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Figure_5_6_7_8_SIR_OptimalSubcarrierSpacing.m
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Figure_5_6_7_8_SIR_OptimalSubcarrierSpacing.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 Signal-to-Interference Ratio (SIR) for an optimal
% subcarrier spacing. The SIR values, depending on velocitiy and subcarrier
% spacing, are precalulated in the folder "./Results". This script then
% combines those pre-calulated SIR values.
clear; close all;
PlotAddionalResults = false; % If true, plot additional information.
%% Plot Pedestrian A
ColorFBMC = [0 0 1]*0.5; % Color for PHYDYAS pulse
M_Velocity_kmh = [0:2:8 10:10:500];
M_SubcarrierSpacingInterpolated = 1e3*[5:0.1:180];
NrMethods = 4;
PowerDelayProfile = 'PedestrianA';
Method{1} = 'OFDM';
PrototypeFilter{1} = '';
Method{2} = 'FBMC-OQAM';
PrototypeFilter{2} = 'Hermite';
Method{3} = 'FBMC-OQAM';
PrototypeFilter{3} = 'PHYDYAS';
Method{4} = 'CP-OFDM-007LTE';
PrototypeFilter{4} = '';
% Load results and find optimum (using interpolation to obtain smoother curves)
for i_method = 1:NrMethods
for i_velocity = 1:length(M_Velocity_kmh)
Velocity_kmh = M_Velocity_kmh(i_velocity);
FileName = ['.\Results\' Method{i_method} '_' PrototypeFilter{i_method} '_' PowerDelayProfile int2str(Velocity_kmh) '.mat'];
L1 = load(FileName);
% Needed for interpolation: remove double subcarriers
IndexSameSubcarrierSpacing = find(diff(L1.M_RealSubcarrierSpacing)==0);
L1.M_RealSubcarrierSpacing(IndexSameSubcarrierSpacing) = [];
L1.SIR_Theory(IndexSameSubcarrierSpacing) = [];
% Interpolate to get smoother curves
M_SIR_Interpolated(:,i_velocity) = interp1(L1.M_RealSubcarrierSpacing,L1.SIR_Theory,M_SubcarrierSpacingInterpolated,'spline',nan);
if strcmp(Method{i_method},'CP-OFDM-007LTE') % To check if theoretical equations are correct (interpolation is wrong in case of CP-OFDM!)
M_SIR007_Interpolated_True(:,i_velocity) = L1.SIR_Theory;
end
end
M_SIR_Interpolated_ALL(:,:,i_method) = M_SIR_Interpolated;
[SIRoptimal,IndexSIRoptimal] = max(M_SIR_Interpolated);
SubcarrierSpacingOptimal = M_SubcarrierSpacingInterpolated(IndexSIRoptimal);
M_SIR_15kHZ(:,i_method) = M_SIR_Interpolated(M_SubcarrierSpacingInterpolated==15e3,:);
M_SIRoptimal(:,i_method) = SIRoptimal.';
M_SubcarrierSpacingOptimal(:,i_method) = SubcarrierSpacingOptimal.';
end
M_SIR_15kHZ(:,4)=nan; % Values are wrong for CP-OFDM due to discontinuity
M_SIRoptimal(:,4)=nan;
M_SubcarrierSpacingOptimal(:,4)=nan;
% Calculate theoretical SIR for OFDM (no ISI)
Kappa = 1/14; % LTE efficiency loss
TCP = 410e-9; % maximum delay of Pedestrian A
F = Kappa/TCP; % optimal subcarrier spacing (no ISI)
M_DopplerShift = M_Velocity_kmh/3.6*2.5e9/2.998e8;
P_S_CPOFDM = hypergeom([1/2],[3/2 2],-(M_DopplerShift/F*pi).^2);
P_I_CPOFDM = 1-P_S_CPOFDM;
SIR_CPOFDM = 10*log10(P_S_CPOFDM./P_I_CPOFDM);
figure(11);
plot(M_Velocity_kmh,M_SIRoptimal(:,1),':','color', [0.5 0.5 0]);
hold on;
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,1)>5e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,1)>5e3,1),'color', [0.5 0.5 0]);
plot(M_Velocity_kmh,M_SIRoptimal(:,2),': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>5e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,2)>5e3,2),'blue');
plot(M_Velocity_kmh,M_SIRoptimal(:,3),'color',ColorFBMC);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>5e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,3)>5e3,3),'color',ColorFBMC);
plot(M_Velocity_kmh,SIR_CPOFDM,'red');
xlabel('Velocity [km/h]');
ylabel('Signal-to-Interference Ratio [dB]');
ylim([0 50]);
p1 = plot(nan,nan,': black');
p2 = plot(nan,nan,'black');
legend([p1 p2],{'Subcarrier Spacing, F=5kHz','Subcarrier Spacing, F>5kHz'},'Location','SouthWest');
if PlotAddionalResults
% Optimal subcarrier spacing according to the rule of thumb
RMS_Doppler = 1/sqrt(2)*M_DopplerShift;
RMS_Tau = 46e-9;
ApproxOptimalSubcarrierSpacing_PHYDYAS = sqrt(0.2745/0.328*RMS_Doppler/RMS_Tau);
ApproxOptimalSubcarrierSpacing_Hermite = sqrt(0.2015/0.403*RMS_Doppler/RMS_Tau);
figure(12);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,1)>5e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,1)>5e3,1)/1e3,'red');
hold on;
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>15e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,2)>15e3,2)/1e3,'blue');
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_Hermite/1e3,': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>15e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,3)>15e3,3)/1e3,'color',ColorFBMC);
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_PHYDYAS/1e3,':','color',ColorFBMC);
xlabel('Velocity [km/h], f_c=2.5GHz$');
ylabel('Optimal Subcarrier Spacing [kHz]');
title('Pedestrian A');
p1 = plot(nan,nan,'black');
p2 = plot(nan,nan,': black');
legend([p1 p2],{'Exhaustive search','Approximation'},'Location','NorthWest');
% SIR for approximate optimal subcarrier spacing
rep1 = length(ApproxOptimalSubcarrierSpacing_PHYDYAS);
rep2 = length(M_SubcarrierSpacingInterpolated);
[~,index_PHYDYAS] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_PHYDYAS,[rep2,1])),[],1);
[~,index_Hermite] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_Hermite,[rep2,1])),[],1);
M_SIR_Interploated_PHYDYAS = M_SIR_Interpolated_ALL(:,:,3);
M_SIR_Interploated_Hermite = M_SIR_Interpolated_ALL(:,:,2);
for i_velocity = 1:length(M_Velocity_kmh)
M_SIR_ApproxOpt_PHYDYAS(i_velocity) = M_SIR_Interploated_PHYDYAS(index_PHYDYAS(i_velocity),i_velocity);
M_SIR_ApproxOpt_Hermite(i_velocity) = M_SIR_Interploated_Hermite(index_Hermite(i_velocity),i_velocity);
end
figure(13);plot(M_SIRoptimal(:,3)-M_SIR_ApproxOpt_PHYDYAS.');
hold on;
plot(M_SIRoptimal(:,2)-M_SIR_ApproxOpt_Hermite.');
xlabel('Velocity [km/h], f_c=2.5GHz');
ylabel('SIR Error in dB!!! between approx. and exhaustive search');
title('Pedestrian A');
% SIR of theory vs simulations
% plot(M_Velocity_kmh,[max(M_SIR007_Interpolated_True,[],1).' SIR_CPOFDM.']);
end
%% Plot Vehicular A
clear M_SIR_Interpolated_ALL M_SIRoptimal M_SIR_Interpolated M_SIR_15kHZ M_SubcarrierSpacingOptimal M_SIR007_Interpolated_True;
M_Velocity_kmh = [0 2:2:8 10:10:500];
M_SubcarrierSpacingInterpolated = 1e3*[5:0.1:60];
NrMethods = 4;
