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

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)?

Looking forward for your answers

Answer 1

[Honglei Chen]

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

[DM]

Thank you very much. Actually, I have a question for your answer on number 2. Do you mean that wn vector is not divided by 1/Ntx where Ntx is the number of antennas?

[Honglei Chen]

Yes, you are right. But for the purpose of comparison, it doesn't matter, as long as they are consistent.

[Chris Jagielski]

Yes wn'*wn equals to 10, in the example, because there are 10 antenna elements in the ULA.

[Chris Jagielski]

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);