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Figure_13_Throughput.m
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% =========================================================================
% (c) 2018 Ronald Nissel, https://www.linkedin.com/in/ronaldnissel/
% =========================================================================
% This script simulates the throughput of pruned DFT spread FBMC, SC-FDMA,
% OFDM and FBMC. Note that the achievable rate can also be calculated, but
% the parameter "CalculateTheory" must be set to true.
% Allows to reproduce Figure 13 of "Pruned DFT Spread FBMC: Low PAPR, Low
% Latency, High Spectral Efficiency", R. Nissel and M. Rupp, IEEE
% Transactions on Communications
% #### We recommend using parfor, that is, commenting out line 264-266 ####
clear; close all;
addpath('./Theory');
%% Parameters
% Simulation
M_SNR_dB = [-10:4:30]; % Signal-to-Noise Ratio in dB
NrRepetitions = 4; % Number of Monte Carlo repetitions
CalculateTheory = false; % If set to true, calculate the achievable rate, an upper bound of the throughput. To keep the simulation time short we set it to false.
% FBMC and OFDM Parameters
NrSubcarriers = 256; % Number of subcarriers
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 = [-10:1.25:30];
% SamplingRate = 15e3*14*12*8;
% NrRepetitions = 1000;
% CalculateTheory = true;
% #########################################################################
%% Adaptive Modulation and Coding (CQI Table)
% The first column represents the modulation order: 4, 16, 64, 256, 1024...
% The second column represents the code rate (must be between zero and one)
% Currently, values are chosen according to the (old) LTE standard:
M_CQI = [4 , 78/1024;...
4 , 120/1024;...
4 , 193/1024;...
4 , 308/1024;...
4 , 449/1024;...
4 , 602/1024;...
16 , 378/1024;...
16 , 490/1024;...
16 , 616/1024;...
64 , 466/1024;...
64 , 567/1024;...
64 , 666/1024;...
64 , 772/1024;...
64 , 873/1024;...
64 , 948/1024]; % page 48 of http://www.etsi.org/deliver/etsi_ts/136200_136299/136213/08.08.00_60/ts_136213v080800p.pdf
if not(strcmp(mexext,'mexw64'))
% We use a win64 mexfile for code rates smaller than 1/3 => only works
% in 64-bit Windows
IndexCodeRateSmallerOneThird = find(M_CQI(:,2)<1/3);
if numel(IndexCodeRateSmallerOneThird)>0
M_CQI(IndexCodeRateSmallerOneThird,:) = [];
warning('A code rate smaller than 1/3 is only supported in Windows 64-bit => CQI values which contain a code rate smaller than 1/3 are discarded!');
end
end
%% FBMC Objects
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)
% We use the short notation "FBMC_DFT" to indicate pruned DFT spread FBMC.
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 Objects
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;
%% 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.
);
%% Pre-initialize CQI: Turbo Coder and QAM
for i_cqi = 1:size(M_CQI,1)
QAMModulationOrder = M_CQI(i_cqi,1);
PAMModulationOrder = sqrt(QAMModulationOrder);
CodeRate = M_CQI(i_cqi,2);
QAM{i_cqi} = Modulation.SignalConstellation(QAMModulationOrder,'QAM');
PAM{i_cqi} = Modulation.SignalConstellation(PAMModulationOrder,'PAM');
NrTransmittedBits_OFDM = NrSubcarriers*K_OFDM*log2(QAMModulationOrder);
NrTransmittedBits_OFDMnoCP = NrSubcarriers*K_OFDMnoCP*log2(QAMModulationOrder);
NrTransmittedBits_FBMC = NrSubcarriers*K_FBMC*log2(PAMModulationOrder);
NrTransmittedBits_FBMC_DFT = (NrSubcarriers-CP_Length_FBMC_DFT)/2*K_FBMC*log2(QAMModulationOrder);
TurboCoding_OFDM{i_cqi} = Coding.TurboCoding( NrTransmittedBits_OFDM , round(CodeRate*NrTransmittedBits_OFDM));
TurboCoding_OFDMnoCP{i_cqi} = Coding.TurboCoding( NrTransmittedBits_OFDMnoCP , round(CodeRate*NrTransmittedBits_OFDMnoCP));
TurboCoding_FBMC{i_cqi} = Coding.TurboCoding( NrTransmittedBits_FBMC , round(CodeRate*NrTransmittedBits_FBMC));
TurboCoding_FBMC_DFT{i_cqi} = Coding.TurboCoding( NrTransmittedBits_FBMC_DFT , round(CodeRate*NrTransmittedBits_FBMC_DFT));
end
%% 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 and 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 which represents 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
SINR_FBMC_dB = nan(NrSubcarriers,K_FBMC,length(M_SNR_dB),NrRepetitions);
SINR_FBMC_DFT_dB = nan((NrSubcarriers-CP_Length_FBMC_DFT)/2,K_FBMC,length(M_SNR_dB),NrRepetitions);
% Preallocate simulation results (needed for parfor)
M_Througput_OFDM = nan( length(M_SNR_dB) , NrRepetitions , size(M_CQI,1) );
M_Througput_OFDMnoCP = nan( length(M_SNR_dB) , NrRepetitions , size(M_CQI,1) );
M_Througput_FBMC = nan( length(M_SNR_dB) , NrRepetitions , size(M_CQI,1) );
M_Througput_DFT_OFDM = nan( length(M_SNR_dB) , NrRepetitions , size(M_CQI,1) );
M_Througput_DFT_OFDMnoCP = nan( length(M_SNR_dB) , NrRepetitions , size(M_CQI,1) );
M_Througput_FBMC_DFT = nan( length(M_SNR_dB) , NrRepetitions , size(M_CQI,1) );
disp('The simulation may take a while ... ');
%% Start Simulation (Calculation)
NrWorkers = 1; % Conventional FOR loop
for i_Rep = 1:NrRepetitions % Conventional FOR loop
% cluster = parcluster('local'); % PARFOR
% NrWorkers = cluster.NumWorkers; % PARFOR
% parfor i_Rep = 1:NrRepetitions % PARFOR
tic;
% Channel
ChannelModel.NewRealization;
H = ChannelModel.GetConvolutionMatrix{1};
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, [] ) );
% Preallocate simulation result for one realization (needed for parfor)
M_Througput_OFDM_OneRealization = nan( length(M_SNR_dB) , size(M_CQI,1) );
M_Througput_OFDMnoCP_OneRealization = nan( length(M_SNR_dB) , size(M_CQI,1) );
M_Througput_FBMC_OneRealization = nan( length(M_SNR_dB) , size(M_CQI,1) );
