Uniform Circular Array (UCA)

• Uniform Circular Array (UCA) is a planar antenna configuration with N equally spaced elements on a circle, providing 360° rotational symmetry.
• The UCA enables omni-directional transmission and reception, foundational for applications in MIMO, millimeter-wave and terahertz communications, and spatial signal processing.
• Its design supports near-field beamforming and spatial mode multiplexing by leveraging propagation invariance and spectral decomposability for precise directional control.

A uniform circular array (UCA) is a planar antenna geometry in which $N$ radiating elements are placed with equal angular spacing on a circle of radius $R$ in a reference plane, typically the $x$–$y$ plane. This configuration provides full $360^\circ$ rotational symmetry, enabling omni-directional or spatially selective transmission and reception, and forms the basis for a wide range of spatial signal processing strategies in communications, radar, and sensing. UCA structures are foundational in modern research on massive MIMO, millimeter-wave and terahertz transmission, near-field beamforming, spatial mode multiplexing (especially orbital angular momentum, OAM), and high-dimensional parameter estimation, due to their unique propagation invariance, spectral decomposability, and suitability for novel code and beam designs.

1. Fundamental Geometry and Steering Properties

A canonical UCA with $N$ elements of radius $R$ situates its $n$-th sensor at

$\phi_n = \frac{2\pi n}{N}, \quad n=0,\ldots,N-1$

with Cartesian coordinates $(x_n, y_n, z_n) = (R \cos\phi_n, R \sin\phi_n, 0)$. The array manifold (steering vector) for an impinging wave of wavenumber $R$0 from azimuth $R$1 and elevation $R$2 is

$R$3

For a plane wave from broadside, this reduces to uniform phases; for OAM and spatial mode decomposition, the symmetry of the geometry matches the eigenfunctions of angular momentum around the $R$4-axis. In near-field scenarios, the exact spherical-wave propagation distance from a point at polar $R$5 is $R$6 (Guo et al., 2024, Wu et al., 2022).

2. Near-Field Focusing, Effective Rayleigh Distance, and Coverage

The transition from far to near field is governed by the Rayleigh distance $R$7. The UCA, unlike ULAs, achieves an angle-invariant effective Rayleigh distance (ERD), given for a tolerable beamforming loss $R$8 by

$R$9

This constant azimuthal ERD provides a large, uniform near-field region, whereas ULAs' near fields shrink substantially off boresight. UCA near-field beamforming employs spherical wavefront matching rather than plane-wave steering, enabling multi-parameter focusing (angle and range) for users or targets anywhere on the $x$0–$x$1 plane [221