RIS_Models/ArrayAliasing.m at main · mitiebin/RIS_Models · GitHub

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clear all;close all;clc;

%%
C = -2;

lambda = 1;

dList = [0.2, 0.5, 0.7];

r_s = 100;

%%
a = 0.1;
b = 0.1;

%%
% anglesIncident = [30, 70]/180*pi;
anglesIncident = [30]/180*pi;
amplitudeIncident = [1, 1, 0.5];

anglesSteer = -50/180*pi;


%%
numUnits = 100;

%% for computation
deltaThetaComp = 0.1;

thetaDegComp = -90:deltaThetaComp:90;
thetaComp = thetaDegComp/180*pi;

%% for plotting
deltaThetaPlot = 0.01;

thetaDegPlot = -90:deltaThetaPlot:90;
thetaPlot = thetaDegPlot/180*pi;

%%
E_ScatteredPlot = zeros(length(thetaDegPlot),length(dList));

%%
for iTest = 1:1:length(dList)
    d = dList(iTest);

    unitsPos = (0:1:numUnits-1)*d;

    %%
    SteeringVectorComp = exp(1i*2*pi.*sin(thetaComp)*d);

    SteeringMatrixIncComp = fliplr(vander(SteeringVectorComp)).';
    SteeringMatrixIncComp = SteeringMatrixIncComp(1:numUnits,:);

    SteeringMatrixDepComp = fliplr(vander(SteeringVectorComp));
    SteeringMatrixDepComp = SteeringMatrixDepComp(:,1:numUnits);

    %%
    E_IncidentComp = zeros(length(thetaComp),1);

    for iAngle = 1:1:length(anglesIncident)
        currentAngle = anglesIncident(iAngle);
        E_IncidentComp(find(thetaComp >= currentAngle, 1, 'first')) = amplitudeIncident(iAngle);
    end

    %%
    w = a*b*exp(-1i*2*pi.*sin(anglesIncident(1)).*unitsPos).*exp(-1i*2*pi.*sin(anglesSteer)*unitsPos);

    %%
    E_ScatteredComp = C/lambda*exp(-1i*2*pi*r_s)/r_s*SteeringMatrixDepComp*diag(w)*SteeringMatrixIncComp*E_IncidentComp;

    %%
    SteeringVectorPlot = exp(1i*2*pi.*sin(thetaPlot)*d);

    SteeringMatrixIncPlot = fliplr(vander(SteeringVectorPlot)).';
    SteeringMatrixIncPlot = SteeringMatrixIncPlot(1:numUnits,:);

    SteeringMatrixDepPlot = fliplr(vander(SteeringVectorPlot));
    SteeringMatrixDepPlot = SteeringMatrixDepPlot(:,1:numUnits);

    %%
    E_IncidentPlot = zeros(length(thetaPlot),1);

    for iAngle = 1:1:length(anglesIncident)
        currentAngle = anglesIncident(iAngle);
        E_IncidentPlot(find(thetaPlot >= currentAngle, 1, 'first')) = amplitudeIncident(iAngle);
    end

    E_ScatteredPlot(:,iTest) = C/lambda*exp(-1i*2*pi*r_s)/r_s*SteeringMatrixDepPlot*diag(w)*SteeringMatrixIncPlot*E_IncidentPlot;
end

%%
figure
yyaxis right
plot(thetaDegPlot, E_IncidentPlot)
% ylim([0, 1.6])
ylabel('$E^i(\theta)$','interpreter','latex')

yyaxis left
plot(thetaDegPlot, abs(E_ScatteredPlot(:,1)))
ylabel('$| E^s(r^s, \theta) |$','interpreter','latex')

xlabel('$\theta$','interpreter','latex')
% ylabel('$E^s$','interpreter','latex')
leg1 = legend('Incident', 'Scattered');
set(leg1,'Interpreter','latex');
xlim([-90, 90])
% ylim([0, max(abs(E_ScatteredPlot(:,1)))])

box on
grid on


figure
plot(thetaDegPlot, E_IncidentPlot)
hold on
plot(thetaDegPlot, abs(E_ScatteredPlot(:,2)))
xlabel('$\theta$','interpreter','latex')
% ylabel('$E^s$','interpreter','latex')
leg1 = legend('Incident', 'Scattered');
set(leg1,'Interpreter','latex');
xlim([-90, 90])
ylim([0, 1.6])
box on
grid on
hold off

figure
plot(thetaDegPlot, E_IncidentPlot)
hold on
plot(thetaDegPlot, abs(E_ScatteredPlot(:,3)))
xlabel('$\theta$','interpreter','latex')
% ylabel('$E^s$','interpreter','latex')
leg1 = legend('Incident', 'Scattered');
set(leg1,'Interpreter','latex');
xlim([-90, 90])
ylim([0, 1.6])
box on
grid on
hold off

%%
axes1 = axes('Parent',figure);

colororder({'r','b'})

yyaxis left
plot(thetaDegPlot, abs(E_ScatteredPlot(:,1)),'LineStyle','-.','Color',[1 0 0])
hold on
% plot(thetaDegPlot, abs(E_ScatteredPlot(:,2)))
plot(thetaDegPlot, abs(E_ScatteredPlot(:,3)),'LineStyle','-','Color',[0.85 0.33 0.1])
hold off
ylabel('$| E^s(r^s, \theta) |$','interpreter','latex')

set(gca,'YColor',[0.85 0.33 0.1])
set(axes1,'GridColor',[0.15 0.15 0.15]);

yyaxis right
plot(thetaDegPlot, E_IncidentPlot)
ylabel('$E^i(\theta)$','interpreter','latex')

xlabel('$\theta$','interpreter','latex')
% ylabel('$E^s$','interpreter','latex')
leg1 = legend('$d / \lambda = 0.2$', '$d / \lambda = 0.7$', 'Incident', 'interpreter','latex');
set(leg1,'Interpreter','latex');
xlim([-90, 90])

box on
grid on


exportgraphics(gcf, 'ArrayAliasing.pdf');