How can i add Elevation Degree to my Script?

clc
clear all
format long %The data show that as long shaping scientific
doa=[30]/180*pi; %Direction of arrival
phi_1 = [30]/180*pi; %Azimuth Degree
theta_1 = [90]/180*pi; %Elevation Degree

N=200;%Snapshots
w=[pi/4]';%Frequency
M=3;%Number of array elements
P=length(w); %The number of signal

snr=20;%SNA

D=[1; cos(phi_1+pi/4)/sin(theta_1); sin(phi_1+pi/4)/sin(theta_1)]; %Steering vector of Single Crossed-Loop/Monopole

xx=10*rand(1,N)+1i*rand(1,N); %Simulate signal
x=D*xx;
%%
x=x+awgn(x,snr);%Insert Gaussian white noise
R=x*x'; %Data covarivance matrix
[N,V]=eig(R); %Find the eigenvalues and eigenvectors of R
NN=N(:,1:2); %Estimate noise subspace
theta=-180:0.5:180; %Peak search
phi = -180:0.5:180; %Peak Search

for ll=1:length(phi);
    for ii=1:length(theta);
        SS=zeros(1,3);
        for jj = 0:M-1
            if jj == 0
                SS(1+jj) = 1; % Rumus untuk elemen pertama SS
            elseif jj == 1
                SS(1+jj) = cos((phi(ll)/180*pi)+pi/4)/sin(theta_1); % Rumus untuk elemen kedua SS
            elseif jj == 2
                SS(1+jj) = sin((phi(ll)/180*pi)+pi/4)/sin(theta_1); % Rumus untuk elemen ketiga SS
            end
        end        
        PP=SS*NN*NN'*SS';
        Pmusic(ll)=abs(1/ PP);
    end
end

Pmusic=10*log10(Pmusic/max(Pmusic)); %Spatial spectrum function

figure;
plot3(phi,theta,Pmusic,'-k')
xlabel('angle \phi/degree')
ylabel('angle \theta/degree')
zlabel('spectrum function P(\theta) /dB')
title('DOA estimation based on MUSIC algorithm ')
grid on

My Plot Show that the Elevation degree is not same with my theta_1

Answer 1

[Rahul]

Hi Dion,

According to the description given by you, the below modeified code to your original code would give you elevation in your plot.

format long %The data show that as long shaping scientific
doa = [30]/180*pi; %Direction of arrival
phi_1 = [30]/180*pi; %Azimuth Degree
theta_1 = [90]/180*pi; %Elevation Degree
N = 200; %Snapshots
w = [pi/4]'; %Frequency
M = 3; %Number of array elements
P = length(w); %The number of signal

snr = 20; %SNA
D = [1; cos(phi_1+pi/4)/sin(theta_1); sin(phi_1+pi/4)/sin(theta_1)]; %Steering vector of Single Crossed-Loop/Monopole
xx = 10*rand(1,N) + 1i*rand(1,N); %Simulate signal
x = D*xx;

x = x + awgn(x, snr); %Insert Gaussian white noise
R = x*x'; %Data covariance matrix
[N,V] = eig(R); %Find the eigenvalues and eigenvectors of R
NN = N(:,1:2); %Estimate noise subspace

theta = -180:0.5:180; %Azimuth angles
phi = -180:0.5:180; %Elevation angles


Pmusic = zeros(length(phi), length(theta)); %Initialize Pmusic matrix

for ll = 1:length(phi)
    for ii = 1:length(theta)
        SS = zeros(1,3);
        for jj = 0:M-1
            if jj == 0
                SS(1+jj) = 1; % Rumus untuk elemen pertama SS
            elseif jj == 1
                SS(1+jj) = cos((phi(ll)/180*pi)+pi/4)/sin(theta(ii)/180*pi); % Rumus untuk elemen kedua SS
            elseif jj == 2
                SS(1+jj) = sin((phi(ll)/180*pi)+pi/4)/sin(theta(ii)/180*pi); % Rumus untuk elemen ketiga SS
            end
        end        
        PP = SS*NN*NN'*SS';
        Pmusic(ll, ii) = abs(1/PP);
    end
end

Pmusic = 10*log10(Pmusic/max(Pmusic(:))); %Spatial spectrum function

figure;
surf(phi, theta, Pmusic', 'EdgeColor', 'none');
xlabel('angle \phi/degree');
ylabel('angle \theta/degree');
zlabel('spectrum function P(\theta) /dB');
title('DOA estimation based on MUSIC algorithm');

In the modified code, I have added the elevation angles (phi) and modified the loop to iterate over both azimuth (ll) and elevation (ii) angles. The Pmusic matrix is now a 2D matrix to store the spatial spectrum function for each combination of azimuth and elevation angles.

Thanks.

Answer 2

[Gandham Heamanth]

hi dion Akmal please have a look after updating the code:

clc
clear all
format long % The data show that as long shaping scientific
doa = [30]/180*pi; % Direction of arrival
phi_1 = [30]/180*pi; % Azimuth Degree
theta_1 = [90]/180*pi; % Elevation Degree

N = 200; % Snapshots
w = [pi/4]'; % Frequency
M = 3; % Number of array elements
P = length(w); % The number of signals

snr = 20; % SNR

D = [1; cos(phi_1+pi/4)/sin(theta_1); sin(phi_1+pi/4)/sin(theta_1)]; % Steering vector of Single Crossed-Loop/Monopole

xx = 10*rand(1,N)+1i*rand(1,N); % Simulate signal
x = D*xx;

x = x + awgn(x,snr); % Insert Gaussian white noise
R = x*x'; % Data covariance matrix
[N,V] = eig(R); % Find the eigenvalues and eigenvectors of R
NN = N(:,1:2); % Estimate noise subspace
theta_range = -180:0.5:180; % Peak search
phi_range = -180:0.5:180; % Peak search

Pmusic = zeros(length(phi_range), length(theta_range)); % Spatial spectrum function

for ll = 1:length(phi_range)
    for ii = 1:length(theta_range)
        SS = zeros(1,3);
        for jj = 0:M-1
            if jj == 0
                SS(1+jj) = 1; % Rumus untuk elemen pertama SS
            elseif jj == 1
                SS(1+jj) = cos((phi_range(ll)/180*pi)+pi/4)/sin(theta_range(ii)/180*pi); % Rumus untuk elemen kedua SS
            elseif jj == 2
                SS(1+jj) = sin((phi_range(ll)/180*pi)+pi/4)/sin(theta_range(ii)/180*pi); % Rumus untuk elemen ketiga SS
            end
        end        
        PP = SS*NN*NN'*SS';
        Pmusic(ll, ii) = abs(1/PP);
    end
end

Pmusic = 10*log10(Pmusic/max(Pmusic)); % Spatial spectrum function

figure;
plot3(phi_range, theta_range, Pmusic, '-k')
xlabel('angle \phi/degree')
ylabel('angle \theta/degree')
zlabel('spectrum function P(\theta) /dB')
title('DOA estimation based on MUSIC algorithm')
grid on

e code: