## How can I calculate the doa for acoustic signals by applying the Music algorithm in MATLAB?

Started by 1 week ago●10 replies●latest reply 21 hours ago●102 viewsfunction [] = Bartlett_algorithm_dao(signal)

degree_inradian = pi/180;

radian_degree = 180/pi;

twp = 2*pi;

d = 5

wave =2; %number of DOA

theta = [-60 -30 30 60];

SNR = 20;

n = 512;

A = exp(-j*twp*d.'*cos(theta*degree_inradian))'%directio matrix

signal_data = signal;% generated signal

X = A.*signal_data

X1 = awgn(X, SNR);

Rxx =X1*X1'/n

[EV,D] = eig(Rxx)

EVA = diag(D)'

[EVA,I] = sort(EVA)

EVA = fliplr(EVA)

EV = fliplr(EV(:,I))

%Music method

for iangl = 1:361

angle(iangl) = (iangl-180)/2

phim = degree_inradian*angle(iangl)

a = exp(-j*twp*d*cos(phim)).'

L = wave

En = EV(:,L+1:3)

SP= (En*a').*(a*En')./En.^2

SP(iangl,:) = abs((1./1-(SP(1,:))))

end

%Plot figure

SP = abs(SP)

SPmax = max(SP(iangl))

SP = 10*log10(SP/SPmax)

h = plot(angle, SP)

set(h,'Linewidth', 4)

xlabel('angle (degree)')

ylabel('magnitude(db)')

axis([-90 90 -60 0])

set(gca, 'XTick',[-90:30:90])

grid on

end

Your calculation of the direction matrix **A** looks incorrect to me. This matrix should include information about the source directions and the geometry of your sensor array.

What is the geometry of your sensor array? I can just see a mysterious scalar **d=5**.

Please use my code below as a reference. In this example, I have assumed the sensor array is linear and uniformly-spaced.

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 eigenvectors 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;

I'm not sure if I understand your question. If you already have some received data, then you don't need to generate it, so you can ignore sections (1) and (2) of my code.

If this is real data taken from real sensors, then I think that you are trying to do something too difficult too soon. MUSIC is very sensitive to calibration errors, so making it work with real data is much more difficult than in my simple synthetic example (where we assume everything is ideal).

I would definitely try some more robust algorithms first. I noticed that your MUSIC function is misnamed "Bartlett" (i.e. a conventional beamformer). Did you get reasonable results with a conventional beamformer? Or perhaps with an MVDR beamformer? I would definitely make sure you have those methods working before you move on to MUSIC.

If the other methods are working, then I'm not sure exactly what you want to know. Presumably, you have already been able to calculate the received signal covariance matrix, Rxx. And you must already know your array geometry, r.

The only extra information you need for MUSIC is an estimate of the number of signal sources, M. If you don't know the number of sources, this can be estimated (for example, by using the MDL or AIC algorithms).

My scalar number is calculated according to the speed of light and the carrier-frequency by the following equation:

`fc = 18000`

`c = 3e8`

`lambda = c/fc`

`d = lambda/2`

So for more precision, how can I insert the MDL or AIC algorithms into my code? May your experience can help me to complete that, thanks.

As you mentioned above, I also think that the number of sources is an important issue to solve in my case, in reference to the localization angles. As long as the number of sources is not well estimated, the `En = Ev(:,L+1:3)` in my code will display errors, hence the rest of the music code is adapted as follows:

`SP= (En*a').*(a*En')./En.^2`

`SP(iang,:) = abs((1./1-(SP(1,:))))`

and I get this result:

One question: If I reshape the code in several dimensions, will my result be displayed like yours in sinusoidal form or with peaks localization? Because It seems like my current result may not be correct and does not satisfy me at all.

When I describe the figure, I assume that the two users represent the two portions and individually emit their own characteristics. I don't know if this is correct. But it's just a brief interpretation in case the assumption is true.

Thank you for your clarification.

There is no sense in thinking about algorithms to estimate the number of sources when you don't yet have an example working where the number of sources is known exactly.

Your equations didn't make sense to me. Please check that they have been typeset correctly.

I didn't understand your comments about reshaping the code.

Your most recent graph is too small to read. It looks incorrect, but I can't read the legend to see what the 4 different lines represent.

To better clarify my work, here is my real signal generated from my smartphone:

. I work only with a smartphone, with no extra device as support. FMCW is used as the transmit signal. I have two targets in my environment which represent my two sources (M=2), except other sources of reflection (maybe the wall, tools...). The exploiting data are those after the pre-processing.

The Music algorithm script is represented as follows:

%Music method

for iangl = 1:361

angle(iangl) = (iangl-180)/2

phim = degree_inradian*angle(iangl)

a = exp(-j*twp*d*cos(phim))'.

L = wave

En = EV(:,L+1:M)

SP(iangl) = (a*a')./(a*En'*En*a)

end

By incompatibility of dimensions I modified this part, to finally compile my data:

%Music method

for iangl = 1:361

angle(iangl) = (iangl-180)/2

phim = degree_inradian*angle(iangl)

a = exp(-j*twp*d*cos(phim))'.

L = wave

En = EV(:,L+1:M)

SP= (En*a').*(a*En')./En.^2

SP(iangl,:) = abs((1./1-(SP(1,:)))))

end

Unfortunately, I find this result,

which seems to be incorrect, but indeed, I want to have more precision on it. And ask for help. I can inbox you to share my data and help me to solve this issue. How to successfully import my data in music algorithm or perhaps more algorithm to suggest.

Please attach your graphs and code for conventional beamforming.

It is only a small modification to convert that to use MUSIC.

Hi Sir, Sorry for being late. Here are my conventional beamforming code and figures. First I performed the pre-processing of my signal and later applied the MVDR algorithm for the conventional beamforming.

I think the result is correct?

So, how can I apply the Music from this result? and plot the spectrogram 1D or 2D?

```

% %Signal beamforming

%MVDR method

signal_data = abs(signal(5000:6000));

nbr_mics = 2;

nbr_snap = 200;

thetas = 30*pi/180;

center_frequency = 18000;

c =3e8;

lamda = c/center_frequency;

d = 0.5*lamda;%cell spacing

Is = zeros(nbr_mics,1);

for n = 1:nbr_mics

Is(n) = exp(j*2*pi*(n-1)*d*sin(thetas)/lamda);

Rxx = (signal_data.'*(signal_data.')')/nbr_snap;

detaS = Is;

Mvdr_algo(:,:,n) = inv(Rxx).*detaS(n).*inv(detaS(n)'.*inv(Rxx).*detaS(n));

end

%Linear array

p = -pi/2:pi/180:pi/2;

for jj = 1:1:length(p)

w_scan = zeros(nbr_mics,1);

scan = p(jj);

for n = 1:nbr_mics

w_scan(n) = exp(j*2*pi*(n-1)*d*sin(scan)/lamda);

end

Fmvdr(jj) = abs(Mvdr_algo(n)'.*w_scan(n));

end

% Figure

Fmax = max((Fmvdr));

Fa = Fmvdr./(Fmax);

Fa = 20*log10(Fa);

figure(1);

plot(180*p/pi,Fa,'b-')

xlabel('angle')

```

My data is so large that I share a fraction of it. You can check it out: