UPA_codebook_generator_DFT.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Generate DFT codebook.
% Author: Ahmed Alkhateeb
% 2019
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [F_CB,all_beams]=UPA_codebook_generator_DFT(Mx,My,Mz,over_sampling_x,over_sampling_y,over_sampling_z,ant_spacing)
%%%%%%%%
% Function arguments:
% Mx: Number of antenna elements on x-axis
% My: Number of antenna elements on y-axis
% Mz: Number of antenna elements on z-axis
% over_sampling_x: sampling factor along x-axis (default = 1)
% over_sampling_y: sampling factor along y-axis (default = 1)
% over_sampling_z: sampling factor along z-axis (default = 1)
% ant_spacing: antenna spacing (default 0.5, half wave-length)
%
% Added by: Muhammad Alrabeiah, 2022.
%%%%%%%%

kd=2*pi*ant_spacing;
antx_index=0:1:Mx-1;
anty_index=0:1:My-1;
antz_index=0:1:Mz-1;
M=Mx*My*Mz;

% Defining the RF beamforming codebook in the x-direction
codebook_size_x=over_sampling_x*Mx;
codebook_size_y=over_sampling_y*My;
codebook_size_z=over_sampling_z*Mz;


theta_qx=0:2*pi/codebook_size_x:2*pi-1e-6; % quantized beamsteering angles
F_CBx=zeros(Mx,codebook_size_x);
for i=1:1:length(theta_qx)
    F_CBx(:,i)=sqrt(1/Mx)*exp(-1j*antx_index'*theta_qx(i));
end
 
theta_qy=0:2*pi/codebook_size_y:2*pi-1e-6; % quantized beamsteering angles
F_CBy=zeros(My,codebook_size_y);
for i=1:1:length(theta_qy)
    F_CBy(:,i)=sqrt(1/My)*exp(-1j*anty_index'*theta_qy(i));
end
 
theta_qz=0:2*pi/codebook_size_z:2*pi-1e-6; % quantized beamsteering angles
F_CBz=zeros(Mz,codebook_size_z);
for i=1:1:length(theta_qz)
    F_CBz(:,i)=sqrt(1/Mz)*exp(-1j*antz_index'*theta_qz(i));
end

F_CBxy=kron(F_CBy,F_CBx);
F_CB=kron(F_CBz,F_CBxy);

beams_x=1:1:codebook_size_x;
beams_y=1:1:codebook_size_y;
beams_z=1:1:codebook_size_z;


Mxx_Ind=repmat(beams_x,1,codebook_size_y*codebook_size_z)';
Myy_Ind=repmat(reshape(repmat(beams_y,codebook_size_x,1),1,codebook_size_x*codebook_size_y),1,codebook_size_z)';
Mzz_Ind=reshape(repmat(beams_z,codebook_size_x*codebook_size_y,1),1,codebook_size_x*codebook_size_y*codebook_size_z)';

Tx=cat(3,Mxx_Ind',Myy_Ind',Mzz_Ind');
all_beams=reshape(Tx,[],3);
end