# Spatial smoothing - 2D MUSIC [FMCW MIMO radar processing]

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Luca Romano on 18 Feb 2019
Commented: mk14 on 24 Aug 2019
Hi everyone,
I'm using a 2D Music algorithm for the estimation of Range-Azimuth info in a ULA FMCW MIMO radar.
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"). I have some doubt with regard the application of the 2D FB spatial smoothing in order to decorrelate the covariance matrix of the data; I'm wondering if I do some error in the following code section (in the way I order the x_win_new vector):
x= DataV'; %Data collected by the ULA (31 Spatial samples-31Antennas), 501 time samples
N = size(x,1); % Number of antennas
M = size(x,2); % Number of samples in fast-time dimension
% window dimension for the smoothing dim[m1xm2]
m1 = 25;
m2 = 300;
p1 = N-m1+1; %positions in the spatial dimension
p2 = M-m2+1; %positions in the time dimension
N_submat = p1*p2; %number of all the possible scan
M_tot = m1*m2;
ind_tot=1;
for p1_ind = 1:p1
for p2_ind = 1:p2
x_win_new(:,ind_tot) = reshape (x(p1_ind:m1+(p1_ind-1),p2_ind:m2+(p2_ind-1)),[1,M_tot])';
ind_tot=ind_tot+1;
end
end
X_win_cor = x_win_new*x_win_new';
X_win_cor_conj = conj(X_win_cor);
J= fliplr(eye(M_tot)); %transition matrix
C=(1/2*N_submat)*(X_win_cor + J*X_win_cor_conj*J); %data smoothed covariance matrix (forward+backward)
so in my case I'm scanning the full 2D [NxM] matrix in this way:
x x x . . x x x . . . . . . . .
x x x . . x x x x x x . . x x x
x x x . . x x x x x x . . x x x
. . . . . . . . x x x . . x x x
If I select m1=M and m2=N (so no spatial smoothing, only forward/backward averaging) I get good results as shown in the attached image.
Best regards,
Luca,

mk14 on 11 Jul 2019
Hi there, did you manage to solve the problem? I am also working on 2D music.
Shirleyuue Jiang on 22 Aug 2019
Hi, I have some problem with 2D music( Range-Azimuth), can you show me your whole code?

mk14 on 5 Aug 2019
Hi there, can you please share your whole code. I cannot plot the data in the right way. Thanks!
Mark

Shirleyuue Jiang on 23 Aug 2019
Hi, I can imagesc the data, but the result is not so good. Can we share the code with each other?
mk14 on 23 Aug 2019
I moved on to the capon beamformer instead of MUSIC.
Shirleyuue Jiang on 24 Aug 2019
So in your experiment, do capon be better than MUSIC?

Shirleyuue Jiang on 24 Aug 2019
Hi, I have some problem with 2D music( Range-Azimuth), can you show me your whole code?
Best regards,
Shirley

#### 1 Comment

mk14 on 24 Aug 2019
For practical implementation, I think MUSIC is prone to interference. Moreover, when using capon you don't need to know number of source.