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Figure_09_PAPR.m
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% =========================================================================
% (c) 2018 Ronald Nissel, https://www.linkedin.com/in/ronaldnissel/
% =========================================================================
% This script shows the simulated peak-to-average-power ratio (PAPR) and
% additionally the simulated power in time and in frequency.
% Reproduces Figure 9 of "Pruned DFT Spread FBMC: Low PAPR, Low Latency,
% High Spectral Efficiency", R. Nissel and M. Rupp, IEEE Transactions on
% Communications
clear; close all;
%% Parameters
% Simulation
NrRepetitions = 2000; % Number of Monte Carlo repetitions.
% FBMC and OFDM Parameters
NrSubcarriers = 256; % Number of subcarriers
QAM_ModulationOrder = 4; % 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; % Frequency domain CP for pruned DFT spread FBMC. Multiple of two: 0, 2, 4... Can usually be set to zero
CP_Length_FBMC_DFT_LCP = 26; % Same as "CP_Length_FBMC_DFT" but different value to check the effect of the frequency CP on the PAPR
CP_Length_FFT_FBMC = 0; % "Time domain" CP for the FFT-FBMC scheme.
SamplingRate = SubcarrierSpacing*14*12*2; % Sampling rate, should approximatly match the power-delay profile of the channel. "14", so that the CP fits the sampling rate
PseudoOverlappingFactor = 4; % Pseudo overlapping factor to keep the implementation simple. The true overlapping factor is 1.56.
% #########################################################################
% % In the paper:
% SamplingRate = 15e3*14*12*8*2;
% NrRepetitions = 200000;
% #########################################################################
%% 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,
PseudoOverlappingFactor, ... % Overlapping factor (also determines oversampling in the frequency domain)
0, ... % Initial phase shift
true ... % Polyphase implementation
);
FBMC_PhaseCondition = Modulation.FBMCphaseCondition(...
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,
PseudoOverlappingFactor, ... % 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
PseudoOverlappingFactor, ... % Overlapping factor (also determines oversampling in the frequency domain)
0, ... % Initial phase shift
true ... % Polyphase implementation
);
FBMC_TimeSpread = 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
'PHYDYAS-OQAM',... % Prototype filter Hermite, PHYDYAS, InversePHYDYAS, HermiteCut, PHYDYASCut, Hann, Blackman
PseudoOverlappingFactor, ... % 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');
%% 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);
% Reduced DFT matrix
W_Tilde = W(:,Index_Tilde) ;
% One-tap scaling of the data symbols
b_Tilde = sqrt(2./(a(Index_Tilde)));
% Final coding matrix for one FBMC symbol
C_DFTspread_TX = T_CP*W_Tilde*diag(b_Tilde);
C_DFTspread_RX = R_CP*W_Tilde*diag(b_Tilde);
%% Larger Frequency CP for the PAPR Plot (essentially the same as above)
T_CP2 = zeros(NrSubcarriers,NrSubcarriers-CP_Length_FBMC_DFT_LCP);
T_CP2(1:CP_Length_FBMC_DFT_LCP/2,end-CP_Length_FBMC_DFT_LCP/2+1:end) = eye(CP_Length_FBMC_DFT_LCP/2);
T_CP2(CP_Length_FBMC_DFT_LCP/2+1:end-CP_Length_FBMC_DFT_LCP/2,:) = eye(NrSubcarriers-CP_Length_FBMC_DFT_LCP);
T_CP2(end-CP_Length_FBMC_DFT_LCP/2+1:end,1:CP_Length_FBMC_DFT_LCP/2) = eye(CP_Length_FBMC_DFT_LCP/2);
R_CP2 = zeros(NrSubcarriers,NrSubcarriers-CP_Length_FBMC_DFT_LCP);
R_CP2(CP_Length_FBMC_DFT_LCP/2+1:end-CP_Length_FBMC_DFT_LCP/2,:) = eye(NrSubcarriers-CP_Length_FBMC_DFT_LCP);
W2 = fft( eye(NrSubcarriers-CP_Length_FBMC_DFT_LCP) ) / sqrt( NrSubcarriers-CP_Length_FBMC_DFT_LCP );
a2 = abs(diag(W2'*R_CP2'*D_temp*T_CP2*W2));
a2 = a2+randn(size(a2))*10^-12; % randn so that sorting is unique
a_Tilde2 = sort(a2,'descend');
alpha2 = a_Tilde2((NrSubcarriers-CP_Length_FBMC_DFT_LCP)/2);
Index_Tilde2 = (a2>=alpha2);
W_Tilde2 = W2(:,Index_Tilde2) ;
b_Tilde2 = sqrt(2./(a2(Index_Tilde2)));
C_DFTspread_TX2 = T_CP2*W_Tilde2*diag(b_Tilde2);
C_DFTspread_RX2 = R_CP2*W_Tilde2*diag(b_Tilde2);
%% Spreading in Time, FFT-FBMC
TrueNrSubcarriers = FBMC_TimeSpread.Nr.Subcarriers;
FBMC_TimeSpread.SetNrSubcarriers(1);
D_temp = FBMC_TimeSpread.GetFBMCMatrix;
FBMC_TimeSpread.SetNrSubcarriers(TrueNrSubcarriers);
T_CP3 = zeros(K_FBMC,K_FBMC-CP_Length_FFT_FBMC);
T_CP3(1:CP_Length_FFT_FBMC/2,end-CP_Length_FFT_FBMC/2+1:end) = eye(CP_Length_FFT_FBMC/2);
T_CP3(CP_Length_FFT_FBMC/2+1:end-CP_Length_FFT_FBMC/2,:) = eye(K_FBMC-CP_Length_FFT_FBMC);
T_CP3(end-CP_Length_FFT_FBMC/2+1:end,1:CP_Length_FFT_FBMC/2) = eye(CP_Length_FFT_FBMC/2);
R_CP3 = zeros(K_FBMC,K_FBMC-CP_Length_FFT_FBMC);
R_CP3(CP_Length_FFT_FBMC/2+1:end-CP_Length_FFT_FBMC/2,:) = eye(K_FBMC-CP_Length_FFT_FBMC);
W3 = fft( eye(K_FBMC-CP_Length_FFT_FBMC) ) / sqrt( K_FBMC-CP_Length_FFT_FBMC );
a3 = abs(diag(W3'*R_CP3'*D_temp*T_CP3*W3));
a3 = a3+randn(size(a3))*10^-12; % randn so that sorting is unique
a_Tilde3 = sort(a3,'descend');
alpha3 = a_Tilde3((K_FBMC-CP_Length_FFT_FBMC)/2);
Index_Tilde3 = (a3>=alpha3);
W_Tilde3_1 = W3(:,Index_Tilde3);
W_Tilde3_2 = W3(:,not(Index_Tilde3));
% W_Tilde3_1 = W_Tilde3_1*diag(sqrt(2./(a3(Index_Tilde3))));
% W_Tilde3_2 = W_Tilde3_2*diag(sqrt(2./(a3(not(Index_Tilde3)))));
C_FFT_FBMC_TX = kron(kron(T_CP3*W_Tilde3_1,sparse(eye(FBMC_TimeSpread.Nr.Subcarriers/2))),[1,0;0,0]) + kron(kron(T_CP3*W_Tilde3_2,sparse(eye(FBMC_TimeSpread.Nr.Subcarriers/2))),[0,0;0,1]);
C_FFT_FBMC_RX = kron(kron(R_CP3*W_Tilde3_1,sparse(eye(FBMC_TimeSpread.Nr.Subcarriers/2))),[1,0;0,0]) + kron(kron(R_CP3*W_Tilde3_2,sparse(eye(FBMC_TimeSpread.Nr.Subcarriers/2))),[0,0;0,1]);
G_temp = FBMC_TimeSpread.GetTXMatrix;
NormalizationFactor = sum(sum(abs(G_temp).^2))/sum(sum(abs(G_temp*C_FFT_FBMC_TX).^2));
C_FFT_FBMC_TX = C_FFT_FBMC_TX*sqrt(NormalizationFactor);
C_FFT_FBMC_RX = C_FFT_FBMC_RX/sqrt(NormalizationFactor);
%% Preallocate
Simulated_TransmitPowerOverTime_OFDM = zeros(N,1);
Simulated_TransmitPowerOverTime_OFDMnoCP = zeros(N,1);
Simulated_TransmitPowerOverTime_FBMC = zeros(N,1);
Simulated_TransmitPowerOverTime_DFT_OFDM = zeros(N,1);
Simulated_TransmitPowerOverTime_DFT_OFDMnoCP = zeros(N,1);
Simulated_TransmitPowerOverTime_FBMC_DFT = zeros(N,1);
dt = 1/SamplingRate; % time-spacing between samples
Simulated_PowerSpectralDensity_OFDM = zeros(N,1);
Simulated_PowerSpectralDensity_OFDMnoCP = zeros(N,1);
Simulated_PowerSpectralDensity_FBMC = zeros(N,1);
Simulated_PowerSpectralDensity_DFT_OFDM = zeros(N,1);
Simulated_PowerSpectralDensity_DFT_OFDMnoCP = zeros(N,1);
Simulated_PowerSpectralDensity_FBMC_DFT = zeros(N,1);
df = 1./(N*dt); % Frequency-spacing between samples
%% Start Simulation
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 CP which, however, is not necesarry most of the time => same bit rate
BinaryDataStream_FBMC_DFT_LCP = randi( [0 1] , K_OFDMnoCP*(NrSubcarriers-CP_Length_FBMC_DFT_LCP)*log2(QAM.ModulationOrder) ,1); % Maybe a reduced bit rate due to the CP which, however, is not necesarry most of the time => same bit rate
BinaryDataStream_FFT_FBMC = randi( [0 1] , K_OFDMnoCP*(NrSubcarriers-CP_Length_FFT_FBMC)*log2(QAM.ModulationOrder) ,1); % Maybe a reduced bit rate due to the CP which, however, is not necesarry most of the time => same bit rate
%% 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 );
x_FBMC_DFT_LCP = reshape( QAM.Bit2Symbol(BinaryDataStream_FBMC_DFT_LCP), (NrSubcarriers - CP_Length_FBMC_DFT_LCP)/2 , K_FBMC );
x_FBMC_FFT_FBMC = QAM.Bit2Symbol(BinaryDataStream_FFT_FBMC);
%% Generate Transmit Signal in the Time Domain
s_OFDM = OFDM.Modulation( x_OFDM );
s_OFDMnoCP = OFDMnoCP.Modulation( x_OFDMnoCP );
s_FBMC = FBMC.Modulation( x_FBMC );
s_DFT_OFDM = OFDM.Modulation( DFTMatrix*x_OFDM );
s_DFT_OFDMnoCP = OFDMnoCP.Modulation( DFTMatrix*x_OFDMnoCP );
s_FBMC_DFT = FBMC_DFT.Modulation( C_DFTspread_TX*x_FBMC_DFT );
s_FBMC_DFT_LCP = FBMC_DFT.Modulation( C_DFTspread_TX2*x_FBMC_DFT_LCP ); % Large frequency CP
s_FBMC_FFT_FBMC = FBMC_TimeSpread.Modulation( reshape( C_FFT_FBMC_TX*x_FBMC_FFT_FBMC(:) , NrSubcarriers, K_FBMC ) );
% Simple DFT spreading which keeps the OQAM structure
x_FBMC_complex = x_FBMC(:,1:2:end) + 1j*x_FBMC(:,2:2:end); % OQAM destaggering
x_FBMC_complex_DFT = DFTMatrix*x_FBMC_complex;
x_FBMC_simpleton = nan(size(x_FBMC));
x_FBMC_simpleton(:,1:2:end) = real(x_FBMC_complex_DFT); % OQAM staggering
x_FBMC_simpleton(:,2:2:end) = imag(x_FBMC_complex_DFT); % OQAM staggering
s_FBMC_SimpletonDFT = FBMC.Modulation( x_FBMC_simpleton );
s_FBMC_SimpletonDFT_PhaseCon = FBMC_PhaseCondition.Modulation( x_FBMC_simpleton );
%% Calculate Transmit Power
Simulated_TransmitPowerOverTime_OFDM = abs(s_OFDM).^2 + Simulated_TransmitPowerOverTime_OFDM;
Simulated_TransmitPowerOverTime_OFDMnoCP = abs(s_OFDMnoCP).^2 + Simulated_TransmitPowerOverTime_OFDMnoCP;
Simulated_TransmitPowerOverTime_FBMC = abs(s_FBMC).^2 + Simulated_TransmitPowerOverTime_FBMC;
Simulated_TransmitPowerOverTime_DFT_OFDM = abs(s_DFT_OFDM).^2 + Simulated_TransmitPowerOverTime_DFT_OFDM;
Simulated_TransmitPowerOverTime_DFT_OFDMnoCP = abs(s_DFT_OFDMnoCP).^2 + Simulated_TransmitPowerOverTime_DFT_OFDMnoCP;
