# how can I create a simple clutter model?

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Kerem Yüksel le 17 Fév 2024
Commenté : William Rose le 18 Fév 2024
what is the easy way to model clutter? without any toolbox. is there any mathematical expression for the clutter model. I want to see these radar signals effected from these clutters.
thanks a lot, have a good day.
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### Réponse acceptée

William Rose le 17 Fév 2024
Modifié(e) : William Rose le 17 Fév 2024
[edit: fix spelling errors]
[Edit 2: My initial implementation had an exponential distribution of clutter radii. I had intended for the areas to be exponentially distributed. That is fixed now.]
Yes there are models of radar clutter that do not require a toolbox.
Here is a good place to start:
Radar Clutter Modeling and Analysis (book chapter, 2014)
I do not have immediate access to the full text above. Maybe you can get it through your university or employer.
The clutter model depends on the type of radar you are using. Is the radar for surface targets only (2-D, as in many marine radars), or for tracking airborne targets (3-D)? You will need to specify the mean clutter reflectivity (an area, for 2D, or a volume, for 3D). If it is a Doppler radar, you need to specify the clutter's Doppler spectrum. The radar signal processing algorithms greatly influence the clutter that is actually observed.
A very simple model, for a 2D non-Doppler radar:
Clutter returns are independent of one another within each sweep, and independent from one sweep to the next. The number of clutter returns per unit area, on each sweep, has a Poisson distribution, with mean λ. The locations of clutter returns are given by a 2D uniform distribution. The amplitude of clutter returns has an exponential distribution, with mean area .
Implementation of the very simple model:
lambda=10; % mean clutter returns per unit area [km^-2]
sigma0=1e-3; % mean clutter return area [km^2]
N1=poissrnd(lambda)*(2*range)^2; % number of clutter returns in 2*range square
x1=-range+2*range*rand(1,N1); % clutter x-coords [km]
y1=-range+2*range*rand(1,N1); % clutter y-coords [km]
a1=exprnd(sigma0,1,N1); % clutter areas [km^2]
x=x1(x1.^2+y1.^2<=range); % clutter returns in range (exclude far corners)
y=y1(x1.^2+y1.^2<=range); % clutter returns in range (exclude far corners)
r=r1(x1.^2+y1.^2<=range); % clutter returns in range (exclude far corners)
N=length(x); % number of clutter returns in range
%% Plot clutter returns
figure
for i=1:N
rectangle('Position',[x(i)-r(i),y(i)-r(i),2*r(i),2*r(i)],...
'Curvature',[1,1],'Facecolor','b','EdgeColor','none')
end
rectangle('Position',0.25*[-1,-1,2,2],'Curvature',[1,1],'EdgeColor','r')
rectangle('Position',0.50*[-1,-1,2,2],'Curvature',[1,1],'EdgeColor','r')
rectangle('Position',0.75*[-1,-1,2,2],'Curvature',[1,1],'EdgeColor','r')
rectangle('Position',1.00*[-1,-1,2,2],'Curvature',[1,1],'EdgeColor','r')
xlim([-range,range]); ylim([-range,range])
axis equal
The clutter amplitude model above (which is that the clutter return areas have an exponential distribution) does not allow us to control the mean and variance independently. A gamma distribution (a scaled chi-squared distribution) allows you to set the mean and the variance independently.
Good luck!
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Kerem Yüksel le 18 Fév 2024
assume you have written your own code to simulate and analyze radar returns. -> no I don' t but looking to write.
William Rose le 18 Fév 2024
I would first write code to simulate and process radar returns without clutter. I would test my code to become confident that it is working as expected. Then I would consider adding clutter to the simulation. I expect this will be a substantial effort. I hope the two books I have recommended above will be helpful.

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