M_Througput_DFT_OFDM_OneRealization = nan( length(M_SNR_dB) , size(M_CQI,1) );
M_Througput_DFT_OFDMnoCP_OneRealization = nan( length(M_SNR_dB) , size(M_CQI,1) );
M_Througput_FBMC_DFT_OneRealization = nan( length(M_SNR_dB) , size(M_CQI,1) );
% Simulate over different modulation orders and code rates
for i_cqi = 1:size(M_CQI,1)
% Generate Data Bit Stream
BinaryDataStream_OFDM = randi( [0 1] , TurboCoding_OFDM{i_cqi}.NrDataBits , 1 );
BinaryDataStream_OFDMnoCP = randi( [0 1] , TurboCoding_OFDMnoCP{i_cqi}.NrDataBits , 1 );
BinaryDataStream_FBMC = randi( [0 1] , TurboCoding_FBMC{i_cqi}.NrDataBits , 1 );
BinaryDataStream_FBMC_DFT = randi( [0 1] , TurboCoding_FBMC_DFT{i_cqi}.NrDataBits , 1 );
% Update Interleaving of the Turbo Coder
TurboCoding_OFDM{i_cqi}.UpdateInterleaving;
TurboCoding_OFDMnoCP{i_cqi}.UpdateInterleaving;
TurboCoding_FBMC{i_cqi}.UpdateInterleaving;
TurboCoding_FBMC_DFT{i_cqi}.UpdateInterleaving;
% Turbo Coding of the Data Bits
CodedBits_OFDM = TurboCoding_OFDM{i_cqi}.TurboEncoder( BinaryDataStream_OFDM );
CodedBits_OFDMnoCP = TurboCoding_OFDMnoCP{i_cqi}.TurboEncoder( BinaryDataStream_OFDMnoCP );
CodedBits_FBMC = TurboCoding_FBMC{i_cqi}.TurboEncoder( BinaryDataStream_FBMC );
CodedBits_FBMC_DFT = TurboCoding_FBMC_DFT{i_cqi}.TurboEncoder( BinaryDataStream_FBMC_DFT );
% Bit Interleaving
BitInterleaving_OFDM = randperm( TurboCoding_OFDM{i_cqi}.NrCodedBits );
BitInterleaving_OFDMnoCP = randperm( TurboCoding_OFDMnoCP{i_cqi}.NrCodedBits );
BitInterleaving_FBMC = randperm( TurboCoding_FBMC{i_cqi}.NrCodedBits );
BitInterleaving_FBMC_DFT = randperm( TurboCoding_FBMC_DFT{i_cqi}.NrCodedBits );
CodedBits_OFDM = CodedBits_OFDM( BitInterleaving_OFDM );
CodedBits_OFDMnoCP = CodedBits_OFDMnoCP( BitInterleaving_OFDMnoCP );
CodedBits_FBMC = CodedBits_FBMC( BitInterleaving_FBMC );
CodedBits_FBMC_DFT = CodedBits_FBMC_DFT( BitInterleaving_FBMC_DFT );
% Map Bit Stream to Symbols
x_OFDM = reshape(QAM{i_cqi}.Bit2Symbol(CodedBits_OFDM) , NrSubcarriers,K_OFDM);
x_OFDMnoCP = reshape(QAM{i_cqi}.Bit2Symbol(CodedBits_OFDMnoCP), NrSubcarriers,K_OFDMnoCP);
x_FBMC = reshape(PAM{i_cqi}.Bit2Symbol(CodedBits_FBMC) , NrSubcarriers,K_FBMC)/sqrt(2); % 1/sqrt(2) => same TX power for OFDM and FBMC
x_FBMC_DFT = reshape(QAM{i_cqi}.Bit2Symbol(CodedBits_FBMC_DFT),(NrSubcarriers-CP_Length_FBMC_DFT)/2,K_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
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;
% Simulate over different SNR values
for i_SNR = 1:length(M_SNR_dB)
SNR_dB = M_SNR_dB(i_SNR);
Pn = 10^(-SNR_dB/10);
% 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);
% Calculate LLR Values
LLR_OFDM = QAM{i_cqi}.LLR_AWGN( x_est_OFDM(:) , Pn .* 1./abs(h_OFDM(:)).^2);
LLR_OFDMnoCP = QAM{i_cqi}.LLR_AWGN( x_est_OFDMnoCP(:) , Pn .* 1./abs(h_OFDMnoCP(:)).^2);
LLR_FBMC = PAM{i_cqi}.LLR_AWGN( x_est_FBMC(:) , 2*Pn .* 1./abs(h_FBMC(:)).^2);
AWGNequivalentNoise_DFT_OFDM = repmat(1./mean(1./(1+Pn./abs(h_OFDM).^2),1)-1 ,NrSubcarriers,1);
AWGNequivalentNoise_DFT_OFDMnoCP = repmat(1./mean(1./(1+Pn./abs(h_OFDMnoCP).^2),1)-1,NrSubcarriers,1);
AWGNequivalentNoise_FBMC_DFT = repmat(1./mean(1./(1+Pn./abs(h_FBMC_DFT(CP_Length_FBMC_DFT/2+1:end-CP_Length_FBMC_DFT/2,:)).^2),1)-1, (NrSubcarriers-CP_Length_FBMC_DFT)/2 , 1 );
LLR_DFT_OFDM = QAM{i_cqi}.LLR_AWGN( x_est_DFT_OFDM(:) , AWGNequivalentNoise_DFT_OFDM(:));
LLR_DFT_OFDMnoCP = QAM{i_cqi}.LLR_AWGN( x_est_DFT_OFDMnoCP(:) , AWGNequivalentNoise_DFT_OFDMnoCP(:));
LLR_FBMC_DFT = QAM{i_cqi}.LLR_AWGN( x_est_FBMC_DFT(:) , AWGNequivalentNoise_FBMC_DFT(:));
% Bitdeinterleaving
LLR_OFDM(BitInterleaving_OFDM) = LLR_OFDM;
LLR_OFDMnoCP(BitInterleaving_OFDMnoCP) = LLR_OFDMnoCP;
LLR_FBMC(BitInterleaving_FBMC) = LLR_FBMC;
LLR_DFT_OFDM(BitInterleaving_OFDM) = LLR_DFT_OFDM;
LLR_DFT_OFDMnoCP(BitInterleaving_OFDMnoCP) = LLR_DFT_OFDMnoCP;
LLR_FBMC_DFT(BitInterleaving_FBMC_DFT) = LLR_FBMC_DFT;
% Decode Bits
DecodedBits_OFDM = TurboCoding_OFDM{i_cqi}.TurboDecoder( LLR_OFDM );
DecodedBits_OFDMnoCP = TurboCoding_OFDMnoCP{i_cqi}.TurboDecoder( LLR_OFDMnoCP );
DecodedBits_FBMC = TurboCoding_FBMC{i_cqi}.TurboDecoder( LLR_FBMC );
DecodedBits_DFT_OFDM = TurboCoding_OFDM{i_cqi}.TurboDecoder( LLR_DFT_OFDM );
DecodedBits_DFT_OFDMnoCP = TurboCoding_OFDMnoCP{i_cqi}.TurboDecoder( LLR_DFT_OFDMnoCP );
DecodedBits_FBMC_DFT = TurboCoding_FBMC_DFT{i_cqi}.TurboDecoder( LLR_FBMC_DFT );
% Simulated throughput after decoding (all bits must be correctly detected. If one bit is wrong, the throughput is zero)
M_Througput_OFDM_OneRealization(i_SNR,i_cqi) = all( DecodedBits_OFDM == BinaryDataStream_OFDM ) * length(BinaryDataStream_OFDM)/(OFDM.PHY.TimeSpacing*(OFDM.Nr.MCSymbols));
M_Througput_OFDMnoCP_OneRealization(i_SNR,i_cqi) = all( DecodedBits_OFDMnoCP == BinaryDataStream_OFDMnoCP ) * length(BinaryDataStream_OFDMnoCP)/(OFDMnoCP.PHY.TimeSpacing*(OFDMnoCP.Nr.MCSymbols));
M_Througput_FBMC_OneRealization(i_SNR,i_cqi) = all( DecodedBits_FBMC == BinaryDataStream_FBMC ) * length(BinaryDataStream_FBMC)/(FBMC.PHY.TimeSpacing*(FBMC.Nr.MCSymbols));
M_Througput_DFT_OFDM_OneRealization(i_SNR,i_cqi) = all( DecodedBits_DFT_OFDM == BinaryDataStream_OFDM ) * length(BinaryDataStream_OFDM)/(OFDM.PHY.TimeSpacing*(OFDM.Nr.MCSymbols));
M_Througput_DFT_OFDMnoCP_OneRealization(i_SNR,i_cqi) = all( DecodedBits_DFT_OFDMnoCP == BinaryDataStream_OFDMnoCP ) * length(BinaryDataStream_OFDMnoCP)/(OFDMnoCP.PHY.TimeSpacing*(OFDMnoCP.Nr.MCSymbols));
M_Througput_FBMC_DFT_OneRealization(i_SNR,i_cqi) = all( DecodedBits_FBMC_DFT == BinaryDataStream_FBMC_DFT ) * length(BinaryDataStream_FBMC_DFT)/(FBMC_DFT.PHY.TimeSpacing*(FBMC_DFT.Nr.MCSymbols));
end
end
M_Througput_OFDM(:,i_Rep,:) = M_Througput_OFDM_OneRealization;
M_Througput_OFDMnoCP(:,i_Rep,:) = M_Througput_OFDMnoCP_OneRealization;
M_Througput_FBMC(:,i_Rep,:) = M_Througput_FBMC_OneRealization;
M_Througput_DFT_OFDM(:,i_Rep,:) = M_Througput_DFT_OFDM_OneRealization;
M_Througput_DFT_OFDMnoCP(:,i_Rep,:) = M_Througput_DFT_OFDMnoCP_OneRealization;
M_Througput_FBMC_DFT(:,i_Rep,:) = M_Througput_FBMC_DFT_OneRealization;
if CalculateTheory
%% Calculate Theoretical SINR
% Precalculate Stuff to Improve Computation time
Precalc_FBMC = G_FBMC' * H * G_FBMC;
Precalc_FBMC_DFT = G_FBMC_DFT' * H * G_FBMC_DFT * C_DFTspread_TX;
SINR_FBMC_dB_OneRealization = nan(NrSubcarriers, K_FBMC, length(M_SNR_dB) );
SINR_FBMC_DFT_dB_OneRealization = nan((NrSubcarriers-CP_Length_FBMC_DFT)/2, K_FBMC, length(M_SNR_dB) );
for i_SNR = 1:length(M_SNR_dB)
SNR_dB = M_SNR_dB(i_SNR);
Pn = 10^(-SNR_dB/10);
% Equalizer
E_FBMC = sparse(diag(1./h_FBMC(:)));
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_FBMC_DFT = Scaling_FBMC_DFT .* conj(h_FBMC) ./ ( abs(h_FBMC).^2 + Pn );
E_FBMC_DFT = sparse( diag( e_FBMC_DFT(:) ) );
% Transmission Matrix
D_FMBC = real(E_FBMC*Precalc_FBMC);
Gamma_FBMC = 1./abs(h_FBMC(:)).^2;
SINR_FBMC_dB_OneRealization(:,:,i_SNR) = 10*log10(1./(reshape( sum(abs(D_FMBC-eye(size(D_FMBC))).^2,2) + Gamma_FBMC * Pn, [NrSubcarriers, K_FBMC])));
D_FBMC_DFT = C_DFTspread_RX' * E_FBMC_DFT * Precalc_FBMC_DFT;
Gamma_FBMC_DFT = C_DFTspread_RX' * E_FBMC_DFT * G_FBMC_DFT';
SINR_FBMC_DFT_dB_OneRealization(:,:,i_SNR) = 10*log10(1./(reshape( sum(abs(D_FBMC_DFT-eye(size(D_FBMC_DFT))).^2,2) + sum(abs(Gamma_FBMC_DFT).^2,2)*Pn , [(NrSubcarriers-CP_Length_FBMC_DFT)/2, K_FBMC])));
end
SINR_FBMC_dB(:,:,:,i_Rep) = SINR_FBMC_dB_OneRealization;
SINR_FBMC_DFT_dB(:,:,:,i_Rep) = SINR_FBMC_DFT_dB_OneRealization;
end
TimePassed = toc;
disp(['Realization ' int2str(i_Rep) ' of ' int2str(NrRepetitions) ' needed ' int2str(TimePassed) 's. Total simulation time:' int2str(TimePassed*NrRepetitions/NrWorkers/60) 'minutes']);
end
if CalculateTheory
%% Calculate Achievable Rate
Load_BICM_QAM = load('Theory\BICM_Capacity_AWGN_4_16_64_QAM');
Load_BICM_PAM = load('Theory\BICM_Capacity_AWGN_2_4_8_PAM');
BICM_QAM = Load_BICM_QAM.C_max;
BICM_PAM = Load_BICM_PAM.C_max;
SNR_Ref_QAM = Load_BICM_QAM.SNR_dB;
SNR_Ref_PAM = Load_BICM_PAM.SNR_dB;
[a,b,c,d] = size(SINR_FBMC_dB);
OneTapRate_FBMC = reshape( interp1( SNR_Ref_PAM , BICM_PAM , SINR_FBMC_dB(:) ,'spline'), a,b,c,d);
R_FBMC = squeeze(mean(sum(sum(OneTapRate_FBMC,1),2),4))/(FBMC.PHY.TimeSpacing*(FBMC.Nr.MCSymbols));
[a,b,c,d] = size(SINR_FBMC_DFT_dB);
OneTapRate_FBMC_DFT = reshape( interp1( SNR_Ref_QAM , BICM_QAM , SINR_FBMC_DFT_dB(:) ,'spline'), a,b,c,d);
