+ Post New Thread
Results 1 to 11 of 11
  1. #1
    Full Member level 4
    Points: 2,621, Level: 11

    Join Date
    Feb 2005
    Posts
    195
    Helped
    1 / 1
    Points
    2,621
    Level
    11

    music algorithm tutorial

    Hi, everyone. I have a simple question about the direction finding by using MUSIC Algorithm.

    since the antenna array output is:

    X=A*F+N

    where A is the steering vectors matrix, F is the excitations (complex number???) and N is the noise.

    and the covariance matrix of the output X vector is:

    S=E(XX*)=AE(FF*)A*+E(NN*)

    For given number of incident wave, for example, D incident wave, the F is a fixed vector, and E(FF*) = FF*, therefore its rank is 1. Is it correct?

    If possible, would you give me some hints about the numerical code for the MUSIC algorithm?

    I am confused how can I construct the E(FF*). Should I use the time average? if so , what is the sampling frequency I should use? Is it larger than the carrier frequency?

    Thanks in advance.

  2. #2
    Junior Member level 2
    Points: 1,191, Level: 7

    Join Date
    Nov 2006
    Posts
    20
    Helped
    1 / 1
    Points
    1,191
    Level
    7

    music direction finding

    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


    1 members found this post helpful.

    •   Alt14th November 2006, 11:07

      advertising

        
       

  3. #3
    Full Member level 4
    Points: 2,621, Level: 11

    Join Date
    Feb 2005
    Posts
    195
    Helped
    1 / 1
    Points
    2,621
    Level
    11

    music algorithm

    Hi, deepabhargavi. Thanks for your reply.

    I built the MATLAB code and do the test a few days ago. I found that the MUSIC algorithm can detect multiple non-coherent signals only, which although FF* at each sample is rank 1, but the time average SUM(FF*)/Number of Sampling is rank M=Number of Waveform.

    When the input waveforms are coherent, for example, several single-frequency sinusoidal plane-wave, the MUSIC algorithm will not be able to distinguish it, since the rank of E(FF*) is always 1.

    I am thinking whether there are other "High-Resolution" Algorithms can be used for Direction Finding of multiple coherent signals?

    Thanks.



  4. #4
    Newbie level 2
    Points: 198, Level: 2

    Join Date
    Nov 2011
    Posts
    2
    Helped
    0 / 0
    Points
    198
    Level
    2

    Re: MUSIC Algorithm for Direction Finding

    Hello,

    I want to implement the MUSIC algorithm in MATLAB.

    I have found a function for MUSIC [S,w] = pmusic(x,p).

    Can any one tell me how i can find the Direction of Arrival


    Bilal



    •   Alt22nd November 2011, 13:48

      advertising

        
       

  5. #5
    Member level 5
    Points: 946, Level: 6
    Achievements:
    Created Blog entry

    Join Date
    Oct 2013
    Posts
    92
    Helped
    31 / 31
    Points
    946
    Level
    6
    Blog Entries
    2

    Re: MUSIC Algorithm for Direction Finding

    Quote Originally Posted by CaseBiall View Post
    I want to implement the MUSIC algorithm in MATLAB.
    I would strongly advise against using the built-in Matlab functions, as I think it's far easier to write your own functions so you can be sure about what is going on.

    I have written some very simple Matlab code for a basic 1D (azimuth only) MUSIC direction of arrival estimation, as many people seem to have trouble getting started with this:

    Code:
    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;
    You can see that the nulls in the spectrum correctly align with the true azimuth directions. Of course, this example is very simple and I am happy to discuss many, many ways that it can be improved. For now, I have put plenty of comments in the code to get people started.



    •   Alt13th October 2013, 18:53

      advertising

        
       

  6. #6
    Newbie level 6
    Points: 115, Level: 1

    Join Date
    Nov 2013
    Posts
    14
    Helped
    0 / 0
    Points
    115
    Level
    1

    Re: MUSIC Algorithm for Direction Finding

    hi..
    will u help me for implementation of music algorithm? plz..



  7. #7
    Member level 5
    Points: 946, Level: 6
    Achievements:
    Created Blog entry

    Join Date
    Oct 2013
    Posts
    92
    Helped
    31 / 31
    Points
    946
    Level
    6
    Blog Entries
    2

    Re: MUSIC Algorithm for Direction Finding

    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.



  8. #8
    Newbie level 6
    Points: 115, Level: 1

    Join Date
    Nov 2013
    Posts
    14
    Helped
    0 / 0
    Points
    115
    Level
    1

    Re: MUSIC Algorithm for Direction Finding

    Quote Originally Posted by weetabixharry View Post
    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.
    ok..
    my work is based on spectrum sensing in cognitive radio.. and i want to implement music algorithm in matlab.. but i am not getting proper work flow. i am confused..
    make my way clear for spectrum estimation by music algorithm,,

    thank you ..



  9. #9
    Newbie level 6
    Points: 115, Level: 1

    Join Date
    Nov 2013
    Posts
    14
    Helped
    0 / 0
    Points
    115
    Level
    1

    Re: music direction finding

    Quote Originally Posted by deepabhargavi View Post
    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
    hi..
    how to implement music algorithm for spectrum sensing in cognitive radio..
    can you give me some idea?



  10. #10
    Newbie level 6
    Points: 115, Level: 1

    Join Date
    Nov 2013
    Posts
    14
    Helped
    0 / 0
    Points
    115
    Level
    1

    Re: MUSIC Algorithm for Direction Finding

    hello sir.. i have doubt

    in received signal you have defined..k ..
    how you select k?

    means i am not getting that you have taken cos and sin term randomly ya thers is some reason behind that?

    thank you sir.



  11. #11
    Member level 5
    Points: 946, Level: 6
    Achievements:
    Created Blog entry

    Join Date
    Oct 2013
    Posts
    92
    Helped
    31 / 31
    Points
    946
    Level
    6
    Blog Entries
    2

    Re: MUSIC Algorithm for Direction Finding

    As stated in my Matlab code, k is the wavenumber vector.

    You can find an excellent, concise explanation of the wavenumber vector on pages 5 - 6 of this pdf: link.

    Please note:
    (1) I hate being called "sir". This is simply not appropriate. You can call me weetabixharry or idiot or pig... but please not "sir".
    (2) Please do not copy your posts to me in private messages. I will only respond here in the forum.



+ Post New Thread
Please login