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Fig9.m
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% This Matlab script generates Figure 9 in the paper:
%
% Özlem Tugfe Demir and Emil Björnson,
% "Is Channel Estimation Necessary to Select Phase-Shifts for
% RIS-Assisted Massive MIMO?,"
% IEEE Transactions on Wireless Communications, vol. 21, no. 11, November
% 2022.
%
% This is version 1.0 (Last edited: 2023-08-23)
%
% License: This code is licensed under the GPLv2 license. If you in any way
% use this code for research that results in publications, please cite our
% paper as described above.
for scenario = 1:2
%Number of RISs
L = 2;
%Number of vertical and horizontal RIS units per RIS
NVer = 16;
NHor = 16;
PorVer = 4;
PorHor = 4;
NVerUE = 16;
NHorUE = 16;
%Number of UEs
K = 8;
%Number of BS antennas
M = 100;
%Select the number of setups with random UE locations
nbrOfSetups = 600;
%Number of channel realizations per setup
nbrOfRealizations = 1000;
%Total uplink pilot transmit power per UE (W)
etaa = 0.1;
%Communication bandwidth
B = 1e6;
%Noise figure (in dB)
noiseFigure = 7;
%Compute noise power
noiseVariancedBm = -174 + 10*log10(B) + noiseFigure;
%Noise power (dB)
noiseVariancedB = noiseVariancedBm-30;
%Select length of coherence block
tau_c = 10000;
%Angular standard deviation per path in the local scattering model (in degrees)
ASDazimDeg = 15;
ASDelevDeg = 15;
%Number of specular components with LOS component, h, G, f
SpecNum_h = 5;
SpecNum_G = 5;
SpecNum_f = 5;
%Power ratio of LOS to other specular components
LOStoSpecPow_h = 0.5;
LOStoSpecPow_G = 0.5;
LOStoSpecPow_f = 0.5;
%Direct link loss (dB)
DirectLoss = 0;
%Total pilot length for RIS
tau_p_RIS = (L*PorHor*PorVer+1)*K;
tau_coef = (L*PorHor*PorVer+1);
tau_p_RIS2 = tau_coef*K;
%Total pilot length for conventional operation without RIS
tau_coef_Conv = 28;
tau_p_Conv = tau_coef_Conv*K;
%Prelog factor for RIS
prelogFactor_RIS1 = (tau_c - tau_p_RIS)/tau_c;
prelogFactor_RIS2 = (tau_c - tau_p_RIS2)/tau_c;
prelogFactor_RIS3 = (tau_c - tau_p_RIS - tau_p_RIS2)/tau_c;
%Prelog factor for conventional operation without RIS
prelogFactor_Conv = (tau_c - tau_p_Conv)/tau_c;
SE_RIS_MR1 = zeros(K,nbrOfSetups,5);
SE_RIS_MR2b = zeros(K,nbrOfSetups,5);
SE_Conv_MR = zeros(K,nbrOfSetups);
SE_RIS_RZF1 = zeros(K,nbrOfSetups,5);
SE_RIS_RZF2b = zeros(K,nbrOfSetups,5);
SE_Conv_RZF = zeros(K,nbrOfSetups);
SE_RIS_AMMSE1 = zeros(K,nbrOfSetups,5);
SE_RIS_AMMSE2b = zeros(K,nbrOfSetups,5);
SE_Conv_AMMSE = zeros(K,nbrOfSetups);
SE_RIS_MR_maxmin1 = zeros(K,nbrOfSetups,5);
SE_RIS_MR_maxmin2b = zeros(K,nbrOfSetups,5);
SE_Conv_MR_maxmin = zeros(K,nbrOfSetups);
SE_RIS_RZF_maxmin1 = zeros(K,nbrOfSetups,5);
SE_RIS_RZF_maxmin2b = zeros(K,nbrOfSetups,5);
SE_Conv_RZF_maxmin = zeros(K,nbrOfSetups);
SE_RIS_AMMSE_maxmin1 = zeros(K,nbrOfSetups,5);
SE_RIS_AMMSE_maxmin2b = zeros(K,nbrOfSetups,5);
SE_Conv_AMMSE_maxmin = zeros(K,nbrOfSetups);
%%%%%%%%%%%%%%%%
RISpositions = zeros(L,1);
RISpositions(1) = 200+50*1i;
RISpositions(2) = 200-50*1i;
%Base UE distance to BS
BaseDistHor = 200;
%UE dropping area
AreaHorSize = 100;
AreaVerSize = 100;
%LOS probability (it is 0.5 if it will be determined by the formula)
probLOSbinary_f = 0.5;
probLOSbinary_h = 0.5;
%Rician factor loss for RIS-UE channels compared to the original formula
%(dB)
if scenario == 1
ricianFactorLoss_f = 0;
else
ricianFactorLoss_f = 9;
end
%Azimuth and elevation angle deviations for the specular components
%(radians)
AzimSpecDev = 60/180*pi;
ElevSpecDev = 15/180*pi;
%% Go through all setups
for setupp = 1:nbrOfSetups
disp(setupp)
%Power distribution among specular components other than LOS
PowDistSpec_h = rand(SpecNum_h-1,K);
PowDistSpec_f = rand(SpecNum_f-1,K,L);
PowDistSpec_G = rand(SpecNum_G-1,L);
%R and HMean is normalized
[Rh,HBar,Rf,fBar,RG_BS,RG_RIS,GBar,...
