Does MATLAB's pattern() function use full-wave MoM or superposition of elements for antenna array analysis?

This question is probably more for MATLAB staffs but I am open to any response.

I am conducting research to compare the results of radiation patterns and electromagnetic behaviors of various antenna arrays. Specifically, for the same array, I am interested in simulations that consider the entire array structure, which includes multiple antenna elements and their excitations, versus simulations of individual array elements followed by superimposing their patterns, EM fields, and phase fronts.

I reviewed the MATLAB documentation on Modeling Mutual Coupling in Large Arrays Using Embedded Element Pattern , which provided a clear example of full-wave Method of Moments (MoM) simulation approaches compared to the superposition of isolated elements. Additionally, the Method of Moments Solver for Metal and Dielectric Structures documentation explained that multiple excitation feeds create a voltage matrix that interacts with the iteration matrix. This process exemplifies the full-wave MoM approach, incorporating the entire array structure and excitation points concurrently.

However, I also came across this PDF, Smart RF Design of Digitally Controlled RF Transmitters and Receivers from MathWorks themselves. On page 15 of the slides, it says:

"Phased Array System Toolbox computes the array pattern using the superposition of the pattern of each individual element – ULA, URA, UCA and conformal arrays use the same pattern for all elements – Heterogeneous arrays have different patterns for different elements"

The statement in the PDF seems to contradict the documentation provided, suggesting that the array pattern is computed using the superposition of each individual element instead of a full-wave Method of Moments (MoM) approach.

After reading, now I am confused, if I simply do the following:

   % Create the first Custom3D object using triangulation
    customShape = shape.Custom3D(tr);
   % Create the second Custom3D object using triangulation
    customShape2 = shape.Custom3D(tr2);
   % Create the third Custom3D object using triangulation
    customShape3 = shape.Custom3D(tr3);
    
   %assign locations to the Custom3D objects
    [~]= translate(customShape,[0 0 0]);
    [~]= translate(customShape2,[1 0 0]);
    [~]= translate(customShape3,[0 0 1]);
   
   %creat the array using the combined Custom3D objects
    antShapearray = customShape + customShape2 + customShape3;
    antarray = customAntenna(Shape=antShapearray);
    [~] = createFeed(antarray,[0 0 0; 1 0 0; 0 0 1],[1 1 1]);
    
   %obtain EM results
    show(antarray)
    pattern(antarray,freq)
   

Does MATLAB analyze the antenna array as a whole, or does it analyze each geometry individually and then superimpose the results?

Many thanks

[Romain]

Hi Singda Chen.

The Antenna Toolbox is the toolbox to use for a full-wave analysis.

The Phased array system toolbox uses Pattern Multiplication to obtain the total radiation pattern. It does it by multiplying the element pattern by the array factor. This method allows for a less intensive and more straightforward calculation of the overall array pattern.

You can see that in the example your mentionned : https://fr.mathworks.com/help/antenna/ug/modeling-mutual-coupling-in-large-arrays-using-embedded-element-pattern.html

In the example, the Full-wave reference is obtained using : myFullWaveArray = rectangularArray.

rectangularArray is a class defined in the antenna toolbox, class which defines for instance a pattern method and as abovementionned it performs a full-wave analysis.

Phased Array toolbox defines a different object (in its case a system object) for rectangular topology aka phased.URA. and it also defines its own pattern() method which will perform pattern multiplication instead of full-wave analysis.

In conclusion, if you want maximum accuracy, i would use the antenna toolbox and its full-wave analysis and if you expect to iterate often for system design, therefore straightforware calculation is preferred, I would use the Phased array toolbox pattern multiplication method. It really depends what you are looking for.

Note that, as explained in the example, you can improve the fidelity of your analysis by using pattern multiplication (fast) using an element pattern obtained with full-wave analysis, the so called Embedded Element method.

Best regards,

Romain