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

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 as per 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 regards to 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). My main questions are:

1) Is it appropriate the use of 2D spatial smoothing to the data collected by an ULA?

2) If yes, which is the right way to organise the subarray? Which directions the subarray has to scan the full data matrix?

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
%data smoothed covariance matrix (forward+backward)
C=(1/2*N_submat)*(X_win_cor + J*X_win_cor_conj*J);


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[the music plot are theta/range type; $$\theta$$ from -20° to 20°; the FFT plot are in cartesian coordinates]. As you can see in the second music plot (where I used m1=25; m2=300) something went wrong; it seems that the data smoothed covariance matrix has been not build correctly. Any suggestions? Thanks a lot in advance,
Best regards, Luca,

• Would it be possible to edit your question to make the specific thing that you are asking about a bit more clear? – A_A Feb 19 at 7:24