Music algorithm for doa estimation

[km99]

Can someone please explain me this matlab code here for angle of arrival estimation in DETAIL.

%CODE FOR MUSIC ALGO FOR DOA
clear all;
close all;
 clc;
% TRANSMITTED SIGNALS %

% Signal source directions
az =[50;70;90] % angles
el = zeros(size(az)); %  
M = length(az); % Number of sources

% Transmitted signals
L = 100; % Number of data snapshos recorded by receiver
rng('default'); %for same random generaor
m = randn(M,L); % normally disributed random signals

    
% ========= (2) RECEIVED SIGNAL ========= %

% Wavenumber vectors (in units of wavelength/2)
k = pi*[cosd(az).*cosd(el), sind(az).*cosd(el), sind(el)].';

% Array geometry [rx,ry,rz]
N = 10; % Number of antennas
r = [(-(N-1)/2:(N-1)/2).',zeros(N,2)]; % Assume uniform linear array

% Matrix of array response vectors
A = exp(-1j*r*k);

% Additive noise
sigma2 = 0.01; % Noise variance
n = sqrt(sigma2)*(randn(N,L) + 1j*randn(N,L))/sqrt(2);

% Received signal
x = A*m + n;

% ========= (3) MUSIC ALGORITHM ========= %

% Sample covariance matrix
Rxx = x*x'/L;

% Eigendecompose
[E,D] = eig(Rxx);
[lambda,idx] = sort(diag(D)); % Vector of sorted eigenvalues
E = E(:,idx); % Sort eigenvalues accordingly
En = E(:,1:end-M); % Noise eigenvectors (ASSUMPTION: M IS KNOWN)

% MUSIC search directions
AzSearch = (0:1:180).'; % Azimuth values to search
ElSearch = zeros(size(AzSearch)); % Simple 1D example

% Corresponding points on array manifold to search
kSearch = pi*[cosd(AzSearch).*cosd(ElSearch), sind(AzSearch).*cosd(ElSearch), sind(ElSearch)].';
ASearch = exp(-1j*r*kSearch);

% MUSIC spectrum
Z = sum(abs(ASearch'*En).^2,2);

% Plot
figure();
plot(AzSearch,10*log10(Z));
title('Simple 1D MUSIC Example');
xlabel('Azimuth (degrees)');
ylabel('MUSIC spectrum (dB)');
grid on; axis tight;

%END OF CODE

Please explain to me all the steps of the code as I am not able to understand it. It will be very helpful for me.
Thank You.

 

[weetabixharry]

This is my code (except you have messed up the formatting at the top). I put a lot of comments in the code, so it should be relatively easy to follow if you are familiar with the MUSIC algorithm. If you are not familiar with the MUSIC algorithm, then these notes will tell you everything you need to know: **broken link removed**.