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DoublySelectiveChannelEstimation.m
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DoublySelectiveChannelEstimation.m
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% =========================================================================
% (c) 2018 Ronald Nissel, ronald.nissel@gmail.com
% =========================================================================
% Allows to reproduce Figure 2, 3, 4 and 5 of "Doubly-Selective Channel
% Estimation in FBMC-OQAM and OFDM Systems", R. Nissel, et al, IEEE VTC
% Fall, 2018. In particular, this script simulates an FBMC and OFDM
% transmission over a doubly-selective channel, including doubly-selective
% MMSE channel estimation and interference cancellation. Note that, to
% truly reproduce the figures, the lines 41-46 must be uncommented.
clear; close all;
addpath('./Theory');
%% Parameters
% Simulation
M_SNR_dB = [10:5:40]; % Signal-to-Noise Ratio in dB
NrRepetitions = 25; % Number of Monte Carlo repetition (different channel realizations)
ZeroThresholdSparse = 8; % Set some matrix values, smaller than "10^(-ZeroThresholdSparse)", to zero.
PlotIterationStepsSNRdB = 35; % Plot the BER over iteration step for an SNR of 35dB.
% FBMC and OFDM parameters
L = 12*2; % Number of Subcarriers, one resource block consists of 12 subcarriers (and 0.5ms in time)
F = 15e3; % Subcarrier Spacing in Hz
SamplingRate = F*12*2; % Sampling rate in (Samples/s)
NrSubframes = 1; % Number of subframes. One subframe requires 1ms for F=15kHz.
QAM_ModulationOrder = 256; % QAM signal constellation order, 4, 16, 64, 256, 1024,...
% Channel estimation parameters
PilotToDataPowerOffset = 2; % Pilot to data power offset for OFDM. In FBMC data spreading, the power offset is twice this number.
PilotToDataPowerOffsetAux = 4.685; % Pilot to data power offset for FBMC, auxiliary method.
NrIterations = 4; % Number of iterations for interference cancellation scheme.
% Channel
Velocity_kmh = 500; % Velocity in km/h. Note that [mph]*1.6=[kmh] and [m/s]*3.6=[kmh]
PowerDelayProfile = 'VehicularA'; % Channel model, 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)
% ###########################################################################
% % In the paper:
% M_SNR_dB = [10:2:40];
% PlotIterationStepsSNRdB = 32;
% NrRepetitions = 1000;
% SamplingRate = F*14*14;
% NrSubframes = 2;
% ###########################################################################
%% FBMC Object
FBMC = Modulation.FBMC(...
L,... % Number subcarriers
30*NrSubframes,... % Number FBMC symbols
F,... % 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,
8, ... % Overlapping factor (also determines oversampling in the frequency domain)
0, ... % Initial phase shift
true ... % Polyphase implementation
);
%% OFDM Object (Add zeroes to the OFDM signal so that it fits the FBMC signal)
ZeroGuardTimeLength = ((FBMC.Nr.SamplesTotal-(round((1/15e3/14)*SamplingRate)+round(SamplingRate/15e3))*14*NrSubframes)/2)/SamplingRate;
OFDM = Modulation.OFDM(...
L,... % Number Subcarriers
14*NrSubframes,... % Number OFDM Symbols
F,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
0,... % Intermediate frequency first subcarrier (Hz)
false,... % Transmitreal valued signal
1/15e3/14, ... % Cyclic prefix length (s)
ZeroGuardTimeLength ... % Zero guard length (s)
);
%% Check Number of Samples
if OFDM.Nr.SamplesTotal~=FBMC.Nr.SamplesTotal
error('Total number of samples must be the same for OFDM and FBMC.');
end
N = OFDM.Nr.SamplesTotal;
%% PAM and QAM Object
PAM = Modulation.SignalConstellation(sqrt(QAM_ModulationOrder),'PAM');
QAM = Modulation.SignalConstellation(QAM_ModulationOrder,'QAM');
%% Pilot Matrices, 0="Data", 1=Pilot
PilotMatrix_OFDM = zeros(OFDM.Nr.Subcarriers,14);
PilotMatrix_OFDM(2:2*6:end,2:2*3.5:end)=1;
PilotMatrix_OFDM(5:2*6:end,6:2*3.5:end)=1;
PilotMatrix_OFDM(8:2*6:end,2:2*3.5:end)=1;
PilotMatrix_OFDM(11:2*6:end,6:2*3.5:end)=1;
PilotMatrix_OFDM = repmat(PilotMatrix_OFDM,[1 NrSubframes]);
PilotMatrix_FBMC = zeros(FBMC.Nr.Subcarriers,30);
PilotMatrix_FBMC(2:12:end,3:16:end) = 1;
PilotMatrix_FBMC(5:12:end,11:16:end) = 1;
PilotMatrix_FBMC(8:12:end,3+1:16:end) = 1;
PilotMatrix_FBMC(11:12:end,11+1:16:end) = 1;
PilotMatrix_FBMC = repmat(PilotMatrix_FBMC,[1 NrSubframes]);
AuxilaryPilotMatrix_FBMC = PilotMatrix_FBMC;
[a,b] = find(PilotMatrix_FBMC);
for i_pilot = 1:length(a)
AuxilaryPilotMatrix_FBMC(a(i_pilot)+1,b(i_pilot))=-1;
AuxilaryPilotMatrix_FBMC(a(i_pilot)-1,b(i_pilot))=-1;
AuxilaryPilotMatrix_FBMC(a(i_pilot),b(i_pilot)+1)=-1;
AuxilaryPilotMatrix_FBMC(a(i_pilot),b(i_pilot)-1)=-1;
end
%% Cancel Imaginary Interference At Pilot Position Object (Precoding Matrix)
AuxiliaryMethod = ChannelEstimation.ImaginaryInterferenceCancellationAtPilotPosition(...
'Auxiliary', ... % Cancellation method
AuxilaryPilotMatrix_FBMC, ... % PilotAndAuxiliaryMatrix
FBMC.GetFBMCMatrix, ... % Imaginary interference matrix
28, ... % Cancel 28 closest interferers
PilotToDataPowerOffsetAux ... % Pilot to data power offset
);
CodingMethod = ChannelEstimation.ImaginaryInterferenceCancellationAtPilotPosition(...
'Coding', ... % Cancellation method
PilotMatrix_FBMC, ... % PilotMatrix
FBMC.GetFBMCMatrix, ... % Imaginary interference matrix
20, ... % Cancel 28 closest interferers
2*PilotToDataPowerOffset ... % Pilot to data power offset
);
NrPilotSymbols = sum(PilotMatrix_OFDM(:)==1);
NrDataSymbols_OFDM = sum(PilotMatrix_OFDM(:)==0);
PilotMapping_OFDM = zeros(numel(PilotMatrix_OFDM));
PilotMapping_OFDM(PilotMatrix_OFDM(:)==1,1:NrPilotSymbols) = sqrt(PilotToDataPowerOffset)*eye(NrPilotSymbols);
PilotMapping_OFDM(PilotMatrix_OFDM(:)==0,NrPilotSymbols+1:end) = eye(NrDataSymbols_OFDM);
PilotMapping_OFDM = PilotMapping_OFDM/sqrt(mean(diag(PilotMapping_OFDM*PilotMapping_OFDM')));
DataPowerReduction_OFDM = numel(PilotMatrix_OFDM)/(NrPilotSymbols*PilotToDataPowerOffset+NrDataSymbols_OFDM);
Kappa_Aux = AuxiliaryMethod.PilotToDataPowerOffset*AuxiliaryMethod.DataPowerReduction;
Kappa_Cod = CodingMethod.PilotToDataPowerOffset*CodingMethod.DataPowerReduction;
Kappa_OFDM = PilotToDataPowerOffset*DataPowerReduction_OFDM;
%% Evaluate only the BER near the center. i.e., ignore edges
ConsideredTimeFrequencyPositions_FBMC = zeros(size(PilotMatrix_FBMC));
ConsideredTimeFrequencyPositions_FBMC(5:end-4,11:end-10)= 1;
ConsideredTimeFrequencyPositions_OFDM = zeros(size(PilotMatrix_OFDM));
ConsideredTimeFrequencyPositions_OFDM(5:end-4,6:end-5)= 1;
for i_lk = 1: AuxiliaryMethod.NrDataSymbols
xD_Temp = zeros(AuxiliaryMethod.NrDataSymbols,1);
xD_Temp(i_lk) = 1;
x_FBMC_Aux = AuxiliaryMethod.PrecodingMatrix*[zeros(NrPilotSymbols,1);xD_Temp];
ConsideredDataPositions_FBMC_Aux(i_lk) = sum(abs(x_FBMC_Aux(1==ConsideredTimeFrequencyPositions_FBMC.*not(AuxilaryPilotMatrix_FBMC))))>AuxiliaryMethod.DataPowerReduction*0.9;
end
for i_lk = 1: CodingMethod.NrDataSymbols
xD_Temp = zeros(CodingMethod.NrDataSymbols,1);
xD_Temp(i_lk) = 1;
x_FBMC_Cod = CodingMethod.PrecodingMatrix*[zeros(NrPilotSymbols,1);xD_Temp];
ConsideredDataPositions_FBMC_Cod(i_lk) =not(any(x_FBMC_Cod(not(ConsideredTimeFrequencyPositions_FBMC))));
end
for i_lk = 1: NrDataSymbols_OFDM
xD_Temp = zeros(NrDataSymbols_OFDM,1);
xD_Temp(i_lk) = 1;
x_OFDM = PilotMapping_OFDM*[zeros(NrPilotSymbols,1);xD_Temp];
ConsideredDataPositions_OFDM(i_lk) = sum(abs(x_OFDM(1==ConsideredTimeFrequencyPositions_OFDM.*not(PilotMatrix_OFDM))))>DataPowerReduction_OFDM*0.9;
end
ConsideredBits_FBMC_Aux = reshape(repmat(ConsideredDataPositions_FBMC_Aux,log2(QAM_ModulationOrder)/2,1),[],1);
ConsideredBits_FBMC_Cod = reshape(repmat(ConsideredDataPositions_FBMC_Cod,log2(QAM_ModulationOrder)/2,1),[],1);
ConsideredBits_OFDM = reshape(repmat(ConsideredDataPositions_OFDM,log2(QAM_ModulationOrder),1),[],1);
%% Channel Model 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*2.5e9/2.998e8,... % 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
1 ... % 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.
);
R_vecH = ChannelModel.GetCorrelationMatrix;
%% Precalculate Transmit and Receive Matrices
G_FBMC = FBMC.GetTXMatrix;
Q_FBMC = (FBMC.GetRXMatrix)';
G_OFDM = OFDM.GetTXMatrix;
Q_OFDM = (OFDM.GetRXMatrix)';
GP_FBMC = G_FBMC(:,PilotMatrix_FBMC(:)==1);
GP_OFDM = G_OFDM(:,PilotMatrix_OFDM(:)==1);
QP_FBMC = Q_FBMC(:,PilotMatrix_FBMC(:)==1);
QP_OFDM = Q_OFDM(:,PilotMatrix_OFDM(:)==1);
G_Aux = G_FBMC*AuxiliaryMethod.PrecodingMatrix;
G_Cod = G_FBMC*CodingMethod.PrecodingMatrix;
G_OFDM_PilotMapping = G_OFDM*PilotMapping_OFDM;
%% Calculate Correlation Matrices
disp('Calculate Correlation Matrix of Pilot Estimates (no Noise, no Interference)...');
R_hP_FBMC = nan(NrPilotSymbols,NrPilotSymbols);
R_hP_OFDM = nan(NrPilotSymbols,NrPilotSymbols);
for j_pilot = 1:NrPilotSymbols
R_hP_FBMC(:,j_pilot) = sum((QP_FBMC'*reshape(R_vecH*kron(GP_FBMC(:,j_pilot).',QP_FBMC(:,j_pilot)')',N,N)).*(GP_FBMC.'),2);
R_hP_OFDM(:,j_pilot) = sum((QP_OFDM'*reshape(R_vecH*kron(GP_OFDM(:,j_pilot).',QP_OFDM(:,j_pilot)')',N,N)).*(GP_OFDM.'),2);
end
disp('Calculate Correlation Matrix of Pilot Estimates (no Interference)...');
R_hP_est_noNoise_FBMC_Aux = R_hP_FBMC;
R_hP_est_noNoise_FBMC_Cod = R_hP_FBMC;
R_hP_est_noNoise_OFDM = R_hP_OFDM;
for i_pilots = 1: NrPilotSymbols
% FBMC Auxiliary Method, Similar as Equation (13) but computationally more efficient
Temp = kron(sparse(eye(N)),QP_FBMC(:,i_pilots)')/sqrt(Kappa_Aux);
R_hP_est_noNoise_FBMC_Aux(i_pilots,i_pilots)=abs(sum(sum((G_Aux.'*(Temp*R_vecH*Temp')).*G_Aux',2)));
% FBMC Coding
Temp = kron(sparse(eye(N)),QP_FBMC(:,i_pilots)')/sqrt(Kappa_Cod);
R_hP_est_noNoise_FBMC_Cod(i_pilots,i_pilots)=abs(sum(sum((G_Cod.'*(Temp*R_vecH*Temp')).*G_Cod',2)));
% OFDM
Temp = kron(sparse(eye(N)),QP_OFDM(:,i_pilots)')/sqrt(Kappa_OFDM);
R_hP_est_noNoise_OFDM(i_pilots,i_pilots)=abs(sum(sum((G_OFDM_PilotMapping.'*(Temp*R_vecH*Temp')).*G_OFDM_PilotMapping',2)));
end
disp('Calculate Correlation Matrix of Pilot Estimates...');
R_hP_est_FBMC_Aux = repmat(R_hP_est_noNoise_FBMC_Aux,[1 1 length(M_SNR_dB)]);
R_hP_est_FBMC_Cod = repmat(R_hP_est_noNoise_FBMC_Cod,[1 1 length(M_SNR_dB)]);
R_hP_est_OFDM = repmat(R_hP_est_noNoise_OFDM,[1 1 length(M_SNR_dB)]);
for i_SNR = 1:length(M_SNR_dB)
SNR_dB = M_SNR_dB(i_SNR);
Pn_time = SamplingRate/(F*L)*10^(-SNR_dB/10);
for i_pilots = 1: NrPilotSymbols
R_hP_est_FBMC_Aux(i_pilots,i_pilots,i_SNR)=R_hP_est_noNoise_FBMC_Aux(i_pilots,i_pilots)+Pn_time*QP_FBMC(:,i_pilots)'*QP_FBMC(:,i_pilots)/(Kappa_Aux);
R_hP_est_FBMC_Cod(i_pilots,i_pilots,i_SNR)=R_hP_est_noNoise_FBMC_Cod(i_pilots,i_pilots)+Pn_time*QP_FBMC(:,i_pilots)'*QP_FBMC(:,i_pilots)/(Kappa_Cod);
R_hP_est_OFDM(i_pilots,i_pilots,i_SNR)=R_hP_est_noNoise_OFDM(i_pilots,i_pilots)+Pn_time*QP_OFDM(:,i_pilots)'*QP_OFDM(:,i_pilots)/Kappa_OFDM;
end
end
R_hP_est_noInterference_FBMC_Aux = R_hP_est_FBMC_Aux-repmat((R_hP_est_noNoise_FBMC_Aux-R_hP_FBMC),[1 1 length(M_SNR_dB)]);
R_hP_est_noInterference_FBMC_Cod = R_hP_est_FBMC_Cod-repmat((R_hP_est_noNoise_FBMC_Cod-R_hP_FBMC),[1 1 length(M_SNR_dB)]);
R_hP_est_noInterference_OFDM = R_hP_est_OFDM-repmat((R_hP_est_noNoise_OFDM-R_hP_OFDM),[1 1 length(M_SNR_dB)]);
disp('Calculate Correlation Matrix between Transmission-Matrix D and Pilot Estimates...');
R_Dij_hP_FBMC = sparse(size(G_FBMC,2)^2,NrPilotSymbols);
R_Dij_hP_OFDM = sparse(size(G_OFDM,2)^2,NrPilotSymbols);
for i_pilot = 1: NrPilotSymbols
R_Dij_hP_FBMC_Temp = reshape(Q_FBMC'*reshape(R_vecH*kron(GP_FBMC(:,i_pilot).',QP_FBMC(:,i_pilot)')',N,N)*G_FBMC,[],1);
R_Dij_hP_OFDM_Temp = reshape(Q_OFDM'*reshape(R_vecH*kron(GP_OFDM(:,i_pilot).',QP_OFDM(:,i_pilot)')',N,N)*G_OFDM,[],1);
R_Dij_hP_FBMC_Temp(abs(R_Dij_hP_FBMC_Temp)<10^(-ZeroThresholdSparse))=0;
R_Dij_hP_OFDM_Temp(abs(R_Dij_hP_OFDM_Temp)<10^(-ZeroThresholdSparse))=0;
R_Dij_hP_FBMC(:,i_pilot) = R_Dij_hP_FBMC_Temp;
R_Dij_hP_OFDM(:,i_pilot) = R_Dij_hP_OFDM_Temp;
end
clear R_vecH;
%% Calculate SIR at Pilot Positions
SIR_P_FBMC_Aux_dB = 10*log10(trace(abs(R_hP_FBMC))./trace(abs(R_hP_est_noNoise_FBMC_Aux-R_hP_FBMC)));
SIR_P_FBMC_Cod_dB = 10*log10(trace(abs(R_hP_FBMC))./trace(abs(R_hP_est_noNoise_FBMC_Cod-R_hP_FBMC)));
SIR_P_OFDM_dB = 10*log10(trace(abs(R_hP_OFDM))./trace(abs(R_hP_est_noNoise_OFDM-R_hP_OFDM)));
%% Calculate MMSE Estimation Matrix Using Correlation
disp('Calculate MMSE Solution ...');
W_MMSE_FBMC_Aux = sparse(size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,length(M_SNR_dB));
W_MMSE_FBMC_Cod = sparse(size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,length(M_SNR_dB));
W_MMSE_OFDM = sparse(size(G_OFDM,2)*size(G_OFDM,2)*NrPilotSymbols,length(M_SNR_dB));
for i_SNR = 1:length(M_SNR_dB)
W_MMSE_FBMC_Aux_Temp = reshape(R_Dij_hP_FBMC*pinv(R_hP_est_FBMC_Aux(:,:,i_SNR)),size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,1);
W_MMSE_FBMC_Cod_Temp = reshape(R_Dij_hP_FBMC*pinv(R_hP_est_FBMC_Cod(:,:,i_SNR)),size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,1);
W_MMSE_OFDM_Temp = reshape(R_Dij_hP_OFDM*pinv(R_hP_est_OFDM(:,:,i_SNR)),size(G_OFDM,2)*size(G_OFDM,2)*NrPilotSymbols,1);
W_MMSE_FBMC_Aux_Temp(abs(W_MMSE_FBMC_Aux_Temp)<10^(-ZeroThresholdSparse))=0;
W_MMSE_FBMC_Cod_Temp(abs(W_MMSE_FBMC_Cod_Temp)<10^(-ZeroThresholdSparse))=0;
W_MMSE_OFDM_Temp(abs(W_MMSE_OFDM_Temp)<10^(-ZeroThresholdSparse))=0;
W_MMSE_FBMC_Aux(:,i_SNR) = W_MMSE_FBMC_Aux_Temp;
W_MMSE_FBMC_Cod(:,i_SNR) = W_MMSE_FBMC_Cod_Temp;
W_MMSE_OFDM(:,i_SNR) = W_MMSE_OFDM_Temp;
end
%% Calculate MMSE Estimation if no Interference is present at the pilot positions
disp('Calculate MMSE Solution (no Interference)...');
W_MMSE_noInterference_FBMC_Aux = sparse(size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,length(M_SNR_dB));
W_MMSE_noInterference_FBMC_Cod = sparse(size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,length(M_SNR_dB));
W_MMSE_noInterference_OFDM = sparse(size(G_OFDM,2)*size(G_OFDM,2)*NrPilotSymbols,length(M_SNR_dB));
for i_SNR = 1:length(M_SNR_dB)
W_MMSE_noInterference_FBMC_Aux_Temp = reshape(R_Dij_hP_FBMC*pinv(R_hP_est_noInterference_FBMC_Aux(:,:,i_SNR)),size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,1);
W_MMSE_noInterference_FBMC_Cod_Temp = reshape(R_Dij_hP_FBMC*pinv(R_hP_est_noInterference_FBMC_Cod(:,:,i_SNR)),size(G_FBMC,2)*size(G_FBMC,2)*NrPilotSymbols,1);
W_MMSE_noInterference_OFDM_Temp = reshape(R_Dij_hP_OFDM*pinv(R_hP_est_noInterference_OFDM(:,:,i_SNR)),size(G_OFDM,2)*size(G_OFDM,2)*NrPilotSymbols,1);
W_MMSE_noInterference_FBMC_Aux_Temp(abs(W_MMSE_noInterference_FBMC_Aux_Temp)<10^(-ZeroThresholdSparse))=0;
W_MMSE_noInterference_FBMC_Cod_Temp(abs(W_MMSE_noInterference_FBMC_Cod_Temp)<10^(-ZeroThresholdSparse))=0;
W_MMSE_noInterference_OFDM_Temp(abs(W_MMSE_noInterference_OFDM_Temp)<10^(-ZeroThresholdSparse))=0;
W_MMSE_noInterference_FBMC_Aux(:,i_SNR) = W_MMSE_noInterference_FBMC_Aux_Temp;
W_MMSE_noInterference_FBMC_Cod(:,i_SNR) = W_MMSE_noInterference_FBMC_Cod_Temp;
W_MMSE_noInterference_OFDM(:,i_SNR) = W_MMSE_noInterference_OFDM_Temp;
end
%% Theoretical BEP for a Doubly Flat Rayleigh Channel
M_SNR_dB_morePoints = min(M_SNR_dB):1:max(M_SNR_dB);
BitErrorProbability = BitErrorProbabilityDoublyFlatRayleigh(M_SNR_dB_morePoints,QAM.SymbolMapping,QAM.BitMapping);
%% Preallocate for Parfor
BER_FBMC_Aux_PerfectCSI_InterferenceCancellation = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Aux_PerfectCSI_InterferenceCancellation_NoEdge = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Cod_PerfectCSI_InterferenceCancellation = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Cod_PerfectCSI_InterferenceCancellation_NoEdge = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_OFDM_PerfectCSI_InterferenceCancellation = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_OFDM_PerfectCSI_InterferenceCancellation_NoEdge = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Aux_OneTapEqualizer_PerfectCSI = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_Aux_OneTapEqualizer_PerfectCSI_NoEdge = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_Cod_OneTapEqualizer_PerfectCSI = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_Cod_OneTapEqualizer_PerfectCSI_NoEdge = nan(length(M_SNR_dB),NrRepetitions);
BER_OFDM_OneTapEqualizer_PerfectCSI = nan(length(M_SNR_dB),NrRepetitions);
BER_OFDM_OneTapEqualizer_PerfectCSI_NoEdge = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_Aux_InterferenceCancellation = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Cod_InterferenceCancellation = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_OFDM_InterferenceCancellation = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Aux_InterferenceCancellation_NoEdge = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Cod_InterferenceCancellation_NoEdge = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_OFDM_InterferenceCancellation_NoEdge = nan(length(M_SNR_dB),NrRepetitions,NrIterations);
BER_FBMC_Aux_OneTapEqualizer = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_Aux_OneTapEqualizer_NoEdge = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_Cod_OneTapEqualizer = nan(length(M_SNR_dB),NrRepetitions);
BER_FBMC_Cod_OneTapEqualizer_NoEdge = nan(length(M_SNR_dB),NrRepetitions);
BER_OFDM_OneTapEqualizer = nan(length(M_SNR_dB),NrRepetitions);
BER_OFDM_OneTapEqualizer_NoEdge = nan(length(M_SNR_dB),NrRepetitions);
%% Start Simulation
tic
disp('Monte Carlo Simulation ...');
for i_rep = 1:NrRepetitions
%% Update Channel
ChannelModel.NewRealization;
%% Binary Data
BinaryDataStream_FBMC_Aux = randi([0 1],AuxiliaryMethod.NrDataSymbols*log2(PAM.ModulationOrder),1);
BinaryDataStream_FBMC_Cod = randi([0 1],CodingMethod.NrDataSymbols*log2(PAM.ModulationOrder),1);
BinaryDataStream_OFDM = randi([0 1],NrDataSymbols_OFDM*log2(QAM.ModulationOrder),1);
%% Data Symbols
xD_FBMC_Aux = PAM.Bit2Symbol(BinaryDataStream_FBMC_Aux);
xD_FBMC_Cod = PAM.Bit2Symbol(BinaryDataStream_FBMC_Cod);
xD_OFDM = QAM.Bit2Symbol(BinaryDataStream_OFDM);
%% Pilot Symbols
xP_FBMC = PAM.SymbolMapping(randi(PAM.ModulationOrder,AuxiliaryMethod.NrPilotSymbols,1));
xP_FBMC = xP_FBMC./abs(xP_FBMC);
xP_OFDM = QAM.SymbolMapping(randi(QAM.ModulationOrder,NrPilotSymbols,1));
xP_OFDM = xP_OFDM./abs(xP_OFDM);
%% Transmitted Data Symbols (Map bin to symbol)
x_FBMC_Aux = AuxiliaryMethod.PrecodingMatrix*[xP_FBMC;xD_FBMC_Aux];
x_FBMC_Cod = CodingMethod.PrecodingMatrix*[xP_FBMC;xD_FBMC_Cod];
x_OFDM = PilotMapping_OFDM*[xP_OFDM;xD_OFDM];
%% Transmitted Signal (time domain)
s_FBMC_Aux = G_FBMC*x_FBMC_Aux(:); % Same as "FBMC.Modulation(x_FBMC_Aux)" which is computationally more efficient. But G_FBMC is consistent with the paper.
s_FBMC_Cod = G_FBMC*x_FBMC_Cod(:);
s_OFDM = G_OFDM*x_OFDM(:);
%% Channel
ConvolutionMatrix = ChannelModel.GetConvolutionMatrix{1};
r_FBMC_Aux_noNoise = ConvolutionMatrix*s_FBMC_Aux;
r_FBMC_Cod_noNoise = ConvolutionMatrix*s_FBMC_Cod;
r_OFDM_noNoise = ConvolutionMatrix*s_OFDM;
%% Transmission Matrix
D_FBMC = Q_FBMC'*ConvolutionMatrix*G_FBMC;
D_OFDM = Q_OFDM'*ConvolutionMatrix*G_OFDM;
%% One-Tap Channel (for perfect channel knowledge)
h_FBMC = diag(D_FBMC);
h_OFDM = diag(D_OFDM);
for i_SNR = 1:length(M_SNR_dB)
%% Add Noise
SNR_dB = M_SNR_dB(i_SNR);
Pn_time = SamplingRate/(F*L)*10^(-SNR_dB/10);
noise = sqrt(Pn_time/2)*(randn(size(s_OFDM))+1j*randn(size(s_OFDM)));
r_FBMC_Aux = r_FBMC_Aux_noNoise+noise;
r_FBMC_Cod = r_FBMC_Cod_noNoise+noise;
r_OFDM = r_OFDM_noNoise+noise;
%% Demodulate FBMC signal
y_FBMC_Aux = Q_FBMC'*r_FBMC_Aux; % Same as "FBMC.Demodulation(r_FBMC_Aux)"
y_FBMC_Cod = Q_FBMC'*r_FBMC_Cod; % Same as "FBMC.Demodulation(r_FBMC_Cod)"
y_FBMC_Cod_PostCod = CodingMethod.PrecodingMatrix'*y_FBMC_Cod;
y_OFDM = Q_OFDM'*r_OFDM; % Same as "OFDM.Demodulation(r_OFDM)"
%% Channel Estimation at Pilot Position
hP_est_FBMC_Aux = y_FBMC_Aux(PilotMatrix_FBMC==1)./xP_FBMC/sqrt(Kappa_Aux);
hP_est_FBMC_Cod = y_FBMC_Cod(PilotMatrix_FBMC==1)./xP_FBMC/sqrt(Kappa_Cod);
hP_est_OFDM = y_OFDM(PilotMatrix_OFDM==1)./xP_OFDM/sqrt(Kappa_OFDM);
%% Estimate Transmit Matix
D_FBMC_est_Aux = sum(bsxfun(@times,...
