MVDR fail with two identical target.

Hi all

I have a problem with MVDR estimator in case of two identical target.

I follow matlab example described at http://www.mathworks.com/products/phased-array/examples.html?file=/products/demos/shipping/phased/doabeamscandemo.html

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

Answer 1

[Honglei Chen]

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

[zohar]

Hi Honglei, Thx.

Your solution works for direction of arrival, but I want to know the power or mag for each direction.

My main goal is to generate beams for all direction Vs time !?

Any suggestion ?

Zohar

[Honglei Chen]

Hi Zohar,

If you have to use MVDR for a correlated signal case, then you may need to build the weights yourself and incorporate the spatial smoothing when estimating the covariance matrix.

HTH

[zohar]

Hi Hongeli,

1) I preform MVDR somthing like this:

for n = 1: length(phi)

p1 = A0(:,n)'*IRf*A0(:,n);

power(n) = 1/p1;

Wcap(:,n) =IRf*A0(:,n)/p1;

end

were IRF is inv(x'x) , A0 - steering vector , n - indx of beam.

How can I do spatial smoothing in that case ?

2) I alsow preform MUSIC somthing like this:

r = 2 ; %Number of estimated signals

[Q ,D]=eig(x'x);

[D,I]=sort(diag(D),1,'descend'); %Find r largest eigenvalues

Q=Q (:,I); %Sort the eigenvectors to put signal eigenvectors first

Qs=Q (:,1:r); %Get the signal eigenvectors

Qn=Q(:,r+1:Ns); %Get the noise eigenvectors Ns number of staves

for n = 1: length(phi)

PowerMusic(n)=(A0(:,n)'*A0(:,n))/(A0(:,n)'*Qn*Qn'*A0(:,n));

end

Any help ?

Thx

[Honglei Chen]

Hi Zohar,

The spatial smoothing is done when estimating covariance matrix. The following paper is a good starting place.

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=17496&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel1%2F29%2F635%2F00017496.pdf%3Farnumber%3D17496

HTH

[zohar]

Hi Honglei, But I do not have Ieee acount :’(

can you send it to me via email?

Thx

[Honglei Chen]

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

http://www.amazon.com/Optimum-Processing-Detection-Estimation-Modulation/dp/0471093904

[zohar]

Thx +1