# What difference AoA algorithm between 4x4 URA and 12 elements square shaped?

I'm reading a paper from Lund University. They show the measurement and compare the accuracy of 3 types of arrays.

The interest and question I got are two types, 4x4 URA and 12 elements square-shaped. The 12 elements square-shaped have similar antennas alignment to 4x4 URA but have no middle antennas.

4x4 URA is easy to find angles by using a built-in function in MATLAB (bleAngleEstimate). This function can calculate only URA type, but not for 12 elements square-shaped.

So I want to know the difference of algorithm between these two antenna types from correlation matrix estimation, steering vector setup to MUSIC estimate.

For the most part there's no difference between the algorithm employed for the three antenna types other than the definition of the steering vector (which will be specific to the particular antenna being used).

The steering vector will be given by: $$\mathbf{e}=\left[\begin{matrix} e^{j\frac{2\pi}{\lambda}(ux_1 + vy_1)} & \cdots & e^{j\frac{2\pi}{\lambda}(ux_N + vy_N)} \end{matrix}\right]^T$$

where $$\lambda$$ is the wavelength, $$u$$ and $$v$$ are sine space directions, $$x_n$$ is the x location of the nth element, $$y_n$$ is the y location of the nth element, and $$N$$ is the number of elements in the array.

Note: I am using the sign and notation conventions from the Wikipedia article MUSIC (algorithm).

• Do you mean the $x_N$ and $y_N$ of missing elements would be skipped? So the steering vector have dimension 12x1 instead of 16x1 for 4x4 URA. If I try to change the switch pattern, the steering vector should be change the in order of $x_N$ and $y_N$. Is it right? Apr 4, 2022 at 3:15
• @Princeth Yes, don't worry about elements that don't exist, one the ones that do count. Also, the elements don't even need to be on a regular grid. Apr 4, 2022 at 23:46