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Figure_12_Throughput.m
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Figure_12_Throughput.m
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% =========================================================================
% Ronald Nissel, [email protected]
% (c) 2017 by Institute of Telecommunications, TU Wien
% www.nt.tuwien.ac.at
% =========================================================================
% This script emulates our throughput measurements. After Turbo decoding,
% all bits must be correctly detected. If one bit is false, the throughput
% is zero. We maximize the throughput over 15 CQI values, representing
% perfect feeback. The channel estimation in FBMC is done either by
% 1) Coding method (same as in our measurements), or
% 2) {1,2,3,4}-Auxiliary symbols
% Note that the current settings of the channel interpolation achieves only
% a good performance for a low delay spread and a low doppler spread.
% If one wants to test other channel conditions, the interpolation method
% must be changed, e.g., set to 'linear', or perfect channel knowledge must
% be considered: "Simulation_IncludePerfectCSI = true;".
% For more information about channel estimation in FBMC, we refer to
% "On Pilot-Symbol Aided Channel Estimation in FBMC-OQAM", R.Nissel, et.al.
% !!!! We recommend using parfor, that is, commenting out line 198-200 !!!!
clear; close all;
%% Parameters
% Simulation parameters
Simulation_MonteCarloRepetitions = 10; % Number of Monte Carlo repetitions (must be larger than 2 so that bootci works)
Simulation_SNR_FBMC_dB = -10:5:30; % Signal-to-noise ratio for FBMC in dB
Simulation_IncludePerfectCSI = false; % If set to true, also calculate the throughput for perfect channel knowledge (takes more time)
Simulation_PlotAdditionalInformation = true; % If set to true, plot additional information: expected signal power in time, power spectral density, pilot pattern
% Channel parameters
Channel_PowerDelayProfile = 'PedestrianA'; % 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)
Channel_Velocity_kmh = 0; % Velocity in km/h
Channel_CarrierFrequency = 2.5e9; % Carrier frequency (has no influence if the velocity is 0)
% Modulation parameters
SubcarrierSpacing = 15e3; % Subcarrier spacing (15kHz, same as LTE)
FBMC_NumberOfSubcarriers = 87; % The number of subcarriers in FBMC. Can be higher than in OFDM due to lower out of band emissions. 1.4MHz/15kHz=93.33. We consider 6 guard symbols => L=93-6=87. We could also choose L=90 (however, it should be a multiple of 3 so that the pilot density is the same as in OFDM).
FBMC_NumberOfSymbolsInTime = 30; % Number of FBMC symbols in time. 30*1/15e3/2=1ms!
FBMC_ImaginaryInterferenceCancelationMethod = 'Coding'; % 'Coding' or 'Auxiliary': Choose between two different methods to cancel the imaginary interference at pilot positions in FBMC
FBMC_NumberOfAuxilarySymbolsPerPilot = 1; % Only relevant if the cancellation method is 'Auxiliary'. Defines the number of auxiliary symbols per pilot. For example, two auxiliary symbols are better than one auxiliary symbol in a low SNR regime. Additionally, the PAPR is better. See "Experimental Evaluation of FBMC-OQAM Channel Estimation Based on Multiple Auxiliary Symbols" R.Nissel et.al
OFDM_NumberOfSubcarriers = 72; % 1.4 MHz LTE => 72 subcarrier
OFDM_NumberOfSymbolsInTime = 14; % Number of OFDM symbols (one subframe). LTE uses 14.
OFDM_CyclicPrefixLength = 1/(14*15e3); % LTE CP length: 4.76µs
SamplingRate = SubcarrierSpacing*12*14*4; % Multiple of 14 so that CP fits into sampling rate
%% 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:https://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 for Windows 64-bit => CQI values which contain a code rate smaller than 1/3 are discarded!');
end
end
%% Objects
% FBMC Object
FBMC = Modulation.FBMC(...
FBMC_NumberOfSubcarriers,... % Number of subcarriers
FBMC_NumberOfSymbolsInTime,... % Number FBMC symbols in time
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
0,... % Intermediate frequency of the first subcarrier (Hz). Must be a multiple of the subcarrier spacing
false,... % Transmit real valued signal (sampling theorem must be fulfilled!)
'Hermite-OQAM',... % Prototype filter (Hermite, PHYDYAS, RRC) and OQAM or QAM. The data rate of QAM is reduced by a factor of two compared to OQAM, but robustness in doubly-selective channels is inceased
4, ... % Overlapping factor (also determines oversampling in the frequency domain)
0, ... % Initial phase shift
true ... % Polyphase implementation
);
FBMC_BlockOverlapTime = (FBMC.PrototypeFilter.OverlappingFactor-1/2)*FBMC.PHY.TimeSpacing;
% OFDM Object
OFDM = Modulation.OFDM(...
OFDM_NumberOfSubcarriers,... % Number of subcarriers
OFDM_NumberOfSymbolsInTime,... % Number OFDM symbols in time
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
0,... % Intermediate frequency of the first subcarrier (Hz). Must be a multiple of the subcarrier spacing
false,... % Transmit real valued signal (sampling theorem must be fulfilled!)
OFDM_CyclicPrefixLength, ... % Length of the cyclic prefix (s)
FBMC_BlockOverlapTime ... % Length of the guard time (s), that is, zeros at the beginning and at the end of the transmission
);
if FBMC.Nr.SamplesTotal == OFDM.Nr.SamplesTotal
N = FBMC.Nr.SamplesTotal;
else
error('Number of samples in OFDM and FBMC have to be the same.'); % To simplify the evaluation
end
% Channel object
ChannelModel = Channel.FastFading(...
SamplingRate,... % Sampling rate (Samples/s)
Channel_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
Channel_Velocity_kmh/3.6*Channel_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.
);
% Channel Estimation Objects
ChannelEstimation_OFDM = ChannelEstimation.PilotSymbolAidedChannelEstimation(...
'Diamond',... % Pilot pattern, 'Diamond','Rectangular', 'Custom'
[... % Matrix that represents the pilot pattern parameters
OFDM.Nr.Subcarriers,... % Number of subcarriers
6; ... % Pilot spacing in the frequency domain
OFDM.Nr.MCSymbols,... % Number of OFDM Symbols
3.5 ... % Pilot spacing in the time domain
],...
'MovingBlockAverage' ,... % Interpolation method: 'MovingBlockAverage' (takes the average of a few close pilots to estimate the channel at the data position), 'FullAverage','linear','nearest','natural'
[6 OFDM.Nr.MCSymbols] ... % For 'MovingBlockAverage' defines the average region in frequency and time
);
ChannelEstimation_FBMC = ChannelEstimation.PilotSymbolAidedChannelEstimation(...
'Diamond',... % Pilot pattern, 'Diamond', 'Rectangular', 'Custom'
[... % Matrix that represents the pilot pattern parameters
FBMC.Nr.Subcarriers,... % Number of subcarriers
6; ... % Pilot spacing in the frequency domain
FBMC.Nr.MCSymbols,... % Number of FBMC Symbols
8 ... % Pilot spacing in the time domain
],...
'MovingBlockAverage', ... % Interpolation method: 'MovingBlockAverage' (takes the average of a few close pilots to estimate the channel at the data position), 'FullAverage','linear','nearest','natural'
[6 FBMC.Nr.MCSymbols]); % For 'MovingBlockAverage' defines the average region in frequency and time
% FBMC: imaginary interference cancellation method at pilot position
ImagInterCancel = ChannelEstimation.ImaginaryInterferenceCancellationAtPilotPosition(...
FBMC_ImaginaryInterferenceCancelationMethod, ... % Cancellation method, either 'Coding' or 'Auxiliary'
ChannelEstimation_FBMC.GetAuxiliaryMatrix(FBMC_NumberOfAuxilarySymbolsPerPilot), ... % PilotMatrix, 0 = Data, 1 = Pilot, -1 = Auxiliary symbol
FBMC.GetFBMCMatrix, ... % FBMC transmission matrix D, i.e., y = D*x with x transmitted data symbols and y received data symbols (before equalization)
16, ... % Cancel 16 closest interferers
2 ... % Pilot to data power offset. 2 guarantees that the SNR is the same at pilot position and at data position => fair comparision.
);
%% Pre-calculate
NrPilotSymbols_OFDM = ChannelEstimation_OFDM.NrPilotSymbols;
NrDataSymbols_OFDM = OFDM.Nr.Subcarriers*OFDM.Nr.MCSymbols-NrPilotSymbols_OFDM;
NrPilotSymbols_FBMC = ImagInterCancel.NrPilotSymbols;
NrDataSymbols_FBMC = ImagInterCancel.NrDataSymbols;
% 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');
OFDM_TurboCoding{i_cqi} = Coding.TurboCoding(log2(QAMModulationOrder)*NrDataSymbols_OFDM,round(CodeRate*log2(QAMModulationOrder)*NrDataSymbols_OFDM));
FBMC_TurboCoding{i_cqi} = Coding.TurboCoding(log2(PAMModulationOrder)*NrDataSymbols_FBMC,round(CodeRate*log2(PAMModulationOrder)*NrDataSymbols_FBMC));
end
% Calculate the SNR. The per-symbol SNR in FBMC and OFDM is different due
% to a different bandwidth and because energy might be wasted (auxiliary
% symbols)
M_SNR_FBMC_dB = Simulation_SNR_FBMC_dB;
for i_SNR = 1:length(Simulation_SNR_FBMC_dB)
Pn_time = 1/FBMC.GetSymbolNoisePower(1) * 10^(-Simulation_SNR_FBMC_dB(i_SNR)/10) * 2 * ImagInterCancel.DataPowerReduction;
M_SNR_OFDM_dB(i_SNR) = -10*log10(OFDM.GetSymbolNoisePower(Pn_time));
end
% Preallocate simulation results (needed for parfor)
M_Througput_OFDM = nan( length(M_SNR_OFDM_dB) , Simulation_MonteCarloRepetitions , size(M_CQI,1) );
M_Througput_OFDM_PerfectCSI = nan( length(M_SNR_OFDM_dB) , Simulation_MonteCarloRepetitions , size(M_CQI,1) );
M_Througput_FBMC = nan( length(M_SNR_OFDM_dB) , Simulation_MonteCarloRepetitions , size(M_CQI,1) );
M_Througput_FBMC_PerfectCSI = nan( length(M_SNR_OFDM_dB) , Simulation_MonteCarloRepetitions , size(M_CQI,1) );
NrWorkers = 1; % Conventional FOR loop
for i_Rep = 1:Simulation_MonteCarloRepetitions % Conventional FOR loop
% cluster = parcluster('local'); % PARFOR
% NrWorkers = cluster.NumWorkers; % PARFOR
% parfor i_Rep = 1:Simulation_MonteCarloRepetitions % PARFOR
tic
% Set random channel and noise
ChannelModel.NewRealization;
noise_Unscaled = sqrt(1/2)*(randn(N,1)+1j*randn(N,1));
% Perfect CSI (only an approximation because pulse form is not taken
% into account. However, the error is very small)
h_perfect_OFDM = ChannelModel.GetTransferFunction( OFDM.GetTimeIndexMidPos, OFDM.Implementation.FFTSize , (1:OFDM.Nr.Subcarriers)+OFDM.Implementation.IntermediateFrequency );
h_perfect_FBMC = ChannelModel.GetTransferFunction( FBMC.GetTimeIndexMidPos, FBMC.Implementation.FFTSize , (1:FBMC.Nr.Subcarriers)+FBMC.Implementation.IntermediateFrequency );
% Preallocate simulation result for one realization (needed for parfor)
M_Througput_OFDM_OneRealization = nan( length(M_SNR_OFDM_dB) , size(M_CQI,1) );
M_Througput_OFDM_PerfectCSI_OneRealization = nan( length(M_SNR_OFDM_dB) , size(M_CQI,1) );
M_Througput_FBMC_OneRealization = nan( length(M_SNR_OFDM_dB) , size(M_CQI,1) );
M_Througput_FBMC_PerfectCSI_OneRealization = nan( length(M_SNR_OFDM_dB) , size(M_CQI,1) );
for i_cqi = 1:size(M_CQI,1)
% Generate Data stream
BinaryDataStream_OFDM = randi( [0 1] , OFDM_TurboCoding{i_cqi}.NrDataBits , 1 );
BinaryDataStream_FBMC = randi( [0 1] , FBMC_TurboCoding{i_cqi}.NrDataBits , 1 );
% Encode Data stream
OFDM_TurboCoding{i_cqi}.UpdateInterleaving;
FBMC_TurboCoding{i_cqi}.UpdateInterleaving;
CodedBits_OFDM = OFDM_TurboCoding{i_cqi}.TurboEncoder( BinaryDataStream_OFDM );
CodedBits_FBMC = FBMC_TurboCoding{i_cqi}.TurboEncoder( BinaryDataStream_FBMC );
% Bit Interleaving
BitInterleaving_OFDM = randperm( OFDM_TurboCoding{i_cqi}.NrCodedBits );
BitInterleaving_FBMC = randperm( FBMC_TurboCoding{i_cqi}.NrCodedBits );
CodedBits_OFDM = CodedBits_OFDM( BitInterleaving_OFDM );
CodedBits_FBMC = CodedBits_FBMC( BitInterleaving_FBMC );
% Pilot Symbols
xP_OFDM = QAM{i_cqi}.SymbolMapping( randi(QAM{i_cqi}.ModulationOrder,[NrPilotSymbols_OFDM 1]) );
xP_OFDM = xP_OFDM./abs(xP_OFDM);
xP_FBMC = PAM{i_cqi}.SymbolMapping( randi(PAM{i_cqi}.ModulationOrder,[NrPilotSymbols_FBMC 1]) );
xP_FBMC = xP_FBMC./abs(xP_FBMC);
% Map coded bits to symbols
xD_OFDM = QAM{i_cqi}.Bit2Symbol( CodedBits_OFDM );
xD_FBMC = PAM{i_cqi}.Bit2Symbol( CodedBits_FBMC );
% transmitted symbols
x_OFDM = nan(OFDM.Nr.Subcarriers,OFDM.Nr.MCSymbols);
x_OFDM(ChannelEstimation_OFDM.PilotMatrix==1) = xP_OFDM;
x_OFDM(ChannelEstimation_OFDM.PilotMatrix==0) = xD_OFDM;
x_FBMC = reshape(ImagInterCancel.PrecodingMatrix*[xP_FBMC;xD_FBMC],[FBMC.Nr.Subcarriers FBMC.Nr.MCSymbols]);
% Generate the transmitted OFDM and FBMC signal in time
s_OFDM = OFDM.Modulation(x_OFDM);
s_FBMC = FBMC.Modulation(x_FBMC);
% Received signal without noise
r_OFDM_noNoise = ChannelModel.Convolution(s_OFDM);
r_FBMC_noNoise = ChannelModel.Convolution(s_FBMC);
for i_SNR = 1:length(M_SNR_OFDM_dB)
SNR_OFDM_dB = M_SNR_OFDM_dB(i_SNR);
Pn_time = 1/OFDM.GetSymbolNoisePower(1)*10^(-SNR_OFDM_dB/10);
% For unit data symbol power and constant transmit power, the noise power scales accordingly
Pn_OFDM = OFDM.GetSymbolNoisePower( Pn_time );
Pn_FBMC = FBMC.GetSymbolNoisePower( Pn_time );
% Add white Gaussian noise
noise = sqrt(Pn_time)*noise_Unscaled;
r_OFDM = r_OFDM_noNoise + noise;
r_FBMC = r_FBMC_noNoise + noise;
% Demodulate OFDM and FBMC signal
y_OFDM = OFDM.Demodulation(r_OFDM);
y_FBMC = FBMC.Demodulation(r_FBMC);
% LS channel estimates at the pilot positions
hP_est_OFDM = y_OFDM(ChannelEstimation_OFDM.PilotMatrix==1)./xP_OFDM;
hP_est_FBMC = y_FBMC(ChannelEstimation_FBMC.PilotMatrix==1)./xP_FBMC/sqrt(ImagInterCancel.PilotToDataPowerOffset*ImagInterCancel.DataPowerReduction);
% Channel estimation (interpolation)
h_est_OFDM = reshape( ChannelEstimation_OFDM.ChannelInterpolation(hP_est_OFDM) , [OFDM.Nr.Subcarriers OFDM.Nr.MCSymbols] );
h_est_FBMC = reshape( ChannelEstimation_FBMC.ChannelInterpolation(hP_est_FBMC) , [FBMC.Nr.Subcarriers FBMC.Nr.MCSymbols] );
% Equalize received symbols at data position
y_EQ_OFDM = y_OFDM(ChannelEstimation_OFDM.PilotMatrix==0) ./ h_est_OFDM( ChannelEstimation_OFDM.PilotMatrix==0 );
NoiseScaling_OFDM = 1./abs(h_est_OFDM(ChannelEstimation_OFDM.PilotMatrix==0 )).^2;
y_EQ_FBMC_all = y_FBMC ./ h_est_FBMC;
if strcmp(FBMC_ImaginaryInterferenceCancelationMethod,'Coding')
% Coding method: we need despreading at the receiver
y_EQ_FBMC = ImagInterCancel.PrecodingMatrix( : , ImagInterCancel.NrPilotSymbols+1:end )' * y_EQ_FBMC_all(:);
h_temp = ImagInterCancel.PostCodingChannelMatrix(ImagInterCancel.NrPilotSymbols+1:end,:)*h_est_FBMC(:);
NoiseScaling_FBMC = 1./abs(h_temp).^2;
else
% Auxiliary symbols method
y_EQ_FBMC = y_EQ_FBMC_all( ImagInterCancel.PilotMatrix==0 ) / sqrt( ImagInterCancel.DataPowerReduction );
NoiseScaling_FBMC = 1./abs(h_est_FBMC( ImagInterCancel.PilotMatrix==0 )).^2;
end
% Calculate LLR assuming perfect channel knowledge and ignoring interference
LLR_OFDM = QAM{i_cqi}.LLR_AWGN( y_EQ_OFDM , Pn_OFDM .* NoiseScaling_OFDM);
LLR_FBMC = PAM{i_cqi}.LLR_AWGN( real(y_EQ_FBMC) , Pn_FBMC .* NoiseScaling_FBMC);
% Bitdeinterleaving
LLR_OFDM(BitInterleaving_OFDM) = LLR_OFDM;
LLR_FBMC(BitInterleaving_FBMC) = LLR_FBMC;
% Decode Bits
DecodedBits_OFDM = OFDM_TurboCoding{i_cqi}.TurboDecoder( LLR_OFDM );
DecodedBits_FBMC = FBMC_TurboCoding{i_cqi}.TurboDecoder( LLR_FBMC );
% 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_FBMC_OneRealization(i_SNR,i_cqi) = all( DecodedBits_FBMC == BinaryDataStream_FBMC ) * length(BinaryDataStream_FBMC)/(FBMC.PHY.TimeSpacing*(FBMC.Nr.MCSymbols));
% Calculate the throughput for perfect channel state information
if Simulation_IncludePerfectCSI
y_EQ_OFDM_PerfectCSI = y_OFDM(ChannelEstimation_OFDM.PilotMatrix==0) ./ h_perfect_OFDM( ChannelEstimation_OFDM.PilotMatrix==0 );
NoiseScaling_OFDM_PerfectCSI = 1./abs(h_perfect_OFDM(ChannelEstimation_OFDM.PilotMatrix==0 )).^2;
y_EQ_FBMC_all_PerfectCSI = y_FBMC ./ h_perfect_FBMC;
if strcmp(FBMC_ImaginaryInterferenceCancelationMethod, 'Coding' )
% Coding method: we need despreading at the receiver
y_EQ_FBMC_PerfectCSI = ImagInterCancel.PrecodingMatrix( : , ImagInterCancel.NrPilotSymbols+1:end )' * y_EQ_FBMC_all_PerfectCSI(:);
h_temp_PerfectCSI = ImagInterCancel.PostCodingChannelMatrix(ImagInterCancel.NrPilotSymbols+1:end,:)*h_perfect_FBMC(:);
NoiseScaling_FBMC_PerfectCSI = 1./abs(h_temp_PerfectCSI).^2;
else
% Auxiliary symbols
y_EQ_FBMC_PerfectCSI = y_EQ_FBMC_all_PerfectCSI( ImagInterCancel.PilotMatrix==0 ) / sqrt( ImagInterCancel.DataPowerReduction );
NoiseScaling_FBMC_PerfectCSI = 1./abs(h_perfect_FBMC( ImagInterCancel.PilotMatrix==0 )).^2;
end
