# 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.

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.
• 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