I want to implement the MUSIC algorithm in MATLAB.
close all; clear all; clc;
% ======= (1) TRANSMITTED SIGNALS ======= %
% Signal source directions
az = [35;39;127]; % Azimuths
el = zeros(size(az)); % Simple example: assume elevations zero
M = length(az); % Number of sources
% Transmitted signals
L = 200; % Number of data snapshots recorded by receiver
m = randn(M,L); % Example: normally distributed 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;
My previous post provides a basic implementation of the MUSIC algorithm. What do you need to know more specifically?
If you want my help, please write whole words; "u" and "plz" are not words.
Refer Array signal processing by Neilson
To construct E(FF*) do u have the signal without noise i mean(F),go for E(XX*). music and espirit of DOA estimation methods coming under subspace methods.
Try understanding subspace methods and orthogonality concepts.
I will try to help with the matlab code for music
Weetabixharry i need your help in implementating MUSIC direction finding algorithm in matlab.
"Weetabixharry as this is the basic 1D code, i need your help for implementing the standard MUSIC codePlease look at my Matlab code above and then let me know if you have any specific questions.
"Weetabixharry as this is the basic 1D code, i need your help for implementing the standard MUSIC code
Regards"
Thank for sharing this piece of code. What if M is not known or set to wrong number? For example, we have 3 real signals, but search for M=10.
I have worked many years with LabVIEW
Can you help me with Matlab code?
So, we don't need to change the code much. The most important thing is that we cannot use a linear array to estimate elevation; we must have a 2D or 3D array (this is obvious if you think about the rotational symmetry of a linear array). Therefore, I changed the array to a uniform circular array.I want to estimate Azimuth and elevation. Please, modify the code for me.
Code Matlab M - [expand] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 close all; clear all; clc; % ======= (1) TRANSMITTED SIGNALS ======= % % Signal source directions az = [35;39;127]; % Azimuths el = [63;14;57]; % Elevations M = length(az); % Number of sources % Transmitted signals L = 200; % Number of data snapshots recorded by receiver m = randn(M,L); % Example: normally distributed random signals % ========= (2) RECEIVED SIGNAL ========= % % Wavenumber vectors (in units of wavelength/2) k = pi*[cosd(az).*cosd(el), sind(az).*cosd(el), sind(el)].'; % Number of antennas N = 10; % Array geometry [rx,ry,rz] (example: uniform circular array) radius = 0.5/sind(180/N); rx = radius*cosd(360*(0:N-1).'/N); ry = radius*sind(360*(0:N-1).'/N); r = [rx, ry, zeros(N,1)]; % 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 = (0:1:90); % Elevation values to search % 2D MUSIC spectrum Z = zeros(length(AzSearch),length(ElSearch)); for i = 1:length(ElSearch) % Elevation search value el = ElSearch(i); % Points on azimuth array manifold curve to search (for this el) kSearch = pi*[cosd(AzSearch)*cosd(el), ... sind(AzSearch)*cosd(el), ... ones(size(AzSearch))*sind(el)].'; ASearch = exp(-1j*r*kSearch); % Compute azimuth spectrum for this elevation Z(:,i) = sum(abs(ASearch'*En).^2,2); end % Plot figure(); surf(AzSearch, ElSearch, -10*log10(Z.'/N)); shading interp; title('2D MUSIC Example'); xlabel('Azimuth (degrees)'); ylabel('Elevation (degrees)'); zlabel('MUSIC spectrum (dB)'); grid on; axis tight;
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