reshape(full(W_MMSE_FBMC_Aux(:,i_SNR)),size(G_FBMC,2),size(G_FBMC,2),NrPilotSymbols),...
reshape(hP_est_FBMC_Aux,1,1,[])),3);
D_FBMC_est_Cod = sum(bsxfun(@times,...
reshape(full(W_MMSE_FBMC_Cod(:,i_SNR)),size(G_FBMC,2),size(G_FBMC,2),NrPilotSymbols),...
reshape(hP_est_FBMC_Cod,1,1,[])),3);
D_OFDM_est = sum(bsxfun(@times,...
reshape(full(W_MMSE_OFDM(:,i_SNR)),size(G_OFDM,2),size(G_OFDM,2),NrPilotSymbols),...
reshape(hP_est_OFDM,1,1,[])),3);
%% One-Tap Equalizer
h_est_FBMC_Aux = diag(D_FBMC_est_Aux);
x_est_OneTapEqualizer_FBMC_Aux = y_FBMC_Aux./h_est_FBMC_Aux;
xD_est_OneTapEqualizer_FBMC_Aux = real(x_est_OneTapEqualizer_FBMC_Aux(AuxilaryPilotMatrix_FBMC(:)==0)./sqrt(AuxiliaryMethod.DataPowerReduction));
DetectedBitStream_OneTapEqualizer_FBMC_Aux = PAM.Symbol2Bit(xD_est_OneTapEqualizer_FBMC_Aux);
BER_FBMC_Aux_OneTapEqualizer(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Aux~=DetectedBitStream_OneTapEqualizer_FBMC_Aux);
BER_FBMC_Aux_OneTapEqualizer_NoEdge(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Aux(ConsideredBits_FBMC_Aux)~=DetectedBitStream_OneTapEqualizer_FBMC_Aux(ConsideredBits_FBMC_Aux));
h_est_FBMC_Cod = diag(D_FBMC_est_Cod);
x_est_OneTapEqualizer_FBMC_Cod = CodingMethod.PrecodingMatrix'*(y_FBMC_Cod./h_est_FBMC_Cod);
xD_est_OneTapEqualizer_FBMC_Cod = real(x_est_OneTapEqualizer_FBMC_Cod(NrPilotSymbols+1:end))/CodingMethod.DataPowerReduction;
DetectedBitStream_OneTapEqualizer_FBMC_Cod = PAM.Symbol2Bit(xD_est_OneTapEqualizer_FBMC_Cod);
BER_FBMC_Cod_OneTapEqualizer(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Cod~=DetectedBitStream_OneTapEqualizer_FBMC_Cod);
BER_FBMC_Cod_OneTapEqualizer_NoEdge(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Cod(ConsideredBits_FBMC_Cod)~=DetectedBitStream_OneTapEqualizer_FBMC_Cod(ConsideredBits_FBMC_Cod));
h_est_OFDM = diag(D_OFDM_est);
x_est_OneTapEqualizer_OFDM = y_OFDM./h_est_OFDM;
xD_est_OneTapEqualizer_OFDM = x_est_OneTapEqualizer_OFDM(PilotMatrix_OFDM(:)==0)./sqrt(DataPowerReduction_OFDM);
DetectedBitStream_OneTapEqualizer_OFDM = QAM.Symbol2Bit(xD_est_OneTapEqualizer_OFDM);
BER_OFDM_OneTapEqualizer(i_SNR,i_rep) = mean(BinaryDataStream_OFDM~=DetectedBitStream_OneTapEqualizer_OFDM);
BER_OFDM_OneTapEqualizer_NoEdge(i_SNR,i_rep) = mean(BinaryDataStream_OFDM(ConsideredBits_OFDM)~=DetectedBitStream_OneTapEqualizer_OFDM(ConsideredBits_OFDM));
%% One-Tap Equalizer, Perfect Channel Knowledge
x_est_OneTapEqualizer_FBMC_Aux_PerfectCSI = y_FBMC_Aux./h_FBMC;
xD_est_OneTapEqualizer_FBMC_Aux_PerfectCSI = real(x_est_OneTapEqualizer_FBMC_Aux_PerfectCSI(AuxilaryPilotMatrix_FBMC(:)==0)./sqrt(AuxiliaryMethod.DataPowerReduction));
DetectedBitStream_OneTapEqualizer_FBMC_Aux_PerfectCSI = PAM.Symbol2Bit(xD_est_OneTapEqualizer_FBMC_Aux_PerfectCSI);
BER_FBMC_Aux_OneTapEqualizer_PerfectCSI(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Aux~=DetectedBitStream_OneTapEqualizer_FBMC_Aux_PerfectCSI);
BER_FBMC_Aux_OneTapEqualizer_PerfectCSI_NoEdge(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Aux(ConsideredBits_FBMC_Aux)~=DetectedBitStream_OneTapEqualizer_FBMC_Aux_PerfectCSI(ConsideredBits_FBMC_Aux));
x_est_OneTapEqualizer_FBMC_Cod_PerfectCSI = CodingMethod.PrecodingMatrix'*(y_FBMC_Cod./h_FBMC);
xD_est_OneTapEqualizer_FBMC_Cod_PerfectCSI = real(x_est_OneTapEqualizer_FBMC_Cod_PerfectCSI(NrPilotSymbols+1:end))/CodingMethod.DataPowerReduction;
DetectedBitStream_OneTapEqualizer_FBMC_Cod_PerfectCSI = PAM.Symbol2Bit(xD_est_OneTapEqualizer_FBMC_Cod_PerfectCSI);
BER_FBMC_Cod_OneTapEqualizer_PerfectCSI(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Cod~=DetectedBitStream_OneTapEqualizer_FBMC_Cod_PerfectCSI);
