# 2D MUSIC algorithm for range-azimuth FMCW data processing

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Shirleyuue Jiang on 22 Aug 2019
Commented: Emre Kurtoglu on 11 Aug 2020
Hi, I want to draw a map of range-azimuth. I can achieve 1D music, but there is some problem with 2D music for range-azimuth.
%X_ is the signal.
J = fliplr(eye(m1*m2,m1*m2));
Cx_ = 1/(2*p1*p2)*(X_*X_' + J*(X_*X_')*J);
[EV,D] = eig(Cx_); %D for eigenvalues and EV for eigenvector
EVA_temp = diag(D)';
[EVA,I] = sort(EVA_temp);
Sort_EV = fliplr(EV(:,I)); %eig
% W_ = Sort_EV(:,K+1:end); %(m1*m2)*(m1*m2-K)
W_ = Sort_EV(:,4:end);
for r = 1:length(VecR)
for theta = 1:length(VecA)
a_1 = [];
for mm1 = 0:m1-1
tao_i(mm1+1) = 2/c*( VecR(r) + mm1*d*sin(VecA(theta)) );
aa = exp(1i*2*pi*tao_i(mm1+1)*(linspace(fc,fc+alpha*(m2-1)/fs,m2) ) ); %0-
a_1 = cat(2,a_1,aa);
end
a = a_1.';
Smusic(r,theta) = 1/(a'*W_*W_'*a);
end
end
S_ = Smusic/(max(max(Smusic)));
figure,imagesc(VecA*180/pi,VecR(1:50),log(abs(S_)));xlabel('Azimuth(deg)');ylabel('Range(m)');title('range-azimuth');
% figure,imagesc(abs(Smusic));

Shirleyuue Jiang on 22 Aug 2019
The algorithm procedure is pretty simple (see "Belfiori F., Application of 2D MUSIC Algorithm to Range-Azimuth FMCW Radar data" or " Manokhin G., MUSIC-based algorithm for range-azimuth FMCW radar data processing without estimating number of targets"). Is there any problem with "aa"?

Patrick Nkam on 18 Jun 2020
Hi Shirleyuue Jiang ,
I work already with MUSIC, and i have some problems to get the Ranges values. Can you help me?
I habe problem with the steering-vector aa
Kun-Lin Hsieh on 23 Jul 2020
Hi Shirleyuue Jiang
I'm working on implementing this algorithm as well, and trying to extend it into a 3D problem by considering elevation dimention. However, there are some problem I met, and I'm even not sure if I have completely realize the whole procedure of this algorithm. Is it possible to share your code kindly if you have sucessfully completed it? We could also share our results to each other.
Emre Kurtoglu on 11 Aug 2020
Hi all,
Is there any update about this implementation? I am able to implement 1D MUSIC but cannot get results using this method and it takes infinitely long time to process since there are three consecutive 'for' loops.

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