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Figure_13_PowerSpectralDensityQuantization.m
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Figure_13_PowerSpectralDensityQuantization.m
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% =====================================================================
% Ronald Nissel, [email protected]
% (c) 2017 by Institute of Telecommunications, TU Wien
% www.nt.tuwien.ac.at
% =====================================================================
% This script plots the power spectal density of FBMC and OFDM in case of
% quantization and clipping.
% See Figure 13 in the paper
clear; close all;
% Important parameters for the quantization
M_BitResolution = [4 8 12 16]; % DAC resolution: 4-bit, 8-bit, 12-bit, 16-bit
M_Clipping_dB = [8 9 11 12]; % The signal has a mean power of one. Values larger(smaller) than Clipping_dB are set to the maximum (minimum) value and affect the Power Spectral Density (PSD)
% additional parameters
NrRepetitions_PSD = 100; %10000 % Number repetitions for the simulation
K_FBMC = 105; % Number of FBMC symbols
K_OFDM = 10; % Number of OFDM symbols
L = 24; % Number of subcarriers
QAM_ModulationOrder = 64; % Modulation order, 4,16,64,...
SubcarrierSpacing = 15e3; % Subcarrier spacing (15kHz, same as LTE)
SamplingRate = SubcarrierSpacing*1024; % A high oversampling factor reduces the quantization effect. We therfore chose 24*42.66=1024 instead of 24*14.
OverlappingFactor = 4; % Overlapping factor for FBMC. For an overlapping factor of 4 and the PHYDYAS pulse, we see a rectangular filering effect
IntermediateSubcarrier = 50; % Shift frequency (for presentation purposes)
ColorFBMC = [0 0 1]*0.5;
ColorOFDM = [1 0 0];
%% FBMC Object
FBMC = Modulation.FBMC(...
L,... % Number subcarriers
K_FBMC,... % Number FBMC symbols
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
SubcarrierSpacing*IntermediateSubcarrier,... % Intermediate frequency first subcarrier (Hz)
false,... % Transmit real valued signal
'PHYDYAS-OQAM',... % Prototype filter (Hermite, PHYDYAS, RRC) and OQAM or QAM,
OverlappingFactor, ... % Overlapping factor (also determines oversampling in the frequency domain)
0, ... % Initial phase shift
true ... % Polyphase implementation
);
%% OFDM Object
OFDM = Modulation.OFDM(...
L,... % Number subcarriers
K_OFDM,... % Number OFDM Symbols
SubcarrierSpacing,... % Subcarrier spacing (Hz)
SamplingRate,... % Sampling rate (Samples/s)
SubcarrierSpacing*IntermediateSubcarrier,... % Intermediate frequency first subcarrier (Hz)
false,... % Transmit real valued signal
1/(14*SubcarrierSpacing), ... % Cyclic prefix length (s)
(OverlappingFactor-1/2)*1/SubcarrierSpacing*1/2 ... % Zero guard length (s)
);
%% Modulation Object
QAM = Modulation.SignalConstellation(QAM_ModulationOrder,'QAM');
PAM = Modulation.SignalConstellation(sqrt(QAM_ModulationOrder),'PAM');
%% Power Spectral Density
for i_BitResolution = 1:size(M_BitResolution,2)
BitResolution = M_BitResolution(i_BitResolution);
Clipping_dB = M_Clipping_dB(i_BitResolution);
disp('===========================================');
disp(['Bit resolution: ' int2str(BitResolution)]);
disp(['Clipping: ' int2str(Clipping_dB) 'dB']);
% PSD...Power Spectral Density
PSD_OFDM_Simulation = zeros(OFDM.Nr.SamplesTotal,1);
PSD_FBMC_Simulation = zeros(FBMC.Nr.SamplesTotal,1);
Scaling = 2^(BitResolution-1)/10^(Clipping_dB/20);
tic
for i_rep = 1:NrRepetitions_PSD
x_OFDM = QAM.SymbolMapping(randi(QAM_ModulationOrder,OFDM.Nr.Subcarriers,OFDM.Nr.MCSymbols));
x_PAM = PAM.SymbolMapping(randi(sqrt(QAM_ModulationOrder),FBMC.Nr.Subcarriers,FBMC.Nr.MCSymbols));
s_OFDM = OFDM.Modulation(x_OFDM);
s_FBMC = FBMC.Modulation(x_PAM);
% Scale and quantization
s_OFDM = round(s_OFDM*Scaling);
s_FBMC = round(s_FBMC*Scaling);
% Clipping OFDM
Real_s_OFDM = real(s_OFDM);
Imag_s_OFDM = imag(s_OFDM);
NumberOfClippedSamples_OFDM(i_rep) = sum(Real_s_OFDM>(2^(BitResolution-1)-1))+sum(Real_s_OFDM<-(2^(BitResolution-1))); % just for information
Real_s_OFDM(Real_s_OFDM > (2^(BitResolution-1)-1)) = (2^(BitResolution-1)-1);
Real_s_OFDM(Real_s_OFDM <-(2^(BitResolution-1))) = -(2^(BitResolution-1));
Imag_s_OFDM(Imag_s_OFDM > (2^(BitResolution-1)-1)) = (2^(BitResolution-1)-1);
Imag_s_OFDM(Imag_s_OFDM <-(2^(BitResolution-1))) = -(2^(BitResolution-1));
s_OFDM = Real_s_OFDM+1j*Imag_s_OFDM;
% Clipping FBMC
Real_s_FBMC = real(s_FBMC);
Imag_s_FBMC = imag(s_FBMC);
NumberOfClippedSamples_FBMC(i_rep) = sum(Real_s_FBMC>(2^(BitResolution-1)-1))+sum(Real_s_FBMC<-(2^(BitResolution-1)));
Real_s_FBMC(Real_s_FBMC > (2^(BitResolution-1)-1)) = (2^(BitResolution-1)-1);
Real_s_FBMC(Real_s_FBMC <-(2^(BitResolution-1))) = -(2^(BitResolution-1));
Imag_s_FBMC(Imag_s_FBMC > (2^(BitResolution-1)-1)) = (2^(BitResolution-1)-1);
Imag_s_FBMC(Imag_s_FBMC <-(2^(BitResolution-1))) = -(2^(BitResolution-1));
s_FBMC = Real_s_FBMC+1j*Imag_s_FBMC;
% Calculate PSD
PSD_OFDM_Simulation = PSD_OFDM_Simulation + abs(fft(s_OFDM)).^2;
PSD_FBMC_Simulation = PSD_FBMC_Simulation + abs(fft(s_FBMC)).^2;
% Calculate Interference Power
PI_OFDM(i_rep) = mean(mean(abs(OFDM.Demodulation(s_OFDM)/Scaling-x_OFDM).^2));
PI_FBMC(i_rep) = mean(mean(abs(real(FBMC.Demodulation(s_FBMC))/Scaling-x_PAM).^2));
TimePassed = toc;
if mod(i_rep,100)==0
disp(['Realization ' int2str(i_rep) ' of ' int2str(NrRepetitions_PSD) '. Time left: ' int2str(TimePassed/i_rep*(NrRepetitions_PSD-i_rep)/60) 'minutes']);
end
end
% Normalize over energy
PSD_FBMC_Simulation = PSD_FBMC_Simulation/(sum(PSD_FBMC_Simulation)*SamplingRate/FBMC.Nr.SamplesTotal);
PSD_OFDM_Simulation = PSD_OFDM_Simulation/(sum(PSD_OFDM_Simulation)*SamplingRate/OFDM.Nr.SamplesTotal);
NormFactor = max([PSD_FBMC_Simulation(:)]);
PSD_OFDM_Simulation = PSD_OFDM_Simulation/NormFactor;
PSD_FBMC_Simulation = PSD_FBMC_Simulation/NormFactor;
disp('Number of clipped samples: OFDM vs FBMC');
disp([sum(NumberOfClippedSamples_OFDM) sum(NumberOfClippedSamples_FBMC)]);
M_SIR_OFDM(i_BitResolution) = -10*log10(mean(PI_OFDM));
M_SIR_FBMC(i_BitResolution) = -10*log10(mean(PI_FBMC));
M_PSD_OFDM_Simulation(:,i_BitResolution) = PSD_OFDM_Simulation;
M_PSD_FBMC_Simulation(:,i_BitResolution) = PSD_FBMC_Simulation;
end
f_OFDM = (0:(size(PSD_OFDM_Simulation,1)-1))*1/(size(PSD_OFDM_Simulation,1)*OFDM.PHY.dt);
f_FBMC = (0:(size(PSD_FBMC_Simulation,1)-1))*1/(size(PSD_FBMC_Simulation,1)*FBMC.PHY.dt);
f_Normalized_OFDM = f_OFDM/OFDM.PHY.SubcarrierSpacing-IntermediateSubcarrier-ceil(L/2)+1;
f_Normalized_FBMC = f_FBMC/FBMC.PHY.SubcarrierSpacing-IntermediateSubcarrier-ceil(L/2)+1;
figure();
plot([-12 -12], [-150,20],'color', [0.8 0.8 0.8]);
hold on;
plot([12 12], [-150,20],'color', [0.8 0.8 0.8]);
plot(f_OFDM/OFDM.PHY.SubcarrierSpacing-IntermediateSubcarrier-ceil(L/2)+1/2,10*log10([M_PSD_OFDM_Simulation(:,end).']),'Color', ColorOFDM);
plot(f_FBMC/FBMC.PHY.SubcarrierSpacing-IntermediateSubcarrier-ceil(L/2)+1/2,10*log10([M_PSD_FBMC_Simulation.']),'Color', ColorFBMC);
ylim([-100 4]);
xlim([-50 50]);
xlabel('Normalized Frequency, $f/F$');
ylabel('Power Spectral Density [dB]');
set(gca,'XTick',[-50:10:50]);
disp('SNR [dB] for OFDM;');
disp(M_SIR_OFDM);
disp('SNR [dB] for FBMC;'); % Increasing the overlapping factor increases the SIR bound
disp(M_SIR_FBMC);