BER_FBMC_Cod_OneTapEqualizer_PerfectCSI_NoEdge(i_SNR,i_rep) = mean(BinaryDataStream_FBMC_Cod(ConsideredBits_FBMC_Cod)~=DetectedBitStream_OneTapEqualizer_FBMC_Cod_PerfectCSI(ConsideredBits_FBMC_Cod));
x_est_OneTapEqualizer_OFDM_PerfectCSI = y_OFDM./h_OFDM;
xD_est_OneTapEqualizer_OFDM_PerfectCSI = x_est_OneTapEqualizer_OFDM_PerfectCSI(PilotMatrix_OFDM(:)==0)./sqrt(DataPowerReduction_OFDM);
DetectedBitStream_OneTapEqualizer_OFDM_PerfectCSI = QAM.Symbol2Bit(xD_est_OneTapEqualizer_OFDM_PerfectCSI);
BER_OFDM_OneTapEqualizer_PerfectCSI(i_SNR,i_rep) = mean(BinaryDataStream_OFDM~=DetectedBitStream_OneTapEqualizer_OFDM_PerfectCSI);
BER_OFDM_OneTapEqualizer_PerfectCSI_NoEdge(i_SNR,i_rep) = mean(BinaryDataStream_OFDM(ConsideredBits_OFDM)~=DetectedBitStream_OneTapEqualizer_OFDM_PerfectCSI(ConsideredBits_OFDM));
%% Improved Channel Estimation and Data Detection
xD_est_FBMC_Aux_Temp = xD_est_OneTapEqualizer_FBMC_Aux; % initialize with one tap estimates
xD_est_FBMC_Cod_Temp = xD_est_OneTapEqualizer_FBMC_Cod; % initialize with one tap estimates
xD_est_OFDM_Temp = xD_est_OneTapEqualizer_OFDM; % initialize with one tap estimates
xD_est_FBMC_Aux_PerfectCSI_Temp = xD_est_OneTapEqualizer_FBMC_Aux_PerfectCSI; % initialize with one tap estimates
xD_est_FBMC_Cod_PerfectCSI_Temp = xD_est_OneTapEqualizer_FBMC_Cod_PerfectCSI; % initialize with one tap estimates
xD_est_OFDM_PerfectCSI_Temp = xD_est_OneTapEqualizer_OFDM_PerfectCSI; % initialize with one tap estimates
D_FBMC_est_Aux_Temp = D_FBMC_est_Aux;
D_FBMC_est_Cod_Temp = D_FBMC_est_Cod;
D_OFDM_est_Temp = D_OFDM_est;
h_est_FBMC_Aux_Temp = h_est_FBMC_Aux;
h_est_FBMC_Cod_Temp = h_est_FBMC_Cod;
h_est_OFDM_Temp = h_est_OFDM;
for i_iteration = 1:NrIterations
y_FBMC_Aux_InterferenceCancellation = (y_FBMC_Aux(:) - (D_FBMC_est_Aux_Temp-diag(h_est_FBMC_Aux_Temp))*AuxiliaryMethod.PrecodingMatrix*[xP_FBMC;PAM.SymbolQuantization(xD_est_FBMC_Aux_Temp)]);
y_FBMC_Cod_InterferenceCancellation = (y_FBMC_Cod - (D_FBMC_est_Cod_Temp-diag(h_est_FBMC_Cod_Temp))*CodingMethod.PrecodingMatrix*[xP_FBMC;PAM.SymbolQuantization(xD_est_FBMC_Cod_Temp)]);
y_OFDM_InterferenceCancellation = (y_OFDM - (D_OFDM_est_Temp-diag(h_est_OFDM_Temp))*PilotMapping_OFDM*[xP_OFDM;QAM.SymbolQuantization(xD_est_OFDM_Temp)]);
% New Channel Estimates at Pilot Positions
hP_est_FBMC_Aux_Temp = y_FBMC_Aux_InterferenceCancellation(PilotMatrix_FBMC==1)./xP_FBMC/sqrt(Kappa_Aux);
hP_est_FBMC_Cod_Temp = y_FBMC_Cod_InterferenceCancellation(PilotMatrix_FBMC==1)./xP_FBMC/sqrt(Kappa_Cod);
hP_est_OFDM_Temp = y_OFDM_InterferenceCancellation(PilotMatrix_OFDM==1)./xP_OFDM/sqrt(Kappa_OFDM);
% Improved Channel Estimation
if i_iteration<=NrIterations/2
D_FBMC_est_Aux_Temp = sum(bsxfun(@times,...
reshape(full(W_MMSE_FBMC_Aux(:,i_SNR)),size(G_FBMC,2),size(G_FBMC,2),NrPilotSymbols),...
reshape(hP_est_FBMC_Aux_Temp,1,1,[])),3);
D_FBMC_est_Cod_Temp = sum(bsxfun(@times,...
reshape(full(W_MMSE_FBMC_Cod(:,i_SNR)),size(G_FBMC,2),size(G_FBMC,2),NrPilotSymbols),...
reshape(hP_est_FBMC_Cod_Temp,1,1,[])),3);
D_OFDM_est_Temp = sum(bsxfun(@times,...
reshape(full(W_MMSE_OFDM(:,i_SNR)),size(G_OFDM,2),size(G_OFDM,2),NrPilotSymbols),...
reshape(hP_est_OFDM_Temp,1,1,[])),3);
else
D_FBMC_est_Aux_Temp = sum(bsxfun(@times,...
reshape(full(W_MMSE_noInterference_FBMC_Aux(:,i_SNR)),size(G_FBMC,2),size(G_FBMC,2),NrPilotSymbols),...
reshape(hP_est_FBMC_Aux_Temp,1,1,[])),3);
D_FBMC_est_Cod_Temp = sum(bsxfun(@times,...
reshape(full(W_MMSE_noInterference_FBMC_Cod(:,i_SNR)),size(G_FBMC,2),size(G_FBMC,2),NrPilotSymbols),...
reshape(hP_est_FBMC_Cod_Temp,1,1,[])),3);
D_OFDM_est_Temp = sum(bsxfun(@times,...
reshape(full(W_MMSE_noInterference_OFDM(:,i_SNR)),size(G_OFDM,2),size(G_OFDM,2),NrPilotSymbols),...
reshape(hP_est_OFDM_Temp,1,1,[])),3);
end
% One-Tap Channel
h_est_FBMC_Aux_Temp = diag(D_FBMC_est_Aux_Temp);
h_est_FBMC_Cod_Temp = diag(D_FBMC_est_Cod_Temp);
h_est_OFDM_Temp = diag(D_OFDM_est_Temp);
x_est_FBMC_Aux_Temp = y_FBMC_Aux_InterferenceCancellation(:)./h_est_FBMC_Aux_Temp;
x_est_FBMC_Cod_Temp = CodingMethod.PrecodingMatrix'*(y_FBMC_Cod_InterferenceCancellation./h_est_FBMC_Cod_Temp);
x_est_OFDM_Temp = y_OFDM_InterferenceCancellation./h_est_OFDM_Temp;
xD_est_FBMC_Aux_Temp = real(x_est_FBMC_Aux_Temp(AuxilaryPilotMatrix_FBMC(:)==0)./sqrt(AuxiliaryMethod.DataPowerReduction));
xD_est_FBMC_Cod_Temp = real(x_est_FBMC_Cod_Temp(NrPilotSymbols+1:end))/CodingMethod.DataPowerReduction;
xD_est_OFDM_Temp = x_est_OFDM_Temp(PilotMatrix_OFDM(:)==0)./sqrt(DataPowerReduction_OFDM);
DetectedBitStream_FBMC_Aux_Temp = PAM.Symbol2Bit(xD_est_FBMC_Aux_Temp);
DetectedBitStream_FBMC_Cod_Temp = PAM.Symbol2Bit(xD_est_FBMC_Cod_Temp);
DetectedBitStream_OFDM_Temp = QAM.Symbol2Bit(xD_est_OFDM_Temp);
BER_FBMC_Aux_InterferenceCancellation(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Aux~=DetectedBitStream_FBMC_Aux_Temp);
BER_FBMC_Cod_InterferenceCancellation(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Cod~=DetectedBitStream_FBMC_Cod_Temp);
BER_OFDM_InterferenceCancellation(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_OFDM~=DetectedBitStream_OFDM_Temp);
BER_FBMC_Aux_InterferenceCancellation_NoEdge(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Aux(ConsideredBits_FBMC_Aux)~=DetectedBitStream_FBMC_Aux_Temp(ConsideredBits_FBMC_Aux));
BER_FBMC_Cod_InterferenceCancellation_NoEdge(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Cod(ConsideredBits_FBMC_Cod)~=DetectedBitStream_FBMC_Cod_Temp(ConsideredBits_FBMC_Cod));
BER_OFDM_InterferenceCancellation_NoEdge(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_OFDM(ConsideredBits_OFDM)~=DetectedBitStream_OFDM_Temp(ConsideredBits_OFDM));
% Perfect Channel Knoweledge
y_FBMC_Aux_InterferenceCancellation_PerfectCSI = (y_FBMC_Aux(:) - (D_FBMC-diag(h_FBMC))*AuxiliaryMethod.PrecodingMatrix*[xP_FBMC;PAM.SymbolQuantization(xD_est_FBMC_Aux_PerfectCSI_Temp)]);
y_FBMC_Cod_InterferenceCancellation_PerfectCSI = (y_FBMC_Cod - (D_FBMC-diag(h_FBMC))*CodingMethod.PrecodingMatrix*[xP_FBMC;PAM.SymbolQuantization(xD_est_FBMC_Cod_PerfectCSI_Temp)]);
y_OFDM_InterferenceCancellation_PerfectCSI = (y_OFDM - (D_OFDM-diag(h_OFDM))*PilotMapping_OFDM*[xP_OFDM;QAM.SymbolQuantization(xD_est_OFDM_PerfectCSI_Temp)]);
x_est_FBMC_Aux_PerfectCSI_Temp = y_FBMC_Aux_InterferenceCancellation_PerfectCSI./h_FBMC;
xD_est_FBMC_Aux_PerfectCSI_Temp = real(x_est_FBMC_Aux_PerfectCSI_Temp(AuxilaryPilotMatrix_FBMC(:)==0)./sqrt(AuxiliaryMethod.DataPowerReduction));
DetectedBitStream_FBMC_Aux_PerfectCSI_Temp = PAM.Symbol2Bit(xD_est_FBMC_Aux_PerfectCSI_Temp);
BER_FBMC_Aux_PerfectCSI_InterferenceCancellation(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Aux~=DetectedBitStream_FBMC_Aux_PerfectCSI_Temp);
BER_FBMC_Aux_PerfectCSI_InterferenceCancellation_NoEdge(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Aux(ConsideredBits_FBMC_Aux)~=DetectedBitStream_FBMC_Aux_PerfectCSI_Temp(ConsideredBits_FBMC_Aux));
x_est_FBMC_Cod_PerfectCSI_Temp = CodingMethod.PrecodingMatrix'*(y_FBMC_Cod_InterferenceCancellation_PerfectCSI./h_FBMC);
xD_est_FBMC_Cod_PerfectCSI_Temp = real(x_est_FBMC_Cod_PerfectCSI_Temp(NrPilotSymbols+1:end))/CodingMethod.DataPowerReduction;
DetectedBitStream_FBMC_Cod_PerfectCSI_Temp = PAM.Symbol2Bit(xD_est_FBMC_Cod_PerfectCSI_Temp);
BER_FBMC_Cod_PerfectCSI_InterferenceCancellation(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Cod~=DetectedBitStream_FBMC_Cod_PerfectCSI_Temp);
BER_FBMC_Cod_PerfectCSI_InterferenceCancellation_NoEdge(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_FBMC_Cod(ConsideredBits_FBMC_Cod)~=DetectedBitStream_FBMC_Cod_PerfectCSI_Temp(ConsideredBits_FBMC_Cod));
x_est_OFDM_PerfectCSI_Temp = y_OFDM_InterferenceCancellation_PerfectCSI./h_OFDM;
xD_est_OFDM_PerfectCSI_Temp = x_est_OFDM_PerfectCSI_Temp(PilotMatrix_OFDM(:)==0)./sqrt(DataPowerReduction_OFDM);
DetectedBitStream_OFDM_PerfectCSI_Temp = QAM.Symbol2Bit(xD_est_OFDM_PerfectCSI_Temp);
BER_OFDM_PerfectCSI_InterferenceCancellation(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_OFDM~=DetectedBitStream_OFDM_PerfectCSI_Temp);
BER_OFDM_PerfectCSI_InterferenceCancellation_NoEdge(i_SNR,i_rep,i_iteration) = mean(BinaryDataStream_OFDM(ConsideredBits_OFDM)~=DetectedBitStream_OFDM_PerfectCSI_Temp(ConsideredBits_OFDM));
end
end
TimeNeededSoFar = toc;
disp([int2str(i_rep/NrRepetitions*100) '% Completed! Time Left: ' int2str(TimeNeededSoFar/i_rep*(NrRepetitions-i_rep)/60) 'min, corresponding to approx. ' int2str(TimeNeededSoFar/i_rep*(NrRepetitions-i_rep)/3600) 'hour']);
%% Plot results
% OFDM
figure(2);
Markersize = 4;
hold off;
semilogy(M_SNR_dB_morePoints, BitErrorProbability,'Color',[1 1 1]*0.75);
hold on;
semilogy(M_SNR_dB, nanmean(BER_OFDM_PerfectCSI_InterferenceCancellation(:,:,end),2),'-x black','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_OFDM_InterferenceCancellation(:,:,end),2),'-s magenta','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_OFDM_InterferenceCancellation_NoEdge(:,:,end),2),'-o blue','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_OFDM_OneTapEqualizer_PerfectCSI,2),'-x','Color',[1 1 0]*0.7,'Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_OFDM_OneTapEqualizer,2),'-s red','Markersize',Markersize);
ylim([10^-2 0.5]);
title(['OFDM, Realization ' int2str(i_rep) '/' int2str(NrRepetitions)])
legend({'Doubly-Flat Theory','Cancellation (Perfect CSI)','Cancellation','Cancellation (no Edges)','One-Tap (Perfect CSI)','One-Tap'});
ylabel('Bit Error Ratio');
xlabel('Signal-to-Noise Ratio [dB]');
% FBMC, Auxiliary Method
figure(3);
hold off;
semilogy(M_SNR_dB_morePoints, BitErrorProbability,'Color',[1 1 1]*0.75);
hold on;
semilogy(M_SNR_dB, nanmean(BER_FBMC_Aux_PerfectCSI_InterferenceCancellation(:,:,end),2),'-x black','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Aux_InterferenceCancellation(:,:,end),2),'-s magenta','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Aux_InterferenceCancellation_NoEdge(:,:,end),2),'-o blue','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Aux_OneTapEqualizer_PerfectCSI,2),'-x','Color',[1 1 0]*0.7,'Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Aux_OneTapEqualizer,2),'-s red','Markersize',Markersize);
ylim([10^-2 0.5]);
semilogy([PlotIterationStepsSNRdB PlotIterationStepsSNRdB],[10^-2 10^-1],'Color',[1 1 1]*0.5,'Linewidth',1);
title(['FBMC Auxiliary Symbols, Realization ' int2str(i_rep) '/' int2str(NrRepetitions)])
legend({'Doubly-Flat Theory','Cancellation (Perfect CSI)','Cancellation','Cancellation (no Edges)','One-Tap (Perfect CSI)','One-Tap'});
ylabel('Bit Error Ratio');
xlabel('Signal-to-Noise Ratio [dB]');
% FBMC, Data Spreading Method
figure(4);
hold off;
semilogy(M_SNR_dB_morePoints, BitErrorProbability,'Color',[1 1 1]*0.75);
hold on;
semilogy(M_SNR_dB, nanmean(BER_FBMC_Cod_PerfectCSI_InterferenceCancellation(:,:,end),2),'-x black','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Cod_InterferenceCancellation(:,:,end),2),'-s magenta','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Cod_InterferenceCancellation_NoEdge(:,:,end),2),'-o blue','Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Cod_OneTapEqualizer_PerfectCSI,2),'-x','Color',[1 1 0]*0.7,'Markersize',Markersize);
semilogy(M_SNR_dB, nanmean(BER_FBMC_Cod_OneTapEqualizer,2),'-s red','Markersize',Markersize);
ylim([10^-2 0.5]);
title(['FBMC Data Spreading, Realization ' int2str(i_rep) '/' int2str(NrRepetitions)])
legend({'Doubly-Flat Theory','Cancellation (Perfect CSI)','Cancellation','Cancellation (no Edges)','One-Tap (Perfect CSI)','One-Tap'});
ylabel('Bit Error Ratio');
xlabel('Signal-to-Noise Ratio [dB]');
% FBMC, Auxiliary Method, BER over Interation
figure(5);
hold off;
semilogy(0:NrIterations, repmat(BitErrorProbability(find(PlotIterationStepsSNRdB==M_SNR_dB_morePoints)),NrIterations+1,1),'Color',[1 1 1]*0.75);
hold on;
Index = find(PlotIterationStepsSNRdB==M_SNR_dB);
semilogy(0:NrIterations, [nanmean(BER_FBMC_Aux_OneTapEqualizer_PerfectCSI(Index,:),2);squeeze(nanmean(BER_FBMC_Aux_PerfectCSI_InterferenceCancellation(Index,:,:),2))],'-x black','Markersize',Markersize);
semilogy(0:NrIterations, [nanmean(BER_FBMC_Aux_OneTapEqualizer(Index,:),2);squeeze(nanmean(BER_FBMC_Aux_InterferenceCancellation(Index,:,:),2))],'-s magenta','Markersize',Markersize);
semilogy(0:NrIterations, [nanmean(BER_FBMC_Aux_OneTapEqualizer_NoEdge(Index,:),2);squeeze(nanmean(BER_FBMC_Aux_InterferenceCancellation_NoEdge(Index,:,:),2))],'-o blue','Markersize',Markersize);
semilogy(0:NrIterations, repmat(nanmean(BER_FBMC_Aux_OneTapEqualizer_PerfectCSI(Index,:),2),NrIterations+1,1),'-x','Color',[1 1 0]*0.7,'Markersize',Markersize);
semilogy(0:NrIterations, repmat(nanmean(BER_FBMC_Aux_OneTapEqualizer(Index,:),2),NrIterations+1,1),'-s red','Markersize',Markersize);
title(['FBMC Auxiliary Symbols, Realization ' int2str(i_rep) '/' int2str(NrRepetitions)])
legend({'Doubly-Flat Theory','Cancellation (Perfect CSI)','Cancellation','Cancellation (no Edges)','One-Tap (Perfect CSI)','One-Tap'});
set(gca, 'XTick',0:NrIterations);
ylabel('Bit Error Ratio');
xlabel('Iteration Step i');
pause(0.01);
end
%% Plot Additional Information
fprintf('=============================\n');
fprintf('========= Data Rate =========\n');
fprintf('OFDM |%7.2f Mbit/s | \n', length(BinaryDataStream_OFDM) / (OFDM.PHY.TimeSpacing*OFDM.Nr.MCSymbols)/1e6 );
fprintf('FBMC, Aux. |%7.2f Mbit/s | \n', length(BinaryDataStream_FBMC_Aux) / (OFDM.PHY.TimeSpacing*OFDM.Nr.MCSymbols)/1e6 );
fprintf('FBMC, Cod. |%7.2f Mbit/s | \n', length(BinaryDataStream_FBMC_Cod) / (OFDM.PHY.TimeSpacing*OFDM.Nr.MCSymbols)/1e6 );
fprintf('=============================\n');
% The power is normalized so that the average transmit power is one
fprintf('================================================\n');
fprintf('============== Relative SNR Shift ==============\n');
fprintf('================================================\n');
fprintf(' | SNR | Data SNR | Pilot SNR |\n');
fprintf('OFDM | %2.1fdB | %2.1fdB | %2.1fdB |\n', 0, 10*log10(DataPowerReduction_OFDM), 10*log10(Kappa_OFDM))
fprintf('FBMC, Aux. | %2.1fdB | %2.1fdB | %2.1fdB |\n', 0, 10*log10(AuxiliaryMethod.DataPowerReduction), 10*log10(Kappa_Aux/2))
fprintf('FBMC, Cod. | %2.1fdB | %2.1fdB | %2.1fdB |\n', 0, 10*log10(CodingMethod.DataPowerReduction), 10*log10(Kappa_Cod/2))
fprintf('================================================\n');