LLR_OFDM_PerfectCSI = QAM{i_cqi}.LLR_AWGN( y_EQ_OFDM_PerfectCSI , Pn_OFDM .* NoiseScaling_OFDM_PerfectCSI);
LLR_FBMC_PerfectCSI = PAM{i_cqi}.LLR_AWGN( real(y_EQ_FBMC_PerfectCSI) , Pn_FBMC .* NoiseScaling_FBMC_PerfectCSI);
LLR_OFDM_PerfectCSI(BitInterleaving_OFDM) = LLR_OFDM_PerfectCSI;
LLR_FBMC_PerfectCSI(BitInterleaving_FBMC) = LLR_FBMC_PerfectCSI;
DecodedBits_OFDM_PerfectCSI = OFDM_TurboCoding{i_cqi}.TurboDecoder(LLR_OFDM_PerfectCSI);
DecodedBits_FBMC_PerfectCSI = FBMC_TurboCoding{i_cqi}.TurboDecoder(LLR_FBMC_PerfectCSI);
M_Througput_OFDM_PerfectCSI_OneRealization(i_SNR,i_cqi) = all( DecodedBits_OFDM_PerfectCSI == BinaryDataStream_OFDM ) * length(BinaryDataStream_OFDM)/(OFDM.PHY.TimeSpacing*(OFDM.Nr.MCSymbols));
M_Througput_FBMC_PerfectCSI_OneRealization(i_SNR,i_cqi) = all( DecodedBits_FBMC_PerfectCSI == BinaryDataStream_FBMC ) * length(BinaryDataStream_FBMC)/(FBMC.PHY.TimeSpacing*(FBMC.Nr.MCSymbols));
end
end
end
M_Througput_OFDM(:,i_Rep,:) = M_Througput_OFDM_OneRealization;
M_Througput_FBMC(:,i_Rep,:) = M_Througput_FBMC_OneRealization;
if Simulation_IncludePerfectCSI
M_Througput_OFDM_PerfectCSI(:,i_Rep,:) = M_Througput_OFDM_PerfectCSI_OneRealization;
M_Througput_FBMC_PerfectCSI(:,i_Rep,:) = M_Througput_FBMC_PerfectCSI_OneRealization;
end
TimePassed = toc;
disp(['Realization ' int2str(i_Rep) ' of ' int2str(Simulation_MonteCarloRepetitions) 'needed ' int2str(TimePassed) 's. Total simulation time:' int2str(TimePassed*Simulation_MonteCarloRepetitions/NrWorkers/60) 'minutes']);
end
%% Calculate Maximum Throughput
% Here, we maximize the throughput over all CQI values, that is, we assume
% perfect feedback.
Througput_OFDM = max(M_Througput_OFDM,[],3);
Mean_Througput_OFDM = mean(Througput_OFDM,2);
ConInterval_Througput_OFDM = bootci(2000,@(x)(mean(x)),Througput_OFDM');
ConInterval_L_Througput_OFDM = Mean_Througput_OFDM - ConInterval_Througput_OFDM(1,:)';
ConInterval_U_Througput_OFDM = ConInterval_Througput_OFDM(2,:)'-Mean_Througput_OFDM;
Througput_FBMC = max(M_Througput_FBMC,[],3);
Mean_Througput_FBMC = mean(Througput_FBMC,2);
ConInterval_Througput_FBMC = bootci(2000,@(x)(mean(x)),Througput_FBMC');
ConInterval_L_Througput_FBMC = Mean_Througput_FBMC - ConInterval_Througput_FBMC(1,:)';
ConInterval_U_Througput_FBMC = ConInterval_Througput_FBMC(2,:)'-Mean_Througput_FBMC;
%% Information Theory
% Calculate the achievable rate (Gaussian inputs)
M_SNR_FBMC_dB_MorePoints = linspace(min(M_SNR_FBMC_dB),max(M_SNR_FBMC_dB),100);
for i_SNR = 1:length(M_SNR_FBMC_dB_MorePoints)
SNR = 10.^(M_SNR_FBMC_dB_MorePoints(i_SNR)/10);
fun = @(h) log2(1+SNR*abs(h).^2).*2.*h.*exp(-(h.^2));
C_OneSymbol = integral(fun,0,inf);
AchievableRate_FBMC(i_SNR) = NrDataSymbols_FBMC*1/2*C_OneSymbol/(FBMC.PHY.TimeSpacing*FBMC.Nr.MCSymbols);
end
% Calculate the achievable rate (BICM: 4-OQAM, 16-OQAM,...)
