⚡ electrical engineering

Uniform Circular Arrays in Near-Field: Omnidirectional Coverage with Limited Capacity

This paper investigates the near-field spatial multiplexing performance of uniform circular arrays (UCAs) compared to uniform linear arrays (ULAs) by introducing a new angle-dependent metric called the effective beamfocusing Rayleigh distance (EBRD), ultimately finding that while UCAs offer enhanced angular coverage, ULAs generally provide superior sum-rate performance under fixed element constraints.

Original authors: Ahmed Hussain, Asmaa Abdallah, Abdulkadir Celik, Ahmed M. Eltawil

Published 2026-04-28

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CC BY 4.0

Original authors: Ahmed Hussain, Asmaa Abdallah, Abdulkadir Celik, Ahmed M. Eltawil

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are at a massive, crowded music festival. You are trying to shine a high-powered flashlight at a specific friend in the crowd so they can see your signal.

This paper is about the best way to design that "flashlight" (an antenna array) to make sure you hit your friend perfectly without accidentally blinding everyone else around them.

The Two "Flashlight" Designs

The researchers compared two main ways to arrange the tiny lights that make up our future 6G antennas:

The ULA (The "Line of Lights"): Imagine holding a long, straight stick with tiny LEDs lined up in a single row.
The UCA (The "Ring of Lights"): Imagine holding a hula hoop with those same LEDs arranged in a circle.

The Problem: The "Near-Field" Blur

In the old days of wireless (the "Far-Field"), signals traveled like flat sheets of paper. But with new, