Draw of envelope of the antenna radiation patterns for all available beams

I am new to the matlab suite.

I have seen several examples of how to draw beams in 5G communications, with different configs.

I am interested to see how to draw the envelope of the antenna radiation patterns for all available beams.

How can I make this in matlab?

Is it possible with sensor array analyzer?

Answer 1

[AR]

Hi @Daniel,

One way to plot the envelope of the antenna radiation patterns for all available beams, is by using the Phased Array System Toolbox in MATLAB.

Here is an example to draw the envelope of radiation patterns using an 8-element Uniform Linear Array (ULA) operating at 28 GHz:

% Parameters 
N = 8; % Number of elements 
fc = 28e9; % Frequency (28 GHz) 
c = physconst('LightSpeed'); 
lambda = c/fc; 
d = lambda/2; % Element spacing 

array = phased.ULA('NumElements', N, 'ElementSpacing', d); 
beamDirs = -60:20:60; % Beam steering directions 
angles = -90:0.5:90;  % Angle grid for plotting 

allPatterns = zeros(length(beamDirs), length(angles)); 

for k = 1:length(beamDirs) 
    % Compute steering vector for this beam direction 
    w = phased.SteeringVector('SensorArray', array, 'IncludeElementResponse', true); 
    sv = w(fc, beamDirs(k)); 
    % Array response object 
    arrayResp = phased.ArrayResponse('SensorArray', array, 'WeightsInputPort', true); 
    resp = arrayResp(fc, angles, sv); % [1 x numAngles], magnitude response 
    pat = 20*log10(abs(resp)); % Convert to dB 
    allPatterns(k, :) = pat; 
    plot(angles, pat, 'DisplayName', ['Beam at ' num2str(beamDirs(k)) '°']); hold on; 

end 
 
env = max(allPatterns, [], 1); % Envelope: max gain across all beams 

plot(angles, env, 'k--', 'LineWidth', 2, 'DisplayName', 'Envelope'); 
xlabel('Angle (degrees)'); 
ylabel('Gain (dB)'); 
legend('show'); 
title('Radiation Patterns and Envelope for All Beams'); 
grid on; hold off; 

The Phased Array Toolbox provides essential system objects such as “phased.ULA”, “phased.SteeringVector”, and “phased.ArrayResponse” used to model Uniform Linear Arrays, compute direction-dependent phase shifts and simulate array’s directional response respectively.

For interactive visualization and beam steering, you can use the Sensor Array Analyzer App. While this app is great for visualizing individual beam patterns, it does not compute the envelope across multiple beams directly. To do so, export the data and use a MATLAB script to calculate and plot the envelope.

Kindly refer to the documentation links below for more information on “phased.ULA”, “phased.SteeringVector”, and “phased.ArrayResponse”:

• https://www.mathworks.com/help/phased/ref/phased.ula-system-object.html
• https://www.mathworks.com/help/phased/ref/phased.steeringvector-system-object.html
• https://www.mathworks.com/help/phased/ref/phased.arrayresponse-system-object.html

I hope this answers your question.

[Daniel]

Hello @AR. Thank you very much for the answer.

It really helped a lot.

It really delivers the envelope that I am looking for in the case of a retangular plot.

The slight difference compared to what I need is that I want it in a polar plot.

How can I make it?

[AR]

Hello @Daniel. Glad the answer helped.

Here is the same example, updated to use a polar axis for plotting the envelope:

% Parameters
N = 8;
fc = 28e9;
c = physconst('LightSpeed');
lambda = c/fc;
d = lambda/2;

array = phased.ULA('NumElements', N, 'ElementSpacing', d);
beamDirs = -60:20:60;
angles = -90:0.5:90;

allPatterns = zeros(length(beamDirs), length(angles));

figure;
polarAxes = polaraxes;
hold on;

for k = 1:length(beamDirs)
    % Create array response object
    arrayResp = phased.ArrayResponse('SensorArray', array, 'WeightsInputPort', false);
    
    % Calculate response
    resp = arrayResp(fc, angles);  
    
    % Steering: shift beam
    shiftedAngles = angles - beamDirs(k);
    shiftedResp = arrayResp(fc, shiftedAngles);
    