% The BICM capacity per symbol is precalulated. Use the script "./Theory/BICM_Capacity_Rayleigh" to calculate those values
BICM_Capacity_Rayleigh_2_4_8_PAM = load('./Theory/BICM_Capacity_Rayleigh_2_4_8_PAM.mat');
AchievableRate_FBMC_BICM_2_4_8_PAM = NrDataSymbols_FBMC * interp1( BICM_Capacity_Rayleigh_2_4_8_PAM.SNR_dB , BICM_Capacity_Rayleigh_2_4_8_PAM.C_max,M_SNR_FBMC_dB_MorePoints , 'spline' )/( FBMC.PHY.TimeSpacing*FBMC.Nr.MCSymbols );
BICM_Capacity_Rayleigh_2_4_8_16_PAM = load('./Theory/BICM_Capacity_Rayleigh_2_4_8_16_PAM.mat');
AchievableRate_FBMC_BICM_2_4_8_16_PAM = NrDataSymbols_FBMC * interp1( BICM_Capacity_Rayleigh_2_4_8_16_PAM.SNR_dB , BICM_Capacity_Rayleigh_2_4_8_16_PAM.C_max,M_SNR_FBMC_dB_MorePoints , 'spline' )/( FBMC.PHY.TimeSpacing*FBMC.Nr.MCSymbols );
%% Plot Results
fprintf('====================================================================================================\n');
fprintf('================================ Basic Settings (without guard) ===================================\n');
fprintf(' |(complex)TF-Spacing| Bandwidth(FL)| Time(KT) | SNR rel. to OFDM | Pilot density | \n');
fprintf('OFDM (with CP) |%17.2f |%8.2f MHz |%8.2f ms |%12.2f dB | %8.3f | \n', OFDM.PHY.TimeSpacing*OFDM.PHY.SubcarrierSpacing , OFDM.PHY.SubcarrierSpacing*OFDM.Nr.Subcarriers/1e6 , OFDM.PHY.TimeSpacing*OFDM.Nr.MCSymbols/1e-3 , 0 , NrPilotSymbols_OFDM/(OFDM.Nr.MCSymbols*OFDM.PHY.TimeSpacing*OFDM.Nr.Subcarriers*OFDM.PHY.SubcarrierSpacing) );
fprintf('FBMC-OQAM |%17.2f |%8.2f MHz |%8.2f ms |%12.2f dB | %8.3f | \n', FBMC.PHY.TimeSpacing*FBMC.PHY.SubcarrierSpacing*2 , FBMC.PHY.SubcarrierSpacing*FBMC.Nr.Subcarriers/1e6 , FBMC.PHY.TimeSpacing*FBMC.Nr.MCSymbols/1e-3 , M_SNR_FBMC_dB(1)-M_SNR_OFDM_dB(1) , NrPilotSymbols_FBMC/(FBMC.Nr.MCSymbols*FBMC.PHY.TimeSpacing*FBMC.Nr.Subcarriers*FBMC.PHY.SubcarrierSpacing) );
fprintf('====================================================================================================\n');
fprintf('====================================================================================================\n');
figure(1);
errorbar( M_SNR_FBMC_dB , Mean_Througput_FBMC/1e6 , ConInterval_L_Througput_FBMC/1e6 , ConInterval_U_Througput_FBMC/1e6 , 'blue');
hold on;
errorbar( M_SNR_FBMC_dB , Mean_Througput_OFDM/1e6 , ConInterval_L_Througput_OFDM/1e6 , ConInterval_U_Througput_OFDM/1e6 , 'red');
semilogy( M_SNR_FBMC_dB_MorePoints , AchievableRate_FBMC/1e6 , 'Color' , [0,0.4,0.6]);
semilogy( M_SNR_FBMC_dB_MorePoints , AchievableRate_FBMC_BICM_2_4_8_PAM/1e6 , 'Color' , [0,0.2,0.8]);
semilogy( M_SNR_FBMC_dB_MorePoints , AchievableRate_FBMC_BICM_2_4_8_16_PAM/1e6 , '--','Color' , [0,0.2,0.8]);
xlim([min(M_SNR_FBMC_dB) max(M_SNR_FBMC_dB)]);
