---
title: Uniform Circular Array (UCA)
url: https://www.emergentmind.com/topics/uniform-circular-array-uca
type: topic
---

# Uniform Circular Array (UCA)

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 $k=2\pi/\lambda$ from azimuth $\phi$ and elevation $\theta$ is
$$
a(\theta, \phi) = \left[ e^{j k R \sin\theta \cos(\phi - \phi_n)} \right]_{n=0}^{N-1}.
$$
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 $z$-axis. In near-field scenarios, the exact spherical-wave propagation distance from a point at polar $(r,\theta)$ is $d_n = \sqrt{r^2 + R^2 - 2 r R \cos(\theta - \phi_n)}$ [2404.02811, 2212.14654].

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

The transition from far to near field is governed by the Rayleigh distance $r_\mathrm{Rayleigh} = {8 R^2}/{\lambda}$. The UCA, unlike ULAs, achieves an angle-invariant effective Rayleigh distance (ERD), given for a tolerable beamforming loss $\delta$ by
$$
r_{\mathrm{ERD}}^{(\mathrm{UCA})} = \frac{\pi R^2}{2 \lambda J_0^{-1}(1-\delta)}.
$$
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 $x$–$y$ plane [221

Source: https://www.emergentmind.com/topics/uniform-circular-array-uca