3D pattern plotting function seems to be wrong !

I wrote the following function for plotting 3D pattern of an array with position vectors in a matrix named ``RIS'' and the beamforming weights in W, there seems to be an error which I am unable to locate, any comments ?

function [G] = Full_3D_Pattern (W, RIS)
theta = -pi/2 : pi/2e2 : pi/2; phi = theta; %angle steps of 1 degree for plotting
G = zeros ( length(theta), length(phi) );
A = zeros ( length(W),     length(theta), length(phi) );
for k = 1:length(phi)
    for tta = 1:length(theta)
        ux = cos(phi(k))*sin(theta(tta)); 
        uy = cos(phi(k))*cos(theta(tta)); 
        uz = sin (phi(k));
        u = [ux; uy; uz];
        A (:,tta,k) = exp (-1i*pi*u'*RIS); % RIS steering vector for tta, k
        G (tta,k)   = abs(W' * A (:,tta,k)) * cos(theta(tta))*cos(phi(k)) * 2;
    end
end
figure('Name','3D Pattern')
set(0,'DefaultAxesFontSize',20,'DefaultTextFontSize',20);
mesh(theta,phi,abs(G).^2);xlim([-pi/2 pi/2]);ylim([-pi/2 pi/2]); %%%% radian space
xlabel('Phi','FontSize',22); ylabel('Theta','FontSize',22); colorbar
end

[Adam Drake]

Can you provide RIS and W in a mat file?

[Krishan Kumar Tiwari]

RIS_Full.mat and W.mat are attached.

W.mat I get from the following function for steering at el = -45*pi/180; and az = -pi/3

function [WS] = Steering (RIS, el, az)

Sx = cos(el) * sin(az); Sy = cos(el)*cos(az); Sz = sin(el); %Steering direction co-ordinates

% St = [Sx,Sy,Sz].'; %Steering direction unit vector

St = [Sx; Sy; Sz];

J = sqrt(-1); WS = exp ( -J*pi*(St'*RIS) ); % RIS steering vector for the steering direction S

% A = exp(-J*pi*(r'*P));

end

[Krishan Kumar Tiwari]

Or for simplicity, RIS and W are as in

clear; clc; close all;

NpH = 64; % # of RIS elements per sub-array

NpV = 5;

RIS_X = ( 0 : (NpH-1) ); % X range of RIS co-ordinates

RIS_X = kron ( ones(1,NpV) , RIS_X );

RIS_Z = ( 0 : (NpV-1) );

RIS_Z = kron ( RIS_Z, ones(1,NpH) );

RIS = [ RIS_X ; zeros(1,NpH*NpV) ; RIS_Z ];

% figure()

% plot3 ( RIS(1,:), RIS(2,:), RIS(3,:), '*'); hold on;

el = -45*pi/180;

az = -pi/3;

Sx = cos(el) * sin(az); Sy = cos(el)*cos(az); Sz = sin(el); %Steering direction co-ordinates

St = [Sx; Sy; Sz];

W = exp ( -1i*pi*(St'*RIS) );

Full_3D_Pattern ( ones(320,1).*W.', RIS );

[Star Strider]

The code runs without error. Is there a problem with the result?

LD1 = load('RIS_Full.mat');
RIS = LD1.RIS_Full;

LD2 = load('W.mat');
W = LD2.W;

G = Full_3D_Pattern (W, RIS);

function [G] = Full_3D_Pattern (W, RIS)
theta = -pi/2 : pi/2e2 : pi/2; phi = theta; %angle steps of 1 degree for plotting
G = zeros ( length(theta), length(phi) );
A = zeros ( length(W),     length(theta), length(phi) );
for k = 1:length(phi)
    for tta = 1:length(theta)
        ux = cos(phi(k))*sin(theta(tta)); 
        uy = cos(phi(k))*cos(theta(tta)); 
        uz = sin (phi(k));
        u = [ux; uy; uz];
        A (:,tta,k) = exp (-1i*pi*u'*RIS); % RIS steering vector for tta, k
        G (tta,k)   = abs(W' * A (:,tta,k)) * cos(theta(tta))*cos(phi(k)) * 2;
    end
end
figure('Name','3D Pattern')
set(0,'DefaultAxesFontSize',20,'DefaultTextFontSize',20);
mesh(theta,phi,abs(G).^2);xlim([-pi/2 pi/2]);ylim([-pi/2 pi/2]); %%%% radian space
xlabel('Phi','FontSize',22); ylabel('Theta','FontSize',22); colorbar
end

.

[Krishan Kumar Tiwari]

Yes, there is a problem, if you give el = az = 0, then you get a fan / blade beam, when you steer it, it gets curved -- just steering causes the curvature -- it should not !!

[Krishan Kumar Tiwari]

For el = az = 0, use W = ones (320,1), sorry i should have written it earlier .