Simulated_TransmitPowerOverTime_FBMC_DFT = abs(s_FBMC_DFT).^2 + Simulated_TransmitPowerOverTime_FBMC_DFT;
%% Calculate Power Spectral Density
Simulated_PowerSpectralDensity_OFDM = abs(fft(s_OFDM)).^2 + Simulated_PowerSpectralDensity_OFDM;
Simulated_PowerSpectralDensity_OFDMnoCP = abs(fft(s_OFDMnoCP)).^2 + Simulated_PowerSpectralDensity_OFDMnoCP;
Simulated_PowerSpectralDensity_FBMC = abs(fft(s_FBMC)).^2 + Simulated_PowerSpectralDensity_FBMC;
Simulated_PowerSpectralDensity_DFT_OFDM = abs(fft(s_DFT_OFDM)).^2 + Simulated_PowerSpectralDensity_DFT_OFDM;
Simulated_PowerSpectralDensity_DFT_OFDMnoCP = abs(fft(s_DFT_OFDMnoCP)).^2 + Simulated_PowerSpectralDensity_DFT_OFDMnoCP;
Simulated_PowerSpectralDensity_FBMC_DFT = abs(fft(s_FBMC_DFT)).^2 + Simulated_PowerSpectralDensity_FBMC_DFT;
%% For the PAPR calculation we chop the signal in time-periods of length 1/F
s_OFDM_reshaped = reshape( s_OFDM((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)) , OFDM.Implementation.FFTSize+OFDM.Implementation.CyclicPrefix , OFDM.Nr.MCSymbols );
s_OFDM_reshaped = s_OFDM_reshaped(OFDM.Implementation.CyclicPrefix+1:end ,:); % Not necessary
s_OFDMnoCP_reshaped = reshape( s_OFDMnoCP((OFDMnoCP.Implementation.ZeroGuardSamples+1):(end-OFDMnoCP.Implementation.ZeroGuardSamples)) , OFDMnoCP.Implementation.FFTSize+OFDMnoCP.Implementation.CyclicPrefix , OFDMnoCP.Nr.MCSymbols );
s_OFDMnoCP_reshaped = s_OFDMnoCP_reshaped(OFDMnoCP.Implementation.CyclicPrefix+1:end,:); % Not necessary
s_FBMC_reshaped = reshape( s_FBMC((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)) , OFDM.Implementation.FFTSize , FBMC.Nr.MCSymbols/2 );
s_FBMC_reshaped(:,[1 end]) = [];
% DFT
s_DFT_OFDM_reshaped = reshape( s_DFT_OFDM((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)) , OFDM.Implementation.FFTSize+OFDM.Implementation.CyclicPrefix , OFDM.Nr.MCSymbols );
s_DFT_OFDM_reshaped = s_DFT_OFDM_reshaped(OFDM.Implementation.CyclicPrefix+1:end,:); % Not necessary
s_DFT_OFDMnoCP_reshaped = reshape( s_DFT_OFDMnoCP((OFDMnoCP.Implementation.ZeroGuardSamples+1):(end-OFDMnoCP.Implementation.ZeroGuardSamples)) , OFDMnoCP.Implementation.FFTSize+OFDMnoCP.Implementation.CyclicPrefix , OFDMnoCP.Nr.MCSymbols);
s_DFT_OFDMnoCP_reshaped = s_DFT_OFDMnoCP_reshaped(OFDMnoCP.Implementation.CyclicPrefix+1:end,:); % Not necessary
s_FBMC_DFT_reshaped = reshape(s_FBMC_DFT((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)),OFDM.Implementation.FFTSize,FBMC.Nr.MCSymbols/2);
s_FBMC_DFT_reshaped(:,[1 end]) = [];
s_FBMC_SimpletonDFT_reshaped = reshape(s_FBMC_SimpletonDFT((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)),OFDM.Implementation.FFTSize,FBMC.Nr.MCSymbols/2);
s_FBMC_SimpletonDFT_reshaped(:,[1 end]) = [];
s_FBMC_SimpletonDFT_PhaseCon_reshaped = reshape(s_FBMC_SimpletonDFT_PhaseCon((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)),OFDM.Implementation.FFTSize,FBMC.Nr.MCSymbols/2);
s_FBMC_SimpletonDFT_PhaseCon_reshaped(:,[1 end]) = [];
s_FBMC_DFT_LCP_reshaped = reshape(s_FBMC_DFT_LCP((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)),OFDM.Implementation.FFTSize,FBMC.Nr.MCSymbols/2);
s_FBMC_DFT_LCP_reshaped(:,[1 end]) = [];
s_FBMC_FFT_FBMC_reshaped = reshape(s_FBMC_FFT_FBMC((OFDM.Implementation.ZeroGuardSamples+1):(end-OFDM.Implementation.ZeroGuardSamples)),OFDM.Implementation.FFTSize,FBMC.Nr.MCSymbols/2);
s_FBMC_FFT_FBMC_reshaped(:,[1 end]) = [];
%% Signal Power, Should be 1
AveragePower_OFDM(i_rep) = mean(mean( abs(s_OFDM_reshaped).^2 ));
AveragePower_OFDMnoCP(i_rep) = mean(mean( abs(s_OFDMnoCP_reshaped).^2 ));
AveragePower_FBMC(i_rep) = mean(mean( abs(s_FBMC_reshaped).^2 ));
AveragePower_DFT_OFDM(i_rep) = mean(mean( abs(s_DFT_OFDM_reshaped).^2 ));
AveragePower_DFT_OFDMnoCP(i_rep) = mean(mean( abs(s_DFT_OFDMnoCP_reshaped).^2 ));
AveragePower_FBMC_DFT(i_rep) = mean(mean( abs(s_FBMC_DFT_reshaped).^2 ));
AveragePower_FBMC_SimpletonDFT(i_rep) = mean(mean( abs(s_FBMC_SimpletonDFT_reshaped).^2 ));
AveragePower_FBMC_SimpletonDFT_PhaseCon(i_rep) = mean(mean( abs(s_FBMC_SimpletonDFT_PhaseCon_reshaped).^2 ));
AveragePower_FBMC_DFT_LCP(i_rep) = mean(mean( abs(s_FBMC_DFT_LCP_reshaped).^2 ));
AveragePower_FBMC_FFT_FBMC(i_rep) = mean(mean( abs(s_FBMC_FFT_FBMC_reshaped).^2 ));
%% Peak power values for each time intervall 1/F (NFFT Samples)
PeakPower_OFDM(i_rep,:) = max( abs(s_OFDM_reshaped).^2 ,[],1);
PeakPower_OFDMnoCP(i_rep,:) = max( abs(s_OFDMnoCP_reshaped).^2 ,[],1);
PeakPower_FBMC(i_rep,:) = max( abs(s_FBMC_reshaped).^2 ,[],1);
PeakPower_DFT_OFDM(i_rep,:) = max( abs(s_DFT_OFDM_reshaped).^2 ,[],1);
PeakPower_DFT_OFDMnoCP(i_rep,:) = max( abs(s_DFT_OFDMnoCP_reshaped).^2 ,[],1);
PeakPower_FBMC_DFT(i_rep,:) = max( abs(s_FBMC_DFT_reshaped).^2 ,[],1);
PeakPower_FBMC_SimpletonDFT(i_rep,:) = max( abs(s_FBMC_SimpletonDFT_reshaped).^2 ,[],1);
PeakPower_FBMC_SimpletonDFT_PhaseCon(i_rep,:) = max( abs(s_FBMC_SimpletonDFT_PhaseCon_reshaped).^2 ,[],1);
PeakPower_FBMC_DFT_LCP(i_rep,:) = max( abs(s_FBMC_DFT_LCP_reshaped).^2 ,[],1);
PeakPower_FBMC_FFT_FBMC(i_rep,:) = max( abs(s_FBMC_FFT_FBMC_reshaped).^2 ,[],1);
TimePassed = toc;
if mod(i_rep,10)==0
disp(['Realization ' int2str(i_rep) ' of ' int2str(NrRepetitions) '. Time left: ' int2str(TimePassed/i_rep*(NrRepetitions-i_rep)/60) 'minutes']);
end
end
%% Plot the Peak-to-average power ratio
PAPR_OFDM = 10*log10(PeakPower_OFDM(:));
PAPR_OFDMnoCP = 10*log10(PeakPower_OFDMnoCP(:));
PAPR_FBMC = 10*log10(PeakPower_FBMC(:));
PAPR_DFT_OFDM = 10*log10(PeakPower_DFT_OFDM(:));
PAPR_DFT_OFDMnoCP = 10*log10(PeakPower_DFT_OFDMnoCP(:));
PAPR_FBMC_DFT = 10*log10(PeakPower_FBMC_DFT(:));
PAPR_FBMC_SimpletonDFT = 10*log10(PeakPower_FBMC_SimpletonDFT(:));
PAPR_FBMC_SimpletonDFT_PhaseCon = 10*log10(PeakPower_FBMC_SimpletonDFT_PhaseCon(:));
PAPR_FBMC_DFT_LCP = 10*log10(PeakPower_FBMC_DFT_LCP(:));
PAPR_FBMC_FFT_FBMC = 10*log10(PeakPower_FBMC_FFT_FBMC(:));
[CCDF_OFDM , CCDF_OFDM_xAxis] = ecdf(PAPR_OFDM); CCDF_OFDM=1-CCDF_OFDM;
[CCDF_OFDMnoCP , CCDF_OFDMnoCP_xAxis] = ecdf(PAPR_OFDMnoCP); CCDF_OFDMnoCP=1-CCDF_OFDMnoCP;
[CCDF_FBMC , CCDF_FBMC_xAxis] = ecdf(PAPR_FBMC); CCDF_FBMC=1-CCDF_FBMC;
[CCDF_DFT_OFDM , CCDF_DFT_OFDM_xAxis] = ecdf(PAPR_DFT_OFDM); CCDF_DFT_OFDM=1-CCDF_DFT_OFDM;
[CCDF_DFT_OFDMnoCP , CCDF_DFT_OFDMnoCP_xAxis] = ecdf(PAPR_DFT_OFDMnoCP); CCDF_DFT_OFDMnoCP=1-CCDF_DFT_OFDMnoCP;
[CCDF_FBMC_DFT , CCDF_FBMC_DFT_xAxis] = ecdf(PAPR_FBMC_DFT); CCDF_FBMC_DFT=1-CCDF_FBMC_DFT;
[CCDF_FBMC_SimpletonDFT , CCDF_FBMC_SimpletonDFT_xAxis] = ecdf(PAPR_FBMC_SimpletonDFT); CCDF_FBMC_SimpletonDFT=1-CCDF_FBMC_SimpletonDFT;
[CCDF_FBMC_SimpletonDFT_PhaseCon , CCDF_FBMC_SimpletonDFT_PhaseCon_xAxis] = ecdf(PAPR_FBMC_SimpletonDFT_PhaseCon); CCDF_FBMC_SimpletonDFT_PhaseCon=1-CCDF_FBMC_SimpletonDFT_PhaseCon;
[CCDF_FBMC_DFT_LCP , CCDF_FBMC_DFT_LCP_xAxis] = ecdf(PAPR_FBMC_DFT_LCP); CCDF_FBMC_DFT_LCP=1-CCDF_FBMC_DFT_LCP;
[CCDF_FBMC_FFT_FBMC , CCDF_FBMC_FFT_FBMC_xAxis] = ecdf(PAPR_FBMC_FFT_FBMC); CCDF_FBMC_FFT_FBMC=1-CCDF_FBMC_FFT_FBMC;
MaxMinAll_noDFT = max([min(CCDF_OFDM_xAxis),min(CCDF_OFDMnoCP_xAxis),min(CCDF_FBMC_xAxis),min(CCDF_FBMC_FFT_FBMC_xAxis)]);
MinMaxAll_noDFT = min([max(CCDF_OFDM_xAxis),max(CCDF_OFDMnoCP_xAxis),max(CCDF_FBMC_xAxis),max(CCDF_FBMC_FFT_FBMC_xAxis)]);
CCDF_OFDM_xAxis_LessPoints = linspace(MaxMinAll_noDFT,MinMaxAll_noDFT,100);
[x, index] = unique(CCDF_OFDM_xAxis);
CCDF_OFDM_LessPoints = 10.^interp1(x,log10(CCDF_OFDM(index)),CCDF_OFDM_xAxis_LessPoints);
CCDF_OFDMnoCP_xAxis_LessPoints = linspace(MaxMinAll_noDFT,MinMaxAll_noDFT,100);
[x, index] = unique(CCDF_OFDMnoCP_xAxis);
CCDF_OFDMnoCP_LessPoints = 10.^interp1(x,log10(CCDF_OFDMnoCP(index)),CCDF_OFDMnoCP_xAxis_LessPoints);
CCDF_FBMC_xAxis_LessPoints = linspace(MaxMinAll_noDFT,MinMaxAll_noDFT,100);
[x, index] = unique(CCDF_FBMC_xAxis);
CCDF_FBMC_LessPoints = 10.^interp1(x,log10(CCDF_FBMC(index)),CCDF_FBMC_xAxis_LessPoints);
CCDF_FBMC_FFT_FBMC_xAxis_LessPoints = linspace(MaxMinAll_noDFT,MinMaxAll_noDFT,100);
[x, index] = unique(CCDF_FBMC_FFT_FBMC_xAxis);
CCDF_FBMC_FFT_FBMC_LessPoints = 10.^interp1(x,log10(CCDF_FBMC_FFT_FBMC(index)),CCDF_FBMC_FFT_FBMC_xAxis_LessPoints);
MaxMinAll_DFT = max([min(CCDF_DFT_OFDM_xAxis),min(CCDF_DFT_OFDMnoCP_xAxis),min(CCDF_FBMC_DFT_xAxis)]);
MinMaxAll_DFT = min([max(CCDF_DFT_OFDM_xAxis),max(CCDF_DFT_OFDMnoCP_xAxis),max(CCDF_FBMC_DFT_xAxis)]);
CCDF_DFT_OFDM_xAxis_LessPoints = linspace(MaxMinAll_DFT,MinMaxAll_DFT,100);
[x, index] = unique(CCDF_DFT_OFDM_xAxis);
CCDF_DFT_OFDM_LessPoints = 10.^interp1(x,log10(CCDF_DFT_OFDM(index)),CCDF_DFT_OFDM_xAxis_LessPoints);
CCDF_DFT_OFDMnoCP_xAxis_LessPoints = linspace(MaxMinAll_DFT,MinMaxAll_DFT,100);
[x, index] = unique(CCDF_DFT_OFDMnoCP_xAxis);
CCDF_DFT_OFDMnoCP_LessPoints = 10.^interp1(x,log10(CCDF_DFT_OFDMnoCP(index)),CCDF_DFT_OFDMnoCP_xAxis_LessPoints);
CCDF_FBMC_DFT_xAxis_LessPoints = linspace(MaxMinAll_DFT,MinMaxAll_DFT,100);
[x, index] = unique(CCDF_FBMC_DFT_xAxis);
CCDF_FBMC_DFT_LessPoints = 10.^interp1(x,log10(CCDF_FBMC_DFT(index)),CCDF_FBMC_DFT_xAxis_LessPoints);
MaxMinAll_SimpletonDFT = max([min(CCDF_FBMC_SimpletonDFT_xAxis)]);
MinMaxAll_SimpletonDFT = min([max(CCDF_FBMC_SimpletonDFT_xAxis)]);
CCDF_FBMC_SimpletonDFT_xAxis_LessPoints = linspace(MaxMinAll_SimpletonDFT,MinMaxAll_SimpletonDFT,100);
[x, index] = unique(CCDF_FBMC_SimpletonDFT_xAxis);
CCDF_FBMC_SimpletonDFT_LessPoints = 10.^interp1(x,log10(CCDF_FBMC_SimpletonDFT(index)),CCDF_FBMC_SimpletonDFT_xAxis_LessPoints);
MaxMinAll_SimpletonDFT_PhaseCon = max([min(CCDF_FBMC_SimpletonDFT_PhaseCon_xAxis)]);
MinMaxAll_SimpletonDFT_PhaseCon = min([max(CCDF_FBMC_SimpletonDFT_PhaseCon_xAxis)]);
CCDF_FBMC_SimpletonDFT_xAxis_LessPoints_PhaseCon = linspace(MaxMinAll_SimpletonDFT_PhaseCon,MinMaxAll_SimpletonDFT_PhaseCon,100);
[x, index] = unique(CCDF_FBMC_SimpletonDFT_PhaseCon_xAxis);
CCDF_FBMC_SimpletonDFT_LessPoints_PhaseCon = 10.^interp1(x,log10(CCDF_FBMC_SimpletonDFT_PhaseCon(index)),CCDF_FBMC_SimpletonDFT_xAxis_LessPoints_PhaseCon);
MaxMinAll_DFT_LCP = max(min(CCDF_FBMC_DFT_LCP_xAxis));
MinMaxAll_DFT_LCP = min(max(CCDF_FBMC_DFT_LCP_xAxis));
CCDF_FBMC_DFT_LCP_xAxis_LessPoints = linspace(MaxMinAll_DFT_LCP,MinMaxAll_DFT_LCP,100);
[x, index] = unique(CCDF_FBMC_DFT_LCP_xAxis);
CCDF_FBMC_DFT_LCP_LessPoints = 10.^interp1(x,log10(CCDF_FBMC_DFT_LCP(index)),CCDF_FBMC_DFT_LCP_xAxis_LessPoints);
figure(9);
markersize = 3;
s1 = semilogy(CCDF_OFDM_xAxis_LessPoints,CCDF_OFDM_LessPoints,'Color',[127 127 0]/255); hold on;
s2 = semilogy(CCDF_FBMC_xAxis_LessPoints,CCDF_FBMC_LessPoints,'magenta'); hold on;
semilogy(CCDF_OFDM_xAxis_LessPoints(30:10:100),CCDF_OFDM_LessPoints(30:10:100),'s','Markersize',markersize,'Color',[127 127 0]/255); hold on;
semilogy(CCDF_FBMC_xAxis_LessPoints(35:10:100),CCDF_FBMC_LessPoints(35:10:100),'magenta o','Markersize',markersize); hold on;
s3 = semilogy(CCDF_FBMC_SimpletonDFT_xAxis_LessPoints,CCDF_FBMC_SimpletonDFT_LessPoints,'Color',[127 127 127]/255); hold on;
semilogy(CCDF_FBMC_SimpletonDFT_xAxis_LessPoints(35:10:100),CCDF_FBMC_SimpletonDFT_LessPoints(35:10:100),'o','Markersize',markersize,'Color',[127 127 127]/255); hold on;
s4 = semilogy(CCDF_FBMC_SimpletonDFT_xAxis_LessPoints_PhaseCon,CCDF_FBMC_SimpletonDFT_LessPoints_PhaseCon,'Color',[80 80 80]/255); hold on;
semilogy(CCDF_FBMC_SimpletonDFT_xAxis_LessPoints_PhaseCon(35:10:100),CCDF_FBMC_SimpletonDFT_LessPoints_PhaseCon(35:10:100),'o','Markersize',markersize,'Color',[80 80 80]/255); hold on;
s5 = semilogy(CCDF_DFT_OFDM_xAxis_LessPoints,CCDF_DFT_OFDM_LessPoints,'black'); hold on;
s6 = semilogy(CCDF_FBMC_DFT_xAxis_LessPoints,CCDF_FBMC_DFT_LessPoints,'blue'); hold on;
semilogy(CCDF_DFT_OFDM_xAxis_LessPoints(30:10:100),CCDF_DFT_OFDM_LessPoints(30:10:100),'black s','Markersize',markersize); hold on;
semilogy(CCDF_FBMC_DFT_xAxis_LessPoints(35:10:100),CCDF_FBMC_DFT_LessPoints(35:10:100),'blue o','Markersize',markersize); hold on;
s7 = semilogy(CCDF_FBMC_DFT_LCP_xAxis_LessPoints,CCDF_FBMC_DFT_LCP_LessPoints,'Color',[0 0 127/255]); hold on;
semilogy(CCDF_FBMC_DFT_LCP_xAxis_LessPoints(35:10:100),CCDF_FBMC_DFT_LCP_LessPoints(35:10:100),'o','Markersize',markersize,'Color',[0 0 127/255]); hold on;
s8 = semilogy(CCDF_FBMC_FFT_FBMC_xAxis_LessPoints,CCDF_FBMC_FFT_FBMC_LessPoints,'Color',[0 0 180/255]); hold on;