channelGaindB_h,channelGaindB_f,channelGaindB_G,...
probLOS_h,probLOS_f,ricianFactor_h,ricianFactor_f,ricianFactor_G,...
Rf_b,fBar_b,RG_RIS_b,GBar_b,...
channelGaindB_f_b,channelGaindB_G_b] =...
function_Setup_specular(L,K,M,NHor,NVer,ASDazimDeg,ASDelevDeg,...
SpecNum_h,SpecNum_G,SpecNum_f,DirectLoss,RISpositions,BaseDistHor,AreaHorSize,AreaVerSize,...
probLOSbinary_h,probLOSbinary_f,ricianFactorLoss_f,AzimSpecDev,ElevSpecDev);
channelGaindB_h = channelGaindB_h - noiseVariancedB;
channelGaindB_f = channelGaindB_f - noiseVariancedB;
channelGaindB_f_b = channelGaindB_f_b - noiseVariancedB;
poww = etaa*ones(K,1);
RISassignments = functionRISassignment(channelGaindB_h,channelGaindB_f,channelGaindB_G,...
L,K,NVer,NHor,NVerUE,NHorUE);
[Rh2,HBar2,H,Hhat_Conv,bb1,bHat1,Ctilde1,bb2,bHat2,Ctilde2,bb3,bHat3,Ctilde3,...
bb4,bHat4,Ctilde4,bb5,bHat5,Ctilde5] = ...
functionChannelEstimationRIS_individual(Rh,HBar,Rf,fBar,RG_BS,RG_RIS,GBar,...
channelGaindB_h,channelGaindB_f,channelGaindB_G,...
probLOS_h,probLOS_f,ricianFactor_h,ricianFactor_f,ricianFactor_G,...
nbrOfRealizations,L,K,M,etaa,NVer,NHor,NVerUE,NHorUE,RISassignments,tau_p_Conv,PorVer,PorHor,...
SpecNum_h,SpecNum_G,SpecNum_f,LOStoSpecPow_h,LOStoSpecPow_G,LOStoSpecPow_f,...
PowDistSpec_h,PowDistSpec_f,PowDistSpec_G);
[SE_MR0, SE_RZF0, SE_AMMSE0, SE_MR_maxmin0, SE_RZF_maxmin0, SE_AMMSE_maxmin0 ] = ...
functionComputeSEConv(Rh2,HBar2,H,Hhat_Conv,K,M,tau_p_Conv,etaa,nbrOfRealizations,poww,SpecNum_h);
SE_Conv_MR(:,setupp) = prelogFactor_Conv*SE_MR0;
SE_Conv_RZF(:,setupp) = prelogFactor_Conv*SE_RZF0;
SE_Conv_AMMSE(:,setupp) = prelogFactor_Conv*SE_AMMSE0;
SE_Conv_MR_maxmin(:,setupp) = prelogFactor_Conv*SE_MR_maxmin0;
SE_Conv_RZF_maxmin(:,setupp) = prelogFactor_Conv*SE_RZF_maxmin0;
SE_Conv_AMMSE_maxmin(:,setupp) = prelogFactor_Conv*SE_AMMSE_maxmin0;
[SE_MR1, SE_RZF1, SE_AMMSE1, SE_MR_maxmin1, SE_RZF_maxmin1, SE_AMMSE_maxmin1 ] = functionComputeSERIS(bb1,bHat1,Ctilde1,K,M,nbrOfRealizations,poww,etaa);
SE_RIS_MR1(:,setupp,1) = prelogFactor_RIS1*SE_MR1;
SE_RIS_RZF1(:,setupp,1) = prelogFactor_RIS1*SE_RZF1;
SE_RIS_AMMSE1(:,setupp,1) = prelogFactor_RIS1*SE_AMMSE1;
SE_RIS_MR_maxmin1(:,setupp,1) = prelogFactor_RIS1*SE_MR_maxmin1;
SE_RIS_RZF_maxmin1(:,setupp,1) = prelogFactor_RIS1*SE_RZF_maxmin1;
SE_RIS_AMMSE_maxmin1(:,setupp,1) = prelogFactor_RIS1*SE_AMMSE_maxmin1;
%%%%%%%%%%%%%%%
[bb1,bHat1,Ctilde1,bb2,bHat2,Ctilde2,bb3,bHat3,Ctilde3,...
bb4,bHat4,Ctilde4,bb5,bHat5,Ctilde5] = ...
functionChannelEstimationRIS_cascadedDominant(Rh,HBar,Rf,fBar,RG_BS,RG_RIS,GBar,...
channelGaindB_h,channelGaindB_f,channelGaindB_G,...
probLOS_h,probLOS_f,ricianFactor_h,ricianFactor_f,ricianFactor_G,...
nbrOfRealizations,L,K,M,etaa,NVer,NHor,NVerUE,NHorUE,RISassignments,tau_p_RIS2,...
SpecNum_h,SpecNum_G,SpecNum_f,LOStoSpecPow_h,LOStoSpecPow_G,LOStoSpecPow_f,...
PowDistSpec_h,PowDistSpec_f,PowDistSpec_G);
[SE_MR2, SE_RZF2, SE_AMMSE2, SE_MR_maxmin2, SE_RZF_maxmin2, SE_AMMSE_maxmin2 ] = functionComputeSERIS(bb1,bHat1,Ctilde1,K,M,nbrOfRealizations,poww,etaa);
SE_RIS_MR2b(:,setupp,1) = prelogFactor_RIS2*SE_MR2;
SE_RIS_RZF2b(:,setupp,1) = prelogFactor_RIS2*SE_RZF2;
SE_RIS_AMMSE2b(:,setupp,1) = prelogFactor_RIS2*SE_AMMSE2;
SE_RIS_MR_maxmin2b(:,setupp,1) = prelogFactor_RIS2*SE_MR_maxmin2;
SE_RIS_RZF_maxmin2b(:,setupp,1) = prelogFactor_RIS2*SE_RZF_maxmin2;
SE_RIS_AMMSE_maxmin2b(:,setupp,1) = prelogFactor_RIS2*SE_AMMSE_maxmin2;
%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%
end
if scenario==1
ConvA = vec(SE_Conv_RZF_maxmin);
RIS1A = vec(SE_RIS_RZF_maxmin1(:,:,1));
RIS2bA = vec(SE_RIS_RZF_maxmin2b(:,:,1));
else
ConvB = vec(SE_Conv_RZF_maxmin);
RIS1B = vec(SE_RIS_RZF_maxmin1(:,:,1));
RIS2bB = vec(SE_RIS_RZF_maxmin2b(:,:,1));
end
end
%% Figure 9
nbrOfPoints = length(ConvA);
figure;
hold on; box on; grid on;
set(gca,'fontsize',16);
ppp1 = plot(sort(ConvA),linspace(0,1,nbrOfPoints),'k:','LineWidth',2);
ppp2 = plot(sort(RIS1A),linspace(0,1,nbrOfPoints),'k:o','LineWidth',2);
ppp3 = plot(sort(RIS2bA),linspace(0,1,nbrOfPoints),'k-','LineWidth',2);
ppp5 = plot(sort(RIS1B),linspace(0,1,nbrOfPoints),'b:o','LineWidth',3);
ppp6 = plot(sort(RIS2bB),linspace(0,1,nbrOfPoints),'b-','LineWidth',3);
ppp2.MarkerSize = 6;
ppp2.MarkerIndices = 1:ceil(nbrOfPoints/7):nbrOfPoints;
ppp5.MarkerSize = 6;
ppp5.MarkerIndices = 1:ceil(nbrOfPoints/7):nbrOfPoints;
xlabel('SE per UE [b/s/Hz]','Interpreter','Latex');
ylabel('CDF','Interpreter','Latex');
legend({'Conv-mMIMO', 'RIS-mMIMO, Short-Term', 'RIS-mMIMO, Long-Term', 'RIS-mMIMO, Short-Term, reduced $\mathcal{K}$', 'RIS-mMIMO, Long-Term, reduced $\mathcal{K}$' },'Interpreter','Latex','Location','SouthEast');
xlim([0 6]);