PowerDelayProfile = 'VehicularA';
Method{1} = 'OFDM';
PrototypeFilter{1} = '';
Method{2} = 'FBMC-OQAM';
PrototypeFilter{2} = 'Hermite';
Method{3} = 'FBMC-OQAM';
PrototypeFilter{3} = 'PHYDYAS';
Method{4} = 'CP-OFDM-007LTE';
PrototypeFilter{4} = '';
% Load results and find optimum (using interpolation to obtain smoother curves)
for i_method = 1:NrMethods
for i_velocity = 1:length(M_Velocity_kmh)
Velocity_kmh = M_Velocity_kmh(i_velocity);
FileName = ['.\Results\' Method{i_method} '_' PrototypeFilter{i_method} '_' PowerDelayProfile int2str(Velocity_kmh) '.mat'];
L1 = load(FileName);
% Needed for interpolation: remove double subcarriers
IndexSameSubcarrierSpacing = find(diff(L1.M_RealSubcarrierSpacing)==0);
L1.M_RealSubcarrierSpacing(IndexSameSubcarrierSpacing) = [];
L1.SIR_Theory(IndexSameSubcarrierSpacing) = [];
% Interpolate to get smoother curves
M_SIR_Interpolated(:,i_velocity) = interp1(L1.M_RealSubcarrierSpacing,L1.SIR_Theory,M_SubcarrierSpacingInterpolated,'spline',nan);
if strcmp(Method{i_method},'CP-OFDM-007LTE') % To check if theoretical equations are correct (interpolation is wrong in case of CP-OFDM!)
M_SIR007_Interpolated_True(:,i_velocity) = L1.SIR_Theory;
end
end
M_SIR_Interpolated_ALL(:,:,i_method) = M_SIR_Interpolated;
[SIRoptimal,IndexSIRoptimal] = max(M_SIR_Interpolated);
SubcarrierSpacingOptimal = M_SubcarrierSpacingInterpolated(IndexSIRoptimal);
M_SIR_15kHZ(:,i_method) = M_SIR_Interpolated(M_SubcarrierSpacingInterpolated==15e3,:);
M_SIRoptimal(:,i_method) = SIRoptimal.';
M_SubcarrierSpacingOptimal(:,i_method) = SubcarrierSpacingOptimal.';
end
M_SIR_15kHZ(:,4)=nan; % Values are wrong for CP-OFDM due to discontinuity
M_SIRoptimal(:,4)=nan;
M_SubcarrierSpacingOptimal(:,4)=nan;
% Calculate Theoretical SIR for OFDM (no ISI)
Kappa = 1/14; % LTE efficiency loss
TCP = 2510e-9; % maximum delay of Pedestrian A
F = Kappa/TCP; %optimal subcarrier spacing (no ISI)
M_DopplerShift = M_Velocity_kmh/3.6*2.5e9/2.998e8;
P_S_CPOFDM = hypergeom([1/2],[3/2 2],-(M_DopplerShift/F*pi).^2);
P_I_CPOFDM = 1-P_S_CPOFDM;
SIR_CPOFDM = 10*log10(P_S_CPOFDM./P_I_CPOFDM);
figure(21);
plot(M_Velocity_kmh,M_SIRoptimal(:,1),':','color', [0.5 0.5 0]);
hold on;
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,1)>5e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,1)>5e3,1),'color', [0.5 0.5 0]);
maxTemp = max(M_SIR007_Interpolated_True);
plot(M_Velocity_kmh(maxTemp>SIR_CPOFDM),maxTemp(maxTemp>SIR_CPOFDM),'black');
plot(M_Velocity_kmh,SIR_CPOFDM,'red');
plot(M_Velocity_kmh,M_SIRoptimal(:,2),': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>5e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,2)>5e3,2),'blue');
plot(M_Velocity_kmh,M_SIRoptimal(:,3),':','color',ColorFBMC);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>5e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,3)>5e3,3),'color',ColorFBMC);
xlabel('Velocity [km/h]');
ylabel('Signal-to-Interference Ratio [dB]');
ylim([0 50]);
p1 = plot(nan,nan,': black');
p2 = plot(nan,nan,'black');
legend([p1 p2],{'Subcarrier Spacing, F=5kHz','Subcarrier Spacing, F>5kHz'},'Location','SouthWest');
if PlotAddionalResults
% Optimal subcarrier spacing according to the rule of thumb
RMS_Doppler = 1/sqrt(2)*M_DopplerShift;
RMS_Tau = 370e-9; % we have 44ns and not 46ns due to sampling
ApproxOptimalSubcarrierSpacing_PHYDYAS = sqrt(0.2745/0.328*RMS_Doppler/RMS_Tau);
ApproxOptimalSubcarrierSpacing_Hermite = sqrt(0.2015/0.403*RMS_Doppler/RMS_Tau);
figure(22);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,1)>5e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,1)>5e3,1)/1e3,'red');
hold on;
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>5e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,2)>5e3,2)/1e3,'blue');
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_Hermite/1e3,': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>5e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,3)>5e3,3)/1e3,'color',ColorFBMC);
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_PHYDYAS/1e3,':','color',ColorFBMC);
xlabel('Velocity [km/h], f_c=2.5GHz');
ylabel('Optimal Subcarrier Spacing [kHz]');
title('Vehicular A');
p1 = plot(nan,nan,'black');
p2 = plot(nan,nan,': black');
legend([p1 p2],{'Exhaustive search','Approximation'},'Location','NorthWest');
% SIR for approximate optimal subcarrier spacing
rep1 = length(ApproxOptimalSubcarrierSpacing_PHYDYAS);
rep2 = length(M_SubcarrierSpacingInterpolated);
[~,index_PHYDYAS] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_PHYDYAS,[rep2,1])),[],1);
[~,index_Hermite] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_Hermite,[rep2,1])),[],1);
M_SIR_Interploated_PHYDYAS = M_SIR_Interpolated_ALL(:,:,3);
M_SIR_Interploated_Hermite = M_SIR_Interpolated_ALL(:,:,2);
for i_velocity = 1:length(M_Velocity_kmh)
M_SIR_ApproxOpt_PHYDYAS(i_velocity) = M_SIR_Interploated_PHYDYAS(index_PHYDYAS(i_velocity),i_velocity);
M_SIR_ApproxOpt_Hermite(i_velocity) = M_SIR_Interploated_Hermite(index_Hermite(i_velocity),i_velocity);
end
figure(23);plot(M_SIRoptimal(:,3)-M_SIR_ApproxOpt_PHYDYAS.');
hold on;
plot(M_SIRoptimal(:,2)-M_SIR_ApproxOpt_Hermite.');
xlabel('Velocity [km/h], f_c=2.5GHz');
ylabel('SIR Error in dB!!! between approx. and exhaustive search');
title('Vehicular A');
% SIR of theory vs simulations
% plot(M_Velocity_kmh,[max(M_SIR007_Interpolated_True,[],1).' SIR_CPOFDM.']);
end
%% Plot TDL-A_30ns A
clear M_SIR_Interpolated_ALL M_SIRoptimal M_SIR_Interpolated M_SIR_15kHZ M_SubcarrierSpacingOptimal M_SIR007_Interpolated_True;
M_Velocity_kmh = [0 2 4 6 8 10 12 14 16 20:10:500];
M_SubcarrierSpacingInterpolated = 1e3*[100:1:1000];
NrMethods = 4;
PowerDelayProfile = 'TDL-A_30ns';
Method{1} = 'OFDM';
PrototypeFilter{1} = '';
Method{2} = 'FBMC-OQAM';
PrototypeFilter{2} = 'Hermite';
Method{3} = 'FBMC-OQAM';
PrototypeFilter{3} = 'PHYDYAS';
Method{4} = 'CP-OFDM-007LTE';
PrototypeFilter{4} = '';
% Load Results and find optimum (using interpolation to obtain smoother curves)
for i_method = 1:NrMethods
for i_velocity = 1:length(M_Velocity_kmh)
Velocity_kmh = M_Velocity_kmh(i_velocity);
FileName = ['.\Results\' Method{i_method} '_' PrototypeFilter{i_method} '_' PowerDelayProfile int2str(Velocity_kmh) '.mat'];