xlabel('Signal-to-Noise Ratio for FBMC [dB]');
ylabel('Throughput, Achievable Rate [Mbit/s]');
if Simulation_IncludePerfectCSI
Througput_OFDM_PerfectCSI = max(M_Througput_OFDM_PerfectCSI,[],3);
Mean_Througput_OFDM_PerfectCSI = mean(Througput_OFDM_PerfectCSI,2);
Througput_FBMC_PerfectCSI = max(M_Througput_FBMC_PerfectCSI,[],3);
Mean_Througput_FBMC_PerfectCSI = mean(Througput_FBMC_PerfectCSI,2);
figure(2);
errorbar( M_SNR_FBMC_dB , Mean_Througput_FBMC/1e6 , ConInterval_L_Througput_FBMC/1e6 , ConInterval_U_Througput_FBMC/1e6 , 'blue');
hold on;
errorbar( M_SNR_FBMC_dB , Mean_Througput_OFDM/1e6 , ConInterval_L_Througput_OFDM/1e6 , ConInterval_U_Througput_OFDM/1e6 , 'red');
semilogy( M_SNR_FBMC_dB_MorePoints , AchievableRate_FBMC/1e6 , 'Color' , [0,0.4,0.6]);
semilogy( M_SNR_FBMC_dB_MorePoints , AchievableRate_FBMC_BICM_2_4_8_PAM/1e6 , 'Color' , [0,0.2,0.8]);
semilogy( M_SNR_FBMC_dB_MorePoints , AchievableRate_FBMC_BICM_2_4_8_16_PAM/1e6 , '--','Color' , [0,0.2,0.8]);
semilogy( M_SNR_FBMC_dB , Mean_Througput_OFDM_PerfectCSI/1e6 , 'black');
semilogy( M_SNR_FBMC_dB , Mean_Througput_FBMC_PerfectCSI/1e6 , 'black');
xlim([min(M_SNR_FBMC_dB) max(M_SNR_FBMC_dB)]);
xlabel('Signal-to-Noise Ratio for FBMC [dB]');
ylabel('Throughput, Achievable Rate [Mbit/s]');
end
if Simulation_PlotAdditionalInformation
% Expected signal power in time (per subframe)
disp('Calculate expected signal power in time ...');
[PS_OFDM , t] = OFDM.PlotTransmitPower;
PS_FBMC = FBMC.PlotTransmitPower(ImagInterCancel.PrecodingMatrix*ImagInterCancel.PrecodingMatrix');
figure(3);
disp('Calculate power spectral density ...');
plot((t-FBMC_BlockOverlapTime)/1e-3 , PS_OFDM , 'red'); hold on;
plot((t-FBMC_BlockOverlapTime)/1e-3 , PS_FBMC , 'blue');
xlabel('Time [ms]');
ylabel('Signal Power');
% Power spectral density (normalization so that Parseval's theorem is fullfilled)
[PSD_OFDM , f] = OFDM.PlotPowerSpectralDensity;
PSD_FBMC = FBMC.PlotPowerSpectralDensity(ImagInterCancel.PrecodingMatrix*ImagInterCancel.PrecodingMatrix');
figure(4);
plot(f/1e6 , 10*log10(PSD_OFDM) ,'red'); hold on;
plot(f/1e6 , 10*log10(PSD_FBMC) ,'blue');
xlabel('Frequency [MHz]');
ylabel('Power Spectral Density [dB]');
ylim( [-100 2] + 10*log10( max([PSD_OFDM;PSD_FBMC]) ) );
% Pilot pattern for OFDM and FBMC
figure(5);
ChannelEstimation_OFDM.PlotPilotPattern;
title('Pilot Pattern: OFDM');
figure(6);
if strcmp(FBMC_ImaginaryInterferenceCancelationMethod,'Coding');
ChannelEstimation_FBMC.PlotPilotPattern(-(ImagInterCancel.ConsideredInterferenceMatrix<0)+(ImagInterCancel.ConsideredInterferenceMatrix>0))
else
ChannelEstimation_FBMC.PlotPilotPattern(ImagInterCancel.PilotMatrix);
end
title('Pilot Pattern: FBMC');
end