ... % Overlapping factor (also determines oversampling in the frequency domain)
0, ... % Initial phase shift
true ... % Polyphase implementation
);
% The only difference between DFT_FBMC and FBMC is the prototype filter, which is slightly reduced in DFT_FBMC (improves the SIR a litte bit and reduces the complexity)
FBMC_DFT = Modulation.FBMC(...
NrSubcarriers,... % Number of subcarriers
K_FBMC,... % Number of FBMC symbols
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
0,... % Intermediate frequency first subcarrier (Hz)
false,... % Transmit real valued signal
'HermiteCut-OQAM',... % Prototype filter Hermite, PHYDYAS, InversePHYDYAS, HermiteCut, PHYDYASCut, Hann, Blackman
4, ... % Overlapping factor (also determines oversampling in the frequency domain)
0, ... % Initial phase shift
true ... % Polyphase implementation
);
%% OFDM Object
ZeroGuardTimeLength = ((FBMC.Nr.SamplesTotal-(round(SamplingRate/SubcarrierSpacing)+0*SamplingRate)*K_OFDMnoCP)/2)/SamplingRate;
OFDMnoCP = Modulation.OFDM(...
NrSubcarriers,... % Number of active subcarriers
K_OFDMnoCP,... % Number of OFDM Symbols
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
0,... % Intermediate frequency first subcarrier (Hz)
false,... % Transmit real valued signal
0, ... % Cyclic prefix length (s) 1/SubcarrierSpacing/(K/2-1)
ZeroGuardTimeLength ... % Zero guard length (s)
);
ZeroGuardTimeLength = ((FBMC.Nr.SamplesTotal-(round(SamplingRate/SubcarrierSpacing)+CP_Length*SamplingRate)*K_OFDM)/2)/SamplingRate;
OFDM = Modulation.OFDM(...
NrSubcarriers,... % Number of active subcarriers
K_OFDM,... % Number of OFDM Symbols
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
0,... % Intermediate frequency first subcarrier (Hz)
false,... % Transmit real valued signal
CP_Length, ... % Cyclic prefix length (s) 1/SubcarrierSpacing/(K/2-1)
ZeroGuardTimeLength ... % Zero guard length (s)
);
%% Check Number of Samples
if OFDM.Nr.SamplesTotal~=FBMC.Nr.SamplesTotal || OFDMnoCP.Nr.SamplesTotal~=FBMC.Nr.SamplesTotal
error('Total number of samples must be the same for OFDM and FBMC.');
end
N = OFDM.Nr.SamplesTotal;
%% Modulation Object
QAM = Modulation.SignalConstellation(QAM_ModulationOrder,'QAM');
PAM = Modulation.SignalConstellation(sqrt(QAM_ModulationOrder),'PAM');
%% Channel Object
ChannelModel = Channel.FastFading(...
SamplingRate,... % Sampling rate (Samples/s)
PowerDelayProfile,... % Power delay profile, either string or vector: 'Flat', 'AWGN', 'PedestrianA', 'PedestrianB', 'VehicularA', 'VehicularB', 'ExtendedPedestrianA', 'ExtendedPedestrianB', or 'TDL-A_xxns','TDL-B_xxns','TDL-C_xxns' (with xx the RMS delay spread in ns, e.g. 'TDL-A_30ns'), or [1 0 0.2] (Self-defined power delay profile which depends on the sampling rate)
N,... % Number of total samples
Velocity_kmh/3.6*CarrierFrequency/2.998e8,... % Maximum Doppler shift: Velocity_kmh/3.6*CarrierFrequency/2.998e8
'Jakes',... % Which Doppler model: 'Jakes', 'Uniform', 'Discrete-Jakes', 'Discrete-Uniform'. For "Discrete-", we assume a discrete Doppler spectrum to improve the simulation time. This only works accuratly if the number of samples and the velocity is sufficiently large
200, ... % Number of paths for the WSSUS process. Only relevant for a 'Jakes' and 'Uniform' Doppler spectrum
1,... % Number of transmit antennas
1,... % Number of receive antennas
true ... % Gives a warning if the predefined delay taps of the channel do not fit the sampling rate. This is usually not much of a problem if they are approximatly the same.
);
%% DFT Matrix
DFTMatrix = fft(eye(NrSubcarriers))/sqrt(NrSubcarriers);
%% Generate coding matrix for pruned DFT spread FBMC
TrueNrMCSymbols = FBMC_DFT.Nr.MCSymbols;
FBMC_DFT.SetNrMCSymbols(1);
D_temp = FBMC_DFT.GetFBMCMatrix;
FBMC_DFT.SetNrMCSymbols(TrueNrMCSymbols);
% Note that, if CP_Length==0, then T_CP and R_CP are identity matrices
T_CP = zeros(NrSubcarriers,NrSubcarriers-CP_Length_FBMC_DFT);
T_CP(1:CP_Length_FBMC_DFT/2,end-CP_Length_FBMC_DFT/2+1:end) = eye(CP_Length_FBMC_DFT/2);
T_CP(CP_Length_FBMC_DFT/2+1:end-CP_Length_FBMC_DFT/2,:) = eye(NrSubcarriers-CP_Length_FBMC_DFT);
T_CP(end-CP_Length_FBMC_DFT/2+1:end,1:CP_Length_FBMC_DFT/2) = eye(CP_Length_FBMC_DFT/2);
R_CP = zeros(NrSubcarriers,NrSubcarriers-CP_Length_FBMC_DFT);
R_CP(CP_Length_FBMC_DFT/2+1:end-CP_Length_FBMC_DFT/2,:) = eye(NrSubcarriers-CP_Length_FBMC_DFT);
% DFT matrix for the coding process
W = fft( eye(NrSubcarriers-CP_Length_FBMC_DFT) ) / sqrt( NrSubcarriers-CP_Length_FBMC_DFT );
% Diagonal elements of the FBMC transmission matrix after DFT spreading despreading
a = abs(diag(W'*R_CP'*D_temp*T_CP*W));
a = a+randn(size(a))*10^-12; % randn so that sorting is unique
% Sort a
a_Tilde = sort(a,'descend');
% Get index representing the largest values of a
alpha = a_Tilde((NrSubcarriers-CP_Length_FBMC_DFT)/2);
Index_Tilde = (a>=alpha);
% Pruned DFT matrix
W_Tilde = W(:,Index_Tilde) ;
% One-tap scaling of the data symbols
b_Tilde = sqrt(1./(a(Index_Tilde)));
% Final coding matrix for one FBMC symbol
Cf_DFTspread_TX = T_CP*W_Tilde*diag(b_Tilde);
Cf_DFTspread_RX = R_CP*W_Tilde*diag(b_Tilde);
C_DFTspread_TX = kron(sparse(eye(K_FBMC)),Cf_DFTspread_TX);
C_DFTspread_RX = kron(sparse(eye(K_FBMC)),Cf_DFTspread_RX);
%% Get OFDM and FBMC Transmit and Receive Matrices
GTX_OFDM = sparse(OFDM.GetTXMatrix);
GRX_OFDM = sparse(OFDM.GetRXMatrix');
GTX_OFDMnoCP = sparse(OFDMnoCP.GetTXMatrix);
GRX_OFDMnoCP = sparse(OFDMnoCP.GetRXMatrix');
G_FBMC = sparse(FBMC.GetTXMatrix);
G_FBMC_DFT = sparse(FBMC_DFT.GetTXMatrix);
%% Normalize OFDM and FBMC (the default matrices are normalized to have unit transmit power for unit power data symbols)
NormalizationOFDM = sqrt((GRX_OFDM(:,1)'*GRX_OFDM(:,1)));
NormalizationOFDMnoCP = sqrt((GRX_OFDMnoCP(:,1)'*GRX_OFDMnoCP(:,1)));
NormalizationFBMC = 1/sqrt((G_FBMC(:,1)'*G_FBMC(:,1)));
NormalizationFBMC_DFT = 1/sqrt((G_FBMC_DFT(:,1)'*G_FBMC_DFT(:,1)));
GTX_OFDM = GTX_OFDM*NormalizationOFDM;
GRX_OFDM = GRX_OFDM/NormalizationOFDM;
GTX_OFDMnoCP = GTX_OFDMnoCP*NormalizationOFDMnoCP;
GRX_OFDMnoCP = GRX_OFDMnoCP/NormalizationOFDMnoCP;
G_FBMC = G_FBMC*NormalizationFBMC;
G_FBMC_DFT = G_FBMC_DFT*NormalizationFBMC;
%% Preallocate for parfor
BER_OFDM = nan(length(M_SNR_dB),NrRepetitions);
BER_OFDMnoCP = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC = nan(length(M_SNR_dB),NrRepetitions);
BER_DFT_OFDM = nan(length(M_SNR_dB),NrRepetitions);
BER_DFT_OFDMnoCP = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_DFT = nan(length(M_SNR_dB),NrRepetitions);
SINR_DFT_OFDM_dB = nan(NrSubcarriers,K_OFDM,length(M_SNR_dB),NrRepetitions);
SINR_DFT_OFDMnoCP_dB = nan(NrSubcarriers,K_OFDMnoCP,length(M_SNR_dB),NrRepetitions);
SINR_FBMC_DFT_dB = nan((NrSubcarriers-CP_Length_FBMC_DFT)/2,K_FBMC,length(M_SNR_dB),NrRepetitions);
SINR_Approx_DFT_OFDM_dB = nan(NrSubcarriers,K_OFDM,length(M_SNR_dB),NrRepetitions);
SINR_Approx_DFT_OFDMnoCP_dB = nan(NrSubcarriers,K_OFDMnoCP,length(M_SNR_dB),NrRepetitions);
SINR_Approx_FBMC_DFT_dB = nan((NrSubcarriers-CP_Length_FBMC_DFT)/2,K_FBMC,length(M_SNR_dB),NrRepetitions);
%% Start Simulation (Calculation)
tic;
for i_rep = 1:NrRepetitions
% Generate Bit Stream
BinaryDataStream = randi([0 1],K_OFDMnoCP*NrSubcarriers*log2(QAM.ModulationOrder),1);
BinaryDataStream_OFDM = randi([0 1],K_OFDM*NrSubcarriers*log2(QAM.ModulationOrder),1); % Reduced bit rate due to the CP
BinaryDataStream_FBMC_DFT = randi([0 1],K_OFDMnoCP*(NrSubcarriers-CP_Length_FBMC_DFT)*log2(QAM.ModulationOrder),1); % Maybe a reduced bit rate due to the frequency CP (but not necesarry most of the time!)