semilogy(CCDF_FBMC_FFT_FBMC_xAxis_LessPoints(33:10:100),CCDF_FBMC_FFT_FBMC_LessPoints(33:10:100),'o','Markersize',markersize,'Color',[0 0 180/255]); hold on;
ylim([10^-3 1]);
xlim([4 11]);
ylabel('CCDF');
xlabel('Peak-to-Average Power Ratio [dB]');
legend([s1 s2 s3 s4 s5 s6 s7 s8],{'OFDM','FBMC','Simple DFT-s FBMC','Simple DFT-s FBMC (phase)','SC-FDMA','Pruned DFT-s FBMC','Pruned DFT-s FBMC (L_CP = 26)','FFT-FBMC'});
%% Plot the Simulated Transmit Power
Simulated_TransmitPowerOverTime_OFDM = Simulated_TransmitPowerOverTime_OFDM/i_rep;
Simulated_TransmitPowerOverTime_OFDMnoCP = Simulated_TransmitPowerOverTime_OFDMnoCP/i_rep;
Simulated_TransmitPowerOverTime_FBMC = Simulated_TransmitPowerOverTime_FBMC/i_rep;
Simulated_TransmitPowerOverTime_DFT_OFDM = Simulated_TransmitPowerOverTime_DFT_OFDM/i_rep;
Simulated_TransmitPowerOverTime_DFT_OFDMnoCP = Simulated_TransmitPowerOverTime_DFT_OFDMnoCP/i_rep;
Simulated_TransmitPowerOverTime_FBMC_DFT = Simulated_TransmitPowerOverTime_FBMC_DFT/i_rep;
figure(100);
t = (0:N-1)*dt-OFDM.PHY.ZeroGuardTimeLength;
plot(t/1e-3,Simulated_TransmitPowerOverTime_OFDM,': black'); hold on;
plot(t/1e-3,Simulated_TransmitPowerOverTime_FBMC,': blue'); hold on;
plot(t/1e-3,Simulated_TransmitPowerOverTime_DFT_OFDM,'black'); hold on;
plot(t/1e-3,Simulated_TransmitPowerOverTime_FBMC_DFT,'blue'); hold on;
legend({'CP-OFDM','FBMC','DFT-OFDM','DFT-FBMC'})
ylabel('Simulated Transmit Power');
xlabel('Time [ms]');
%% Plot the Simulated Power Spectral Density
figure(101);
f = (0:N-1)*SamplingRate/N;
IndexInBand = f<(FBMC.Nr.Subcarriers-1)*FBMC.PHY.SubcarrierSpacing; % In band minus 1
NormalizeFactorPSD = mean([Simulated_PowerSpectralDensity_OFDM(IndexInBand);Simulated_PowerSpectralDensity_OFDMnoCP(IndexInBand);Simulated_PowerSpectralDensity_FBMC(IndexInBand);Simulated_PowerSpectralDensity_DFT_OFDM(IndexInBand);Simulated_PowerSpectralDensity_DFT_OFDMnoCP(IndexInBand);Simulated_PowerSpectralDensity_FBMC_DFT(IndexInBand)]);
f = f+0.5*FBMC.PHY.SubcarrierSpacing; % -0.5 because the first subcarrier starts at -0.5*FBMC.PHY.SubcarrierSpacing => Shift by 0.5 so that the bandwidth starts at exactly 0
plot(f/1e6,10*log10(Simulated_PowerSpectralDensity_OFDM/NormalizeFactorPSD),': black'); hold on;
plot(f/1e6,10*log10(Simulated_PowerSpectralDensity_FBMC/NormalizeFactorPSD),': blue'); hold on;
plot(f/1e6,10*log10(Simulated_PowerSpectralDensity_DFT_OFDM/NormalizeFactorPSD),'black'); hold on;
plot(f/1e6,10*log10(Simulated_PowerSpectralDensity_FBMC_DFT/NormalizeFactorPSD),'blue'); hold on;
legend({'CP-OFDM','FBMC','DFT-OFDM','DFT-FBMC'})
UpperTransmitFrequency = (FBMC.Nr.Subcarriers)*FBMC.PHY.SubcarrierSpacing;
LowerPlotFrequency = (FBMC.Nr.Subcarriers-5)*FBMC.PHY.SubcarrierSpacing;
UpperPlotFrequency = (FBMC.Nr.Subcarriers+20)*FBMC.PHY.SubcarrierSpacing;
plot([UpperTransmitFrequency/1e6,UpperTransmitFrequency/1e6],[-100,20],'-','Color',[1 1 1]*0.5);
xlim([LowerPlotFrequency/1e6 UpperPlotFrequency/1e6]);
ylim([-60 2]);
xlabel('Frequency [MHz]');
ylabel('Simulated Power Spectral Density');
%% 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');