L1 = load(FileName);
% Needed for interpolation: remove double subcarriers
IndexSameSubcarrierSpacing = find(diff(L1.M_RealSubcarrierSpacing)==0);
L1.M_RealSubcarrierSpacing(IndexSameSubcarrierSpacing) = [];
L1.SIR_Theory(IndexSameSubcarrierSpacing) = [];
% Interpolate to get smoother curves
M_SIR_Interpolated(:,i_velocity) = interp1(L1.M_RealSubcarrierSpacing,L1.SIR_Theory,M_SubcarrierSpacingInterpolated,'spline',nan);
if strcmp(Method{i_method},'CP-OFDM-007LTE') % To check if theoretical equations are correct (interpolation is wrong in case of CP-OFDM!)
M_SIR007_Interpolated_True(:,i_velocity) = L1.SIR_Theory;
end
end
M_SIR_Interpolated_ALL(:,:,i_method) = M_SIR_Interpolated;
[SIRoptimal,IndexSIRoptimal] = max(M_SIR_Interpolated);
SubcarrierSpacingOptimal = M_SubcarrierSpacingInterpolated(IndexSIRoptimal);
M_SIR_100kHZ(:,i_method) = M_SIR_Interpolated(M_SubcarrierSpacingInterpolated==100e3,:);
M_SIRoptimal(:,i_method) = SIRoptimal.';
M_SubcarrierSpacingOptimal(:,i_method) = SubcarrierSpacingOptimal.';
end
M_SIR_100kHZ(:,4)=nan; % Values are wrong for CP-OFDM due to discontinuity
M_SIRoptimal(:,4)=nan;
M_SubcarrierSpacingOptimal(:,4)=nan;
% Calculate Theoretical SIR for OFDM (no ISI)
Kappa = 1/14; % LTE efficiency loss
TCP = 289e-9; % maximum delay
F = Kappa/TCP; %optimal subcarrier spacing (no ISI)
M_DopplerShift = M_Velocity_kmh/3.6*60e9/2.998e8;
P_S_CPOFDM = hypergeom([1/2],[3/2 2],-(M_DopplerShift/F*pi).^2);
P_I_CPOFDM = 1-P_S_CPOFDM;
SIR_CPOFDM = 10*log10(P_S_CPOFDM./P_I_CPOFDM);
figure(31);
plot(M_Velocity_kmh,M_SIRoptimal(:,1),':','color', [0.5 0.5 0]);
hold on;
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,1)>100e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,1)>100e3,1),'color', [0.5 0.5 0]);
maxTemp = max(M_SIR007_Interpolated_True);
plot(M_Velocity_kmh(maxTemp>SIR_CPOFDM),maxTemp(maxTemp>SIR_CPOFDM),'black');
plot(M_Velocity_kmh,SIR_CPOFDM,'red');
plot(M_Velocity_kmh,M_SIRoptimal(:,2),': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>100e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,2)>100e3,2),'blue');
plot(M_Velocity_kmh,M_SIRoptimal(:,3),':','color',ColorFBMC);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>100e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,3)>100e3,3),'color',ColorFBMC);
xlabel('Velocity [km/h]');
ylabel('Signal-to-Interference Ratio [dB]');
ylim([0 50]);
p1 = plot(nan,nan,': black');
p2 = plot(nan,nan,'black');
legend([p1 p2],{'Subcarrier Spacing, F=100kHz','Subcarrier Spacing, F>100kHz'},'Location','SouthWest');
if PlotAddionalResults
% Optimal subcarrier spacing according to the rule of thumb
RMS_Doppler = 1/sqrt(2)*M_DopplerShift;
RMS_Tau = 30e-9; % we have 44ns and not 46ns due to sampling
ApproxOptimalSubcarrierSpacing_PHYDYAS = sqrt(0.2745/0.328*RMS_Doppler/RMS_Tau);
ApproxOptimalSubcarrierSpacing_Hermite = sqrt(0.2015/0.403*RMS_Doppler/RMS_Tau);
figure(32);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,1)>100e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,1)>100e3,1)/1e3,'red');
hold on;
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>100e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,2)>100e3,2)/1e3,'blue');
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_Hermite/1e3,': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>100e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,3)>100e3,3)/1e3,'color',ColorFBMC);
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_PHYDYAS/1e3,':','color',ColorFBMC);
xlabel('Velocity [km/h], f_c=2.5GHz');
ylabel('Optimal Subcarrier Spacing [kHz]');
title('TDL-A');
p1 = plot(nan,nan,'black');
p2 = plot(nan,nan,': black');
legend([p1 p2],{'Exhaustive search','Approximation'},'Location','NorthWest');
% SIR for approximate optimal subcarrier spacing
rep1 = length(ApproxOptimalSubcarrierSpacing_PHYDYAS);
rep2 = length(M_SubcarrierSpacingInterpolated);
[~,index_PHYDYAS] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_PHYDYAS,[rep2,1])),[],1);
[~,index_Hermite] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_Hermite,[rep2,1])),[],1);
M_SIR_Interploated_PHYDYAS = M_SIR_Interpolated_ALL(:,:,3);
M_SIR_Interploated_Hermite = M_SIR_Interpolated_ALL(:,:,2);
for i_velocity = 1:length(M_Velocity_kmh)
M_SIR_ApproxOpt_PHYDYAS(i_velocity) = M_SIR_Interploated_PHYDYAS(index_PHYDYAS(i_velocity),i_velocity);
M_SIR_ApproxOpt_Hermite(i_velocity) = M_SIR_Interploated_Hermite(index_Hermite(i_velocity),i_velocity);
end
figure(33);plot(M_SIRoptimal(:,3)-M_SIR_ApproxOpt_PHYDYAS.');
hold on;
plot(M_SIRoptimal(:,2)-M_SIR_ApproxOpt_Hermite.');
xlabel('Velocity [km/h], f_c=60GHz$');
ylabel('SIR Error in dB!!! between approx. and exhaustive search');
title('TDL-A');
% SIR of theory vs simulations
% plot(M_Velocity_kmh,[max(M_SIR007_Interpolated_True,[],1).' SIR_CPOFDM.']);
end
%% Plot TDL-B_900ns A
clear M_SIR_ApproxOpt_Hermite M_SIR_Interpolated_ALL M_SIRoptimal M_SIR_Interpolated M_SIR_100kHZ M_SubcarrierSpacingOptimal M_SIR007_Interpolated_True;
M_Velocity_kmh = [0:10:500];
M_SubcarrierSpacingInterpolated = 1e3*[100:1:1000];
NrMethods = 4;
PowerDelayProfile = 'TDL-B_900ns';
Method{1} = 'CP-OFDM';
PrototypeFilter{1} = '';
Method{2} = 'FBMC-QAM';
PrototypeFilter{2} = 'Hermite';
Method{3} = 'FBMC-QAM';
PrototypeFilter{3} = 'PHYDYAS';
Method{4} = 'FBMC-OQAM';
PrototypeFilter{4} = 'Hermite';
% Load Results and find optimum (using interpolation to obtain smoother curves)
for i_method = 1:NrMethods
for i_velocity = 1:length(M_Velocity_kmh)
Velocity_kmh = M_Velocity_kmh(i_velocity);
FileName = ['.\Results\' Method{i_method} '_' PrototypeFilter{i_method} '_' PowerDelayProfile int2str(Velocity_kmh) '.mat'];
L1 = load(FileName);
% Needed for interpolation: remove double subcarriers
IndexSameSubcarrierSpacing = find(diff(L1.M_RealSubcarrierSpacing)==0);
L1.M_RealSubcarrierSpacing(IndexSameSubcarrierSpacing) = [];
L1.SIR_Theory(IndexSameSubcarrierSpacing) = [];
% Interpolate to get smoother curves
M_SIR_Interpolated(:,i_velocity) = interp1(L1.M_RealSubcarrierSpacing,L1.SIR_Theory,M_SubcarrierSpacingInterpolated,'spline',nan);
if strcmp(Method{i_method},'CP-OFDM') % To check if theoretical equations are correct (interpolation is wrong in case of CP-OFDM!)
M_SIR2_Interpolated_True(:,i_velocity) = L1.SIR_Theory;
end
end
M_SIR_Interpolated_ALL(:,:,i_method) = M_SIR_Interpolated;
[SIRoptimal,IndexSIRoptimal] = max(M_SIR_Interpolated);
SubcarrierSpacingOptimal = M_SubcarrierSpacingInterpolated(IndexSIRoptimal);
M_SIR_100kHZ(:,i_method) = M_SIR_Interpolated(M_SubcarrierSpacingInterpolated==100e3,:);
M_SIRoptimal(:,i_method) = SIRoptimal.';
M_SubcarrierSpacingOptimal(:,i_method) = SubcarrierSpacingOptimal.';
end
M_SIR_100kHZ(:,1)=nan; % Values are wrong for CP-OFDM due to discontinuity
M_SIRoptimal(:,1)=nan;
M_SubcarrierSpacingOptimal(:,1)=nan;
% Calculate Theoretical SIR for OFDM (no ISI)
Kappa = 1; % LTE efficiency loss
TCP = 4305e-9; % maximum delay
F = Kappa/TCP; %optimal subcarrier spacing (no ISI)
M_DopplerShift = M_Velocity_kmh/3.6*60e9/2.998e8;
P_S_CPOFDM = hypergeom([1/2],[3/2 2],-(M_DopplerShift/F*pi).^2);
P_I_CPOFDM = 1-P_S_CPOFDM;
SIR_CPOFDM = 10*log10(P_S_CPOFDM./P_I_CPOFDM);
figure(41);
maxTemp = max(M_SIR2_Interpolated_True);
plot(M_Velocity_kmh(maxTemp>SIR_CPOFDM),maxTemp(maxTemp>SIR_CPOFDM),'black');
hold on;
plot(M_Velocity_kmh,SIR_CPOFDM,'red');
plot(M_Velocity_kmh,M_SIRoptimal(:,2),': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>100e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,2)>100e3,2),'blue');
plot(M_Velocity_kmh,M_SIRoptimal(:,3),':','color',ColorFBMC);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>100e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,3)>100e3,3),'color',ColorFBMC);
plot(M_Velocity_kmh,M_SIRoptimal(:,4),': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,4)>100e3),M_SIRoptimal(M_SubcarrierSpacingOptimal(:,4)>100e3,4),'blue');
xlabel('Velocity [km/h]');
ylabel('Signal-to-Interference Ratio [dB]');
ylim([0 50]);
p1 = plot(nan,nan,': black');
p2 = plot(nan,nan,'black');
legend([p1 p2],{'Subcarrier Spacing, F=100kHz','Subcarrier Spacing, F>100kHz'},'Location','SouthWest');
if PlotAddionalResults
% Optimal subcarrier spacing according to the rule of thumb
RMS_Doppler = 1/sqrt(2)*M_DopplerShift;
RMS_Tau = 900e-9; % we have 44ns and not 46ns due to sampling
ApproxOptimalSubcarrierSpacing_Hermite = sqrt(0.2015/0.403*RMS_Doppler/RMS_Tau);
ApproxOptimalSubcarrierSpacing_PHYDYAS_TF2 = sqrt(0.2745/0.328*RMS_Doppler/RMS_Tau*2); % in FBMC-QAM we have F=2/T_0 => compared to OQAM (F=1/T_0) we need an additional factor of two
ApproxOptimalSubcarrierSpacing_Hermite_TF2 = sqrt(0.2015/0.403*RMS_Doppler/RMS_Tau*2); % in FBMC-QAM we have F=2/T_0 => compared to OQAM (F=1/T_0) we need an additional factor of two
figure(42);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,2)>100e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,2)>100e3,2)/1e3,'blue');
hold on;
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_Hermite_TF2/1e3,': blue');
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,3)>100e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,3)>100e3,3)/1e3,'color',ColorFBMC);
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_PHYDYAS_TF2/1e3,':','color',ColorFBMC);
plot(M_Velocity_kmh(M_SubcarrierSpacingOptimal(:,4)>100e3),M_SubcarrierSpacingOptimal(M_SubcarrierSpacingOptimal(:,4)>100e3,4)/1e3,'blue');
plot(M_Velocity_kmh,ApproxOptimalSubcarrierSpacing_Hermite/1e3,':','color',ColorFBMC);
xlabel('Velocity [km/h], f_c=2.5GHz');
ylabel('Optimal Subcarrier Spacing [kHz]');
title('TDL-B 900ns');
p1 = plot(nan,nan,'black');
p2 = plot(nan,nan,': black');
legend([p1 p2],{'Exhaustive search','Approximation'},'Location','NorthWest');
% SIR for approximate optimal subcarrier spacing
rep1 = length(ApproxOptimalSubcarrierSpacing_PHYDYAS_TF2);
rep2 = length(M_SubcarrierSpacingInterpolated);
[~,index_PHYDYAS_TF2] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_PHYDYAS_TF2,[rep2,1])),[],1);
[~,index_Hermite_TF2] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_Hermite_TF2,[rep2,1])),[],1);
[~,index_Hermite] = min(abs(repmat(M_SubcarrierSpacingInterpolated.',[1 rep1])-repmat(ApproxOptimalSubcarrierSpacing_Hermite,[rep2,1])),[],1);
M_SIR_Interploated_PHYDYAS_TF2 = M_SIR_Interpolated_ALL(:,:,3);
M_SIR_Interploated_Hermite_TF2 = M_SIR_Interpolated_ALL(:,:,2);
M_SIR_Interploated_Hermite = M_SIR_Interpolated_ALL(:,:,4);
for i_velocity = 1:length(M_Velocity_kmh)
M_SIR_ApproxOpt_PHYDYAS_TF2(i_velocity) = M_SIR_Interploated_PHYDYAS_TF2(index_PHYDYAS_TF2(i_velocity),i_velocity);
M_SIR_ApproxOpt_Hermite_TF2(i_velocity) = M_SIR_Interploated_Hermite_TF2(index_Hermite_TF2(i_velocity),i_velocity);
M_SIR_ApproxOpt_Hermite(i_velocity) = M_SIR_Interploated_Hermite(index_Hermite(i_velocity),i_velocity);
end
figure(43);plot(M_SIRoptimal(:,3)-M_SIR_ApproxOpt_PHYDYAS_TF2.');
hold on;
plot(M_SIRoptimal(:,2)-M_SIR_ApproxOpt_Hermite_TF2.');
plot(M_SIRoptimal(:,4)-M_SIR_ApproxOpt_Hermite.');
xlabel('Velocity [km/h], f_c=60GHz');
ylabel('SIR Error in dB!!! between approx. and exhaustive search');
title('TDL-B 900ns');
% SIR of theory vs simulations
% plot(M_Velocity_kmh,[max(M_SIR2_Interpolated_True,[],1).' SIR_CPOFDM.']);
end