How to plot array beampattern with Frost beamformer weights?

I am trying to plot beampattern of an array after using Frost Beamforming algorithm to adapt weights. Below is sample code for frost beamformer.

clear; close all; clc;

h = phased.URA('Size',[4 4],'ElementSpacing',[1 0.6]);
h.Element.FrequencyRange = [20 20000];

fs = 8e3;
t = 0:1/fs:0.3;
x = chirp(t,0,1,500);
c = 340;
collector = phased.WidebandCollector('Sensor',h,...
    'PropagationSpeed',c,'SampleRate',fs,...
    'ModulatedInput',false,'NumSubbands',8192);
incidentAngle = [-50;30];
x = step(collector,x.',incidentAngle);
noise = 0.2*randn(size(x));
rx = x + noise;

beamformer = phased.FrostBeamformer('SensorArray',h,...
    'PropagationSpeed',c,'SampleRate',fs,...
    'Direction',incidentAngle,'FilterLength',5,...
    'WeightsOutputPort',true);
[y,yweights] = step(beamformer,rx);

plot(t,rx(:,6),'r:',t,y)
xlabel('Time')
ylabel('Amplitude')
legend('Original','Beamformed')

How do I use pattern and yweights to plot the beampattern?

Answer 1

[Honglei Chen]

You can consider translating the weights to frequency domain to obtain the appropriate frequency response. Then you can compute the pattern at the given frequency.

    % plot pattern
    % consider 16 bands and pick the band corresponding to 2 kHz
    M = 16;
    wfreq = fft(reshape(yweights,16,[]).',M);
    freqvec = [0:7 -8:-1]*fs/M;
    bandidx = 5;  % corresponding to 2kHz
    freqbin = 2e3;
    hstv = phased.SteeringVector('SensorArray',h,'PropagationSpeed',c);
    sv = step(hstv,freqbin,incidentAngle);
    figure
    pattern(h,freqbin,-180:180,0,'PropagationSpeed',c,'Weights',sv.*wfreq(bandidx,:).',...
        'CoordinateSystem','polar','Type','powerdb');

HTH