R_FBMC_DFT = squeeze(mean(sum(sum(OneTapRate_FBMC_DFT,1),2),4))/(FBMC_DFT.PHY.TimeSpacing*(FBMC_DFT.Nr.MCSymbols));
end
%% Maximize over CQI => perfect feedback
Througput_OFDM = max(M_Througput_OFDM,[],3);
Througput_OFDMnoCP = max(M_Througput_OFDMnoCP,[],3);
Througput_FBMC = max(M_Througput_FBMC,[],3);
Througput_DFT_OFDM = max(M_Througput_DFT_OFDM,[],3);
Througput_DFT_OFDMnoCP = max(M_Througput_DFT_OFDMnoCP,[],3);
Througput_FBMC_DFT = max(M_Througput_FBMC_DFT,[],3);
%% Plot Throughput
if CalculateTheory
figure(13);
plot(M_SNR_dB,mean(Througput_DFT_OFDM,2)/1e6,'- black'); hold on;
plot(M_SNR_dB,mean(Througput_DFT_OFDMnoCP,2)/1e6,'- red'); hold on;
plot(M_SNR_dB,mean(Througput_FBMC_DFT,2)/1e6,'- blue'); hold on;
plot(M_SNR_dB,mean(Througput_FBMC,2)/1e6,'- magenta'); hold on;
plot(M_SNR_dB,R_FBMC_DFT/1e6,': blue');
plot(M_SNR_dB,R_FBMC/1e6,': magenta');
xlabel('Signal-to-Noise Ratio [dB]');
ylabel('Achievable Rate, Throughput [Mbit/s]');
legend({'SC-FDMA (with CP)','SC-FDMA (no CP)','Pruned DFT-s FBMC','FBMC-OQAM','Rate p-DFT-s FBMC','Rate FBMC-OQAM'},'Location','NorthWest');
else
figure(13);
plot(M_SNR_dB,mean(Througput_DFT_OFDM,2)/1e6,'- black'); hold on;
plot(M_SNR_dB,mean(Througput_DFT_OFDMnoCP,2)/1e6,'- red'); hold on;
plot(M_SNR_dB,mean(Througput_FBMC_DFT,2)/1e6,'- blue'); hold on;
plot(M_SNR_dB,mean(Througput_FBMC,2)/1e6,'- magenta'); hold on;
xlabel('Signal-to-Noise Ratio [dB]');
ylabel('Throughput [Mbit/s]');
legend({'SC-FDMA (with CP)','SC-FDMA (no CP)','Pruned DFT-s FBMC','FBMC-OQAM'},'Location','NorthWest');
end
figure(100);
plot(M_SNR_dB,mean(Througput_OFDM,2)/1e6,'- black'); hold on;
plot(M_SNR_dB,mean(Througput_OFDMnoCP,2)/1e6,'- red'); hold on;
plot(M_SNR_dB,mean(Througput_FBMC,2)/1e6,'- magenta'); hold on;
xlabel('Signal-to-Noise Ratio [dB]');
ylabel('Throughput [Mbit/s]');
legend({'OFDM (with CP)','OFDM (no CP)','FBMC-OQAM'},'Location','NorthWest');
title('Comparision of Multicarrier Schemes (OFDM vs FBMC-OQAM)');
figure(13);
%% Save Results
SaveStuff = false;
if SaveStuff
Name = ['.\Results\SISO_Throughput_' PowerDelayProfile '_v' int2str(Velocity_kmh) '_' int2str(NrSubcarriers) '.mat'];
meanThrougput_OFDM = mean(Througput_OFDM,2);
meanThrougput_OFDMnoCP = mean(Througput_OFDMnoCP,2);
meanThrougput_FBMC = mean(Througput_FBMC,2);
meanThrougput_DFT_OFDM = mean(Througput_DFT_OFDM,2);
meanThrougput_DFT_OFDMnoCP = mean(Througput_DFT_OFDMnoCP,2);
meanThrougput_FBMC_DFT = mean(Througput_FBMC_DFT,2);
meanThrougput_DFT_OFDM = mean(Througput_DFT_OFDM,2);
save(Name,...
'R_FBMC', ...
'R_FBMC_DFT', ...
'C_FBMC', ...
'C_FBMC_DFT', ...
'meanThrougput_OFDM', ...
'meanThrougput_OFDMnoCP', ...
'meanThrougput_FBMC', ...
'meanThrougput_DFT_OFDM', ...
'meanThrougput_DFT_OFDMnoCP', ...
'meanThrougput_FBMC_DFT', ...
'M_SNR_dB',...
'NrRepetitions');
end