Phased Array System toolbox: What is the equations used to calculate the pattern, beamwidth and PhaseShiftBeamformer for URA?

Dear community

I have used the "Phased Array toolbox" to make a simulation to plot the pattern and steer the primary beam to phase "theta" and "phi" in both azimuth and elevation.

I have a URA array. What are the equations used with those functions?

1- phaseshifter = phased.PhaseShiftBeamformer(...)

2- [~, weights(:,i)] = phaseshifter(signal);

3- pattern(...'Type', 'Directivity')

with a lot of thanks

Answer 1

[Dheeraj]

Hi,

I understand that you're working with a Uniform Rectangular Array (URA) and a phased.PhaseShiftBeamformer to steer the primary beam to specific angles in both azimuth (theta) and elevation (phi). Here's a brief explanation of the equations you’re having trouble with :

phaseshifter = phased.PhaseShiftBeamformer(...);

This line of code creates a phased array beamformer object (phaseshifter) that you'll use to steer the primary beam. The 'phaseshifter' object is configured with various parameters, such as the array geometry, steering angles, and possibly other settings depending on your specific scenario.

[~, weights(:,i)] = phaseshifter(signal);

This line of code applies the ‘phaseshifter’object to a received signal (signal) to obtain the beamforming weights (weights) for a specific steering direction. The “I” index likely corresponds to different steering directions you want to explore.

pattern(...'Type', 'Directivity')

This line of code is used to compute and plot the array pattern with a specific type, which in this case is 'Directivity'. The 'Directivity' type typically represents the beamforming pattern and measures the gain of the antenna array in a specific direction. You can visualize the directivity pattern to see how the array responds to different steering angles.

You may refer the following documentation for better understanding of how phaseshift can be used.

https://in.mathworks.com/help/antenna/ref/phaseshift.html