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MVDR fail with two identical target.

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zohar
zohar on 13 Feb 2013
Hi all
I have a problem with MVDR estimator in case of two identical target.
clear all ;close all ;clc;
ha = phased.ULA('NumElements',10,'ElementSpacing',0.5);
ang1 = [30; 0]; ang2 = [40; 0];
t = (0:0.001:1).';
s1 = cos(2*pi*t*300);
s2 = cos(2*pi*t*400);
fc = 300e6; % Operating frequency
angs = [ang1 ang2];
broadsideAngle = az2broadside(angs(1,:),angs(2,:))
hBeamscan = phased.BeamscanEstimator('SensorArray',ha,...
'OperatingFrequency',fc,'ScanAngles',-90:90);
hBeamscan.DOAOutputPort = true;
hBeamscan.NumSignals = 2;
x = collectPlaneWave(ha,[s1 s2],[ang1 ang2],fc);
rs = RandStream.create('mt19937ar','Seed',2007);
nPower = 0.01; % Noise power
noise = sqrt(nPower/2)*(randn(rs,size(x)) + 1i*randn(rs,size(x)));
x = x + noise; % Total received signal
[~,ang] = step(hBeamscan,x)
figure
plotSpectrum(hBeamscan);
hMVDR = phased.MVDREstimator('SensorArray',ha,...
'OperatingFrequency',fc,'ScanAngles',-90:90,...
'DOAOutputPort',true,'NumSignals',2);
[~,ang] = step(hMVDR,x)
figure
plotSpectrum(hMVDR);
Now I change the frequencies
s1 = cos(2*pi*t*300);
s2 = cos(2*pi*t*300);
What am I missing here ?
I also try TimeDelayLCMVBeamformer and I got the same results.
Is there a solution to this problem ?
Thx

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Answers (1)

Honglei Chen
Honglei Chen on 14 Feb 2013
Hi Zohar,
When you set the frequency of the second signal to 300 Hz, your two signals are identical. This represent the case where the two signals are correlated (fully correlated in your case). In that case, the performance of MVDR is degraded. One way to solve this issue is to use a technique called spatial smoothing. This option is not available MVDR beamformer. If your interest is to detect the direction of arrival, you can try to use phased.RootMUSICEstimator which can accommodate the spatial smoothing. For example, if I use the following code with your signal, I get the correct angles
>> estimator = phased.RootMUSICEstimator('SensorArray',ha,...
'OperatingFrequency',fc,'SpatialSmoothing',1);
>> step(estimator,x)
ans =
39.9476 30.0222
HTH

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zohar
zohar on 14 Feb 2013
Hi Honglei, But I do not have Ieee acount :’(
can you send it to me via email?
Thx
Honglei Chen
Honglei Chen on 15 Feb 2013
I don't have subscription for IEEE Xplore either. I just had a hard copy from old days. You can try the following book too. It's well written, but definitely take a while to navigate

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