% Map Bit Stream to Symbols
x_OFDM = reshape(QAM.Bit2Symbol(BinaryDataStream_OFDM),NrSubcarriers,K_OFDM);
x_OFDMnoCP = reshape(QAM.Bit2Symbol(BinaryDataStream),NrSubcarriers,K_OFDMnoCP);
x_FBMC_DFT = reshape(QAM.Bit2Symbol(BinaryDataStream_FBMC_DFT),(NrSubcarriers-CP_Length_FBMC_DFT)/2,K_FBMC);
x_FBMC = reshape(PAM.Bit2Symbol(BinaryDataStream),NrSubcarriers,K_FBMC)/sqrt(2); % 1/sqrt(2) => same TX power for OFDM and FBMC
% Generate Transmit Signal in the Time Domain
s_OFDM = OFDM.Modulation(x_OFDM)*NormalizationOFDM;
s_OFDMnoCP = OFDMnoCP.Modulation(x_OFDMnoCP)*NormalizationOFDMnoCP;
s_FBMC = FBMC.Modulation(x_FBMC)*NormalizationFBMC;
s_DFT_OFDM = OFDM.Modulation(DFTMatrix*x_OFDM)*NormalizationOFDM;
s_DFT_OFDMnoCP = OFDMnoCP.Modulation(DFTMatrix*x_OFDMnoCP)*NormalizationOFDMnoCP;
s_FBMC_DFT = FBMC_DFT.Modulation(Cf_DFTspread_TX*x_FBMC_DFT)*NormalizationFBMC_DFT;
% Channel
ChannelModel.NewRealization;
H = ChannelModel.GetConvolutionMatrix{1};
r_OFDM_noNoise = H * s_OFDM;
r_OFDMnoCP_noNoise = H * s_OFDMnoCP;
r_FBMC_noNoise = H * s_FBMC;
r_DFT_OFDM_noNoise = H * s_DFT_OFDM;
r_DFT_OFDMnoCP_noNoise = H * s_DFT_OFDMnoCP;
r_FBMC_DFT_noNoise = H * s_FBMC_DFT;
noise_unitPower = sqrt(1/2)*( randn(N,1) + 1j * randn(N,1) );
% Calculate One Tap Channels
% Note that diag(G'*H*G)==sum((G'*H).*G.',2)
h_OFDM = full( reshape( sum((GRX_OFDM'*H).*GTX_OFDM.',2), NrSubcarriers, [] ) );
h_OFDMnoCP = full( reshape( sum((GRX_OFDMnoCP'*H).*GTX_OFDMnoCP.',2), NrSubcarriers, [] ) );
h_FBMC = full( reshape( sum((G_FBMC'*H).*G_FBMC.',2), NrSubcarriers, [] ) );
h_FBMC_DFT = full( reshape( sum((G_FBMC_DFT'*H).*G_FBMC_DFT.',2), NrSubcarriers, [] ) );
% Precalculate Stuff to Improve the Computation Time
if CalculateTheory
Precalc_OFDM = GRX_OFDM' * H *GTX_OFDM * kron(sparse(eye(K_OFDM)),DFTMatrix);
Precalc_OFDMnoCP = GRX_OFDMnoCP' * H *GTX_OFDMnoCP * kron(sparse(eye(K_OFDMnoCP)),DFTMatrix);
Precalc_FBMC = G_FBMC_DFT' * H * G_FBMC_DFT * C_DFTspread_TX;
end
for i_SNR = 1:length(M_SNR_dB)
SNR_dB = M_SNR_dB(i_SNR);
Pn = 10^(-SNR_dB/10);
%% Simulation
% Add Noise
noise = sqrt(Pn) * noise_unitPower;
r_OFDM = r_OFDM_noNoise + noise;
r_OFDMnoCP = r_OFDMnoCP_noNoise + noise;
r_FBMC = r_FBMC_noNoise + noise;
r_DFT_OFDM = r_DFT_OFDM_noNoise + noise;
r_DFT_OFDMnoCP = r_DFT_OFDMnoCP_noNoise + noise;
r_FBMC_DFT = r_FBMC_DFT_noNoise + noise;
% Received Symbols (Demodulation)
y_OFDM = OFDM.Demodulation(r_OFDM) / NormalizationOFDM;
y_OFDMnoCP = OFDMnoCP.Demodulation(r_OFDMnoCP) / NormalizationOFDMnoCP;
y_FBMC = FBMC.Demodulation(r_FBMC) / NormalizationFBMC;
y_DFT_OFDM = OFDM.Demodulation(r_DFT_OFDM) / NormalizationOFDM;
y_DFT_OFDMnoCP = OFDMnoCP.Demodulation(r_DFT_OFDMnoCP) / NormalizationOFDMnoCP;
y_FBMC_DFT = FBMC_DFT.Demodulation(r_FBMC_DFT) / NormalizationFBMC_DFT;
% ZF Equalizer for OFDM and FBMC
x_est_OFDM = y_OFDM ./ h_OFDM;
x_est_OFDMnoCP = y_OFDMnoCP ./ h_OFDMnoCP;
x_est_FBMC = real( y_FBMC ./ h_FBMC ) * sqrt(2);
% One-tap (scaled) MMSE followed by despreading
Scaling_DFT_OFDM = repmat(1./(mean(1 ./( 1 + Pn./abs( h_OFDM ).^2 ),1)), NrSubcarriers,1);
Scaling_DFT_OFDMnoCP = repmat(1./(mean(1 ./( 1 + Pn./abs( h_OFDMnoCP ).^2 ),1)), NrSubcarriers,1);
Scaling_FBMC_DFT = repmat(1./(mean(1 ./( 1 + Pn./abs( h_FBMC(CP_Length_FBMC_DFT/2+1:end-CP_Length_FBMC_DFT/2,:) ).^2 ),1)), NrSubcarriers,1);
e_DFT_OFDM = Scaling_DFT_OFDM .*conj(h_OFDM) ./( abs(h_OFDM).^2 + Pn );
e_DFT_OFDMnoCP = Scaling_DFT_OFDMnoCP .*conj(h_OFDMnoCP)./( abs(h_OFDMnoCP).^2 + Pn );
e_FBMC_DFT = Scaling_FBMC_DFT .*conj(h_FBMC) ./( abs(h_FBMC).^2 + Pn );
x_est_DFT_OFDM = DFTMatrix' * (y_DFT_OFDM .* e_DFT_OFDM);
x_est_DFT_OFDMnoCP = DFTMatrix' * (y_DFT_OFDMnoCP .* e_DFT_OFDMnoCP);
x_est_FBMC_DFT = Cf_DFTspread_RX' * (y_FBMC_DFT .* e_FBMC_DFT);
% Symbol to Bit
DetectedBitStream_OFDM = QAM.Symbol2Bit(x_est_OFDM);
DetectedBitStream_OFDMnoCP = QAM.Symbol2Bit(x_est_OFDMnoCP);
DetectedBitStream_FBMC = PAM.Symbol2Bit(x_est_FBMC);
DetectedBitStream_DFT_OFDM = QAM.Symbol2Bit(x_est_DFT_OFDM);
DetectedBitStream_DFT_OFDMnoCP = QAM.Symbol2Bit(x_est_DFT_OFDMnoCP);
DetectedBitStream_FBMC_DFT = QAM.Symbol2Bit(x_est_FBMC_DFT);
% Bit Error Ratio
BER_OFDM(i_SNR,i_rep) = mean( BinaryDataStream_OFDM ~= DetectedBitStream_OFDM );
BER_OFDMnoCP(i_SNR,i_rep) = mean( BinaryDataStream ~= DetectedBitStream_OFDMnoCP );
BER_FBMC(i_SNR,i_rep) = mean( BinaryDataStream ~= DetectedBitStream_FBMC );
BER_DFT_OFDM(i_SNR,i_rep) = mean( BinaryDataStream_OFDM ~= DetectedBitStream_DFT_OFDM );
BER_DFT_OFDMnoCP(i_SNR,i_rep) = mean( BinaryDataStream ~= DetectedBitStream_DFT_OFDMnoCP );
BER_FBMC_DFT(i_SNR,i_rep) = mean( BinaryDataStream_FBMC_DFT ~= DetectedBitStream_FBMC_DFT );
%% Theoretical calculations for pruned DFT spread FBMC and SC-FDMA
if CalculateTheory
% Equalizer
E_DFT_OFDM = sparse( diag( e_DFT_OFDM(:) ) );
E_DFT_OFDMnoCP = sparse( diag( e_DFT_OFDMnoCP(:) ) );
E_FBMC_DFT = sparse( diag( e_FBMC_DFT(:) ) );
% Full transmission matrix
D_DFT_OFDM = kron(sparse(eye(K_OFDM)),DFTMatrix)' * E_DFT_OFDM * Precalc_OFDM;
Gamma_DFT_OFDM = kron(sparse(eye(K_OFDM)),DFTMatrix)' * E_DFT_OFDM * GRX_OFDM';
D_DFT_OFDMnoCP = kron(sparse(eye(K_OFDMnoCP)),DFTMatrix)' * E_DFT_OFDMnoCP * Precalc_OFDMnoCP;
Gamma_DFT_OFDMnoCP = kron(sparse(eye(K_OFDMnoCP)),DFTMatrix)' * E_DFT_OFDMnoCP * GRX_OFDMnoCP';
D_FBMC_DFT = C_DFTspread_RX' * E_FBMC_DFT * Precalc_FBMC;
Gamma_FBMC_DFT = C_DFTspread_RX' * E_FBMC_DFT * G_FBMC_DFT';
% Calculate the approximated SINR
SINR_Approx_DFT_OFDM_dB(:,:,i_SNR,i_rep) = 10*log10(repmat(1./(1./mean(1./(1+Pn./abs(h_OFDM).^2)) - 1),NrSubcarriers,1));
SINR_Approx_DFT_OFDMnoCP_dB(:,:,i_SNR,i_rep) = 10*log10(repmat(1./(1./mean(1./(1+Pn./abs(h_OFDMnoCP).^2)) - 1),NrSubcarriers,1));
SINR_Approx_FBMC_DFT_dB(:,:,i_SNR,i_rep) = 10*log10(repmat(1./(1./mean(1./(1+Pn./abs(h_FBMC_DFT(CP_Length_FBMC_DFT/2+1:end-CP_Length_FBMC_DFT/2,:)).^2)) - 1),(NrSubcarriers-CP_Length_FBMC_DFT)/2 , 1 ));
% Calculate the true SINR
SINR_DFT_OFDM_dB(:,:,i_SNR,i_rep) = 10*log10(1./(reshape( sum(abs(D_DFT_OFDM-eye(size(D_DFT_OFDM))).^2,2) + sum(abs(Gamma_DFT_OFDM).^2,2)*Pn , size(x_OFDM))));
SINR_DFT_OFDMnoCP_dB(:,:,i_SNR,i_rep) = 10*log10(1./(reshape( sum(abs(D_DFT_OFDMnoCP-eye(size(D_DFT_OFDMnoCP))).^2,2) + sum(abs(Gamma_DFT_OFDMnoCP).^2,2)*Pn , size(x_OFDMnoCP))));
SINR_FBMC_DFT_dB(:,:,i_SNR,i_rep) = 10*log10(1./(reshape( sum(abs(D_FBMC_DFT-eye(size(D_FBMC_DFT))).^2,2) + sum(abs(Gamma_FBMC_DFT).^2,2)*Pn , size(x_FBMC_DFT))));
end
end
TimePassed = toc;
if mod(i_rep,1)==0
disp(['Realization ' int2str(i_rep) ' of ' int2str(NrRepetitions) '. Time left: ' int2str(TimePassed/i_rep*(NrRepetitions-i_rep)/60) 'minutes = ' int2str(TimePassed/i_rep*(NrRepetitions-i_rep)/60/60) 'hours']);
end
end
if CalculateTheory
%% Calculate the Bit Error Probability (BEP)
M_SNR_dB_morePoints = -30:0.1:50;
ReferenceBitErrorProability = BitErrorProbabilityAWGN( M_SNR_dB_morePoints, QAM.SymbolMapping , QAM.BitMapping );
% Use interpolation because it is faster than directly using the function "BitErrorProbabilityAWGN(.)"
[a,b,c,d] = size(SINR_DFT_OFDM_dB);
BEP_DFT_OFDM_all = reshape( interp1( M_SNR_dB_morePoints , ReferenceBitErrorProability , SINR_DFT_OFDM_dB(:) ,'spline'), a,b,c,d);
BEP_DFT_OFDM = squeeze(mean(mean(mean(BEP_DFT_OFDM_all,1),2),4));
[a,b,c,d] = size(SINR_DFT_OFDMnoCP_dB);
BEP_DFT_OFDMnoCP_all = reshape( interp1( M_SNR_dB_morePoints , ReferenceBitErrorProability , SINR_DFT_OFDMnoCP_dB(:) ,'spline'), a,b,c,d);
BEP_DFT_OFDMnoCP = squeeze(mean(mean(mean(BEP_DFT_OFDMnoCP_all,1),2),4));
[a,b,c,d] = size(SINR_FBMC_DFT_dB);
BEP_FBMC_DFT_all = reshape( interp1( M_SNR_dB_morePoints , ReferenceBitErrorProability , SINR_FBMC_DFT_dB(:) ,'spline'), a,b,c,d);
BEP_FBMC_DFT = squeeze(mean(mean(mean(BEP_FBMC_DFT_all,1),2),4));
%% Error between the true SINR and the approximated SINR
Error_SINR_DFT_OFDM_dB = 10*log10(1./(squeeze(mean(mean(mean(10.^(-SINR_DFT_OFDM_dB./10),1),2),4)))) - 10*log10(1./(squeeze(mean(mean(mean(10.^(-SINR_Approx_DFT_OFDM_dB./10),1),2),4))));
Error_SINR_DFT_OFDMnoCP_dB = 10*log10(1./(squeeze(mean(mean(mean(10.^(-SINR_DFT_OFDMnoCP_dB./10),1),2),4)))) - 10*log10(1./(squeeze(mean(mean(mean(10.^(-SINR_Approx_DFT_OFDMnoCP_dB./10),1),2),4))));
Error_SINR_FBMC_DFT_dB = 10*log10(1./(squeeze(mean(mean(mean(10.^(-SINR_FBMC_DFT_dB./10),1),2),4)))) - 10*log10(1./(squeeze(mean(mean(mean(10.^(-SINR_Approx_FBMC_DFT_dB./10),1),2),4))));
end
if CalculateTheory
%% Plot the Approximation Error
figure(10);
plot(M_SNR_dB,-Error_SINR_DFT_OFDM_dB,'black');
hold on;
plot(M_SNR_dB,-Error_SINR_DFT_OFDMnoCP_dB,'red');
plot(M_SNR_dB,-Error_SINR_FBMC_DFT_dB,'blue');
ylim([-2 8]);
xlabel('Signal-to-Noise Ratio');
ylabel('SINRapprox - SINR [dB]');
legend({'SC-FDMA','SC-FDMD (noCP)','Pruned DFT-s FBMC'})
%% Plot the BEP and BER
figure(12);
markersize =4;
semilogy(M_SNR_dB,BEP_DFT_OFDM,'- black','Markersize',markersize);
hold on;
semilogy(M_SNR_dB,BEP_DFT_OFDMnoCP,'- red','Markersize',markersize);
semilogy(M_SNR_dB,BEP_FBMC_DFT,'- blue','Markersize',markersize);
semilogy(M_SNR_dB,mean(BER_DFT_OFDM,2),'x black','Markersize',markersize);
semilogy(M_SNR_dB,mean(BER_DFT_OFDMnoCP,2),'s red','Markersize',markersize);
semilogy(M_SNR_dB,mean(BER_FBMC_DFT,2),'o blue','Markersize',markersize);
ylim([10^-4 1]);
xlabel('Signal-to-Noise Ratio');
ylabel('Bit Error Probability, Bit Error Ratio');
legend({'SC-FDMA','SC-FDMA (noCP)','Pruned DFT-s FBMC'})
else
figure(12);
markersize =4;
semilogy(M_SNR_dB,mean(BER_DFT_OFDM,2),'-x black','Markersize',markersize);
hold on;
semilogy(M_SNR_dB,mean(BER_DFT_OFDMnoCP,2),'-s red','Markersize',markersize);
semilogy(M_SNR_dB,mean(BER_FBMC_DFT,2),'-o blue','Markersize',markersize);
ylim([10^-4 1]);
xlabel('Signal-to-Noise Ratio');
ylabel('Bit Error Ratio');
legend({'SC-FDMA','SC-FDMA (noCP)','Pruned DFT-s FBMC'})
end
%% Plot BER, including multicarrier modulation
figure(100)
semilogy(M_SNR_dB,mean(BER_DFT_OFDM,2),'black');
hold on;
semilogy(M_SNR_dB,mean(BER_DFT_OFDMnoCP,2),'red');
semilogy(M_SNR_dB,mean(BER_FBMC_DFT,2),'blue');
semilogy(M_SNR_dB,mean(BER_OFDM,2),'-- black');
semilogy(M_SNR_dB,mean(BER_OFDMnoCP,2),'-- red');
semilogy(M_SNR_dB,mean(BER_FBMC,2),'-- blue');
xlabel('Signal-to-Noise Ratio');
ylabel('Bit Error Ratio');
legend({'SC-FDMA','SC-FDMD (noCP)','Pruned DFT-s FBMC','OFDM','OFDM (noCP)','FBMC'})
figure(12);
%% Show the Bitrates
BitRate_OFDM = length(BinaryDataStream_OFDM)/(OFDM.PHY.TimeSpacing*OFDM.Nr.MCSymbols);
BitRate_OFDMnoCP = length(BinaryDataStream)/(OFDMnoCP.PHY.TimeSpacing*OFDMnoCP.Nr.MCSymbols);
BitRate_FBMC = length(BinaryDataStream)/(FBMC.PHY.TimeSpacing*FBMC.Nr.MCSymbols);
BitRate_FBMC_DFT = length(BinaryDataStream_FBMC_DFT)/(FBMC_DFT.PHY.TimeSpacing*FBMC_DFT.Nr.MCSymbols);
fprintf('=================================================================\n');
fprintf(' | CP-OFDM | OFDM(noCP) | FBMC | pDFTsFBMC |\n');
fprintf('Bit Rate [Bits/s] |%10.0f|%12.0f|%10.0f|%11.0f|\n',BitRate_OFDM,BitRate_OFDMnoCP,BitRate_FBMC,BitRate_FBMC_DFT);
fprintf('=================================================================\n');
%% Save Results
SaveStuff = false;
if SaveStuff
Name = ['.\Results\SISO_BER_' PowerDelayProfile '_v' int2str(Velocity_kmh) '_' int2str(QAM_ModulationOrder) '_' int2str(NrSubcarriers) '.mat'];
meanBER_DFT_OFDM = mean(BER_DFT_OFDM,2);
meanBER_DFT_OFDMnoCP = mean(BER_DFT_OFDMnoCP,2);
meanBER_FBMC_DFT = mean(BER_FBMC_DFT,2);
meanBEP_DFT_OFDM = mean(BEP_DFT_OFDM,2);
meanBEP_DFT_OFDMnoCP = mean(BEP_DFT_OFDMnoCP,2);
meanBEP_FBMC_DFT = mean(BEP_FBMC_DFT,2);
meanBER_OFDM = mean(BER_OFDM,2);
meanBER_OFDMnoCP = mean(BER_OFDMnoCP,2);
meanBER_FBMC = mean(BER_FBMC,2);
save(Name,...
'meanBER_DFT_OFDM',...
'meanBER_DFT_OFDMnoCP',...
'meanBER_FBMC_DFT',...
'meanBER_OFDM',...
'meanBER_OFDMnoCP',...
'meanBER_FBMC',...
'M_SNR_dB',...
'NrRepetitions',...
'meanBEP_DFT_OFDM',...
'meanBEP_DFT_OFDMnoCP',...
'meanBEP_FBMC_DFT',...
'Error_SINR_DFT_OFDM_dB',...
'Error_SINR_DFT_OFDMnoCP_dB',...
'Error_SINR_FBMC_DFT_dB' ...
);
end