    % Avoid log(0)
    shiftedResp(abs(shiftedResp) < 1e-6) = 1e-6;
    
    % Take magnitude and dB
    pat = 20*log10(abs(shiftedResp));
    
    % Clip below -40 dB for clean plot
    pat(pat < -40) = -40;
    
    allPatterns(k, :) = pat;
    
    polarplot(deg2rad(angles), pat, 'DisplayName', ['Beam at ' num2str(beamDirs(k)) '°']);
end

% Envelope (max pattern)
env = max(allPatterns, [], 1);

polarplot(deg2rad(angles), env, 'k--', 'LineWidth', 2, 'DisplayName', 'Envelope');

% Set properties to view the polar plot well
polarAxes.RLim = [-40 0];  % dB range
polarAxes.ThetaZeroLocation = 'top';
polarAxes.ThetaDir = 'clockwise';

legend('show', 'Location', 'bestoutside');
title('Envelope for All Beams (Polar Plot)');
hold off;

●

The major changes done are:

• Plots radiation patterns using polarplot() instead of plot().
• Shifts evaluation angles manually (shiftedAngles = angles - beamDirs(k)) instead of using a steering vector.
• Does not use "phased.SteeringVector" and only uses "phased.ArrayResponse".
• Clips small response values below 10^-6 to avoid −∞ in dB.
• Limits gain values to −40 dB minimum for a cleaner polar plot.
• Configures polar plot settings: RLim = [-40 0], ThetaZeroLocation = 'top', ThetaDir = 'clockwise'.
• Moves the legend to outside the plot (bestoutside).

Hope this is helpful!

[Daniel]

Thank you very much for the answer you provided.

It really helped me to better understand how the plot works in polar form.

However, I am interested in seeing an envelope that completely encloses all the beams. Currently, only the portions of the envelope around 90º and 180º are visible.

How can this be done?

By inserting a threshold?

By increasing the drawing reference area?

I am sending a sample of the fully visualization of the envelope that is similar to what I am looking for.

Thanks in advance.

Image source: https://www.mdpi.com/2076-3417/10/15/5280

[AR]

Hi again @Daniel,

The below change in code dynamically adjusts the visible dB range so that the entire envelope (even low gain regions) is visible around all 360°, not just 90° and 180°.

polarAxes.RLim = [minVal, 0];

This was done by:

• Avoiding log(0) via clamping small values (1e-10)
• Calculating the envelope correctly
• Plotting the full dynamic range with proper RLim.

Thresholding would artificially cut values and potentially distort the envelope and therefore, it is not used here. Instead, all gain values are preserved, giving a realistic and complete envelope.

The below change in the code expands the drawing reference area vertically in dB, making low-level sidelobes and backlobes visible.

polarAxes.RLim = [minVal, 0];

Here is an example code by increasing the reference area:

% Parameters
N = 8;
fc = 28e9;
c = physconst('LightSpeed');
lambda = c / fc;
d = lambda / 2;

% Create ULA
array = phased.ULA('NumElements', N, 'ElementSpacing', d);

% Define beam directions and angle sweep
beamDirs = -60:20:60;             % Steering angles
angles = -90:0.5:90;              % Angle range
anglesRad = deg2rad(angles);      % For polar plot

% Initialize response storage
allPatterns = zeros(length(beamDirs), length(angles));

% Loop through beam directions
for k = 1:length(beamDirs)
    pos = array.getElementPosition / lambda;
    steerVec = steervec(pos, beamDirs(k));
    arrayResp = phased.ArrayResponse('SensorArray', array, 'WeightsInputPort', true);
    
    resp = arrayResp(fc, angles, steerVec);
    resp(abs(resp) < 1e-10) = 1e-10;
    pat = 20 * log10(abs(resp));
    
    allPatterns(k, :) = pat;
end

% Compute envelope and average
env = max(allPatterns, [], 1);
gAvg = mean(allPatterns, 1);
boresightBeam = allPatterns(beamDirs == 0, :);

% Create polar plot
figure
polarAxes = polaraxes

polarAxes = 
  PolarAxes with properties:

