- 10th November 2006, 19:13 #1

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## 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.

- 14th November 2006, 12:07 #2

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## 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.

- 14th November 2006, 12:07

- 20th November 2006, 06:28 #3

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## 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.

- 22nd November 2011, 14:48 #4

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## 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

- 22nd November 2011, 14:48

- 13th October 2013, 19:53 #5

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## Re: MUSIC Algorithm for Direction Finding

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;

- 13th October 2013, 19:53

- 15th January 2014, 19:03 #6

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## Re: MUSIC Algorithm for Direction Finding

hi..

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

- 16th January 2014, 21:41 #7

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## 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.

- 19th January 2014, 13:08 #8

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## Re: MUSIC Algorithm for Direction Finding

- 24th January 2014, 12:26 #9

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- 23rd March 2014, 00:13 #10

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## 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.

- 23rd March 2014, 01:14 #11

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## 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__:

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