# Question regarding Antenna toolbox example provided by mathworks ( beam pattern)

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DM on 28 Oct 2015
Commented: Chris Jagielski on 10 Nov 2015
This question is related to the Antenna toolbox in MATLAB. I have found an online example from Mathworks, below is the link which shows the example. In particular I am interested in only the first example (null steering)
http://www.mathworks.com/help/phased/examples/array-pattern-synthesis.html
I don't currently own the antenna toolbox, but I am trying to generate the same figure for the first example (null steering). My questions regarding the exisiting code on the link provided above is
1- Are
w, wd,wn
column or row vectors?
2- Is the product
wn'*wn equal to 1
if so why is it then even used in the current code (it doesn't change the computation) ?
I have tried to write down my own code to plot the pattern that is shown in this link (first figure) as function of theta
Ntx=10;
c=3e8;
fc=1e9;
lambda=c/fc;
theta=-100:1:100;
for k=1:1:length(theta)
h_desired=((1/sqrt(Ntx))*exp(i*(2*pi/lambda)*(lambda/2)*[0:1:(Ntx-1)].*sin(0*pi/180)))'; %desired direction
h_interference=((1/sqrt(Ntx))*exp(i*(2*pi/lambda)*(lambda/2)*[0:1:(Ntx-1)].*sin(40*pi/180)))'; %interference direction
h_test=((1/sqrt(Ntx))*exp(i*(2*pi/lambda)*(lambda/2)*[0:1:(Ntx-1)].*sin(theta(k)*pi/180)))';
rn = h_interference'*h_desired/(h_interference'*h_interference);
w_r = h_desired-h_interference*rn;
magnitude= abs(h_test'*w_r);
y(k)= (20*log10(magnitude));
end
figure
plot(theta,y,'r')
xlabel('theta')
ylabel('Normalized Power dB')
grid on
As you can see I don't obtain correct results, in particular the null at 40 degrees is almost -300 dB what is the problem, the example from mathworks gives -100db (please check link)?

Honglei Chen on 30 Oct 2015
The example actually belongs to Phased Array System Toolbox, not Antenna Toolbox.
1. These are columns
2. wn is the steering vector corresponding to the null direction. It is not normalized but what matters is its phase structure rather than the magnitude. It is used to project the return to the null direction and then remove it from the beam pattern.
Finally, the null is deep, the example figure simply set the lower limit of y axis to -100 dB to get a more balanced picture. A null means the response is close to 0, so theoretically it should -inf.
HTH
Chris Jagielski on 10 Nov 2015
In DM's code, you can change theta to, for example, -180:180 degrees. This will give the full azimuth range.
In the example, it only plots at -90:90 degrees.
Why does the example only show from -90 to +90 degrees? I have tried adding the 'AzimuthAngles' property in the plotResponse() function, but it does not work.
Here is an example that does not work, i.e. it still only displays from -90 to +90 degrees:
plotResponse(myULA,fc,c,'Weights',w,'AzimuthAngles',-120:120);

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