             ThetaLim: [0 360]
                 RLim: [0 1]
       ThetaAxisUnits: 'degrees'
             ThetaDir: 'counterclockwise'
    ThetaZeroLocation: 'right'

  Use GET to show all properties

hold on

% Plot boresight beam (blue)
polarplot(anglesRad, boresightBeam, 'b-', 'LineWidth', 1.5, 'DisplayName', 'Boresight beam')

% Plot G_avg (orange)
polarplot(anglesRad, gAvg, 'Color', [1 0.5 0], 'LineWidth', 1.5, 'DisplayName', 'G_{avg}')

% Plot envelope (green dashed)
polarplot(anglesRad, env, 'g--', 'LineWidth', 2, 'DisplayName', 'Envelope for all beams')

% Fix RLim
minVal = floor(min(env));
if minVal >= 0
    minVal = -40;
end
polarAxes.RLim = [minVal, 0];
polarAxes.ThetaZeroLocation = 'top';
polarAxes.ThetaDir = 'clockwise';

% Add legend and title
legend('show', 'Location', 'bestoutside');
title('Boresight, G_{avg}, and Envelope (Polar Plot)');
hold off;

Hope this is helpful for you!

[Daniel]

Hello. Thank you very much for your contribution.

I have made two changes to the last code sent.

The first was to increase the range of values being plotted, so that it would be possible to fully visualize the boresight beam, envelope and mean value. This was done using:

polarAxes.RLim = [minVal, 40]; %UPD 1: previous value: 0

The second change was to increase the severity of the value cutoff, so that some beans displayed in the boresight beam were not displayed, which are the ones that were appearing at 90º, 150º, 210º and 270º. This was done using:

resp(abs(resp) < 1e-2) = 1e-2; %UPD 2: previous value: 1e-10

The complete code is:

% Parameters
N = 8;
fc = 28e9;
c = physconst('LightSpeed');
lambda = c / fc;
d = lambda / 2;
% Create ULA
array = phased.ULA('NumElements', N, 'ElementSpacing', d);
% Define beam directions and angle sweep
beamDirs = -60:20:60;             % Steering angles
angles = -90:0.5:90;              % Angle range
anglesRad = deg2rad(angles);      % For polar plot
% Initialize response storage
allPatterns = zeros(length(beamDirs), length(angles));
% Loop through beam directions
for k = 1:length(beamDirs)
    pos = array.getElementPosition / lambda;
    steerVec = steervec(pos, beamDirs(k));
    arrayResp = phased.ArrayResponse('SensorArray', array, 'WeightsInputPort', true);
    
    resp = arrayResp(fc, angles, steerVec);
    resp(abs(resp) < 1e-2) = 1e-2; %UPD 2: previous value: 1e-10
    pat = 20 * log10(abs(resp));
    
    allPatterns(k, :) = pat;
end
% Compute envelope and average
env = max(allPatterns, [], 1);
gAvg = mean(allPatterns, 1);
boresightBeam = allPatterns(beamDirs == 0, :);
% Create polar plot
figure
polarAxes = polaraxes
hold on
% Plot boresight beam (blue)
polarplot(anglesRad, boresightBeam, 'b-', 'LineWidth', 1.5, 'DisplayName', 'Boresight beam')
% Plot G_avg (orange)
polarplot(anglesRad, gAvg, 'Color', [1 0.5 0], 'LineWidth', 1.5, 'DisplayName', 'G_{avg}')
% Plot envelope (green dashed)
polarplot(anglesRad, env, 'g--', 'LineWidth', 2, 'DisplayName', 'Envelope for all beams')
% Fix RLim
minVal = floor(min(env));
if minVal >= 0
    minVal = -40;
end
polarAxes.RLim = [minVal, 40]; %UPD 1: previous value: 0
polarAxes.ThetaZeroLocation = 'top';
polarAxes.ThetaDir = 'clockwise';
% Add legend and title
legend('show', 'Location', 'bestoutside');
title('Boresight, G_{avg}, and Envelope (Polar Plot)');
hold off;

The image that was produced:

[AR]

Glad to know that the solution helped and was useful!

[AR]

The graph now looks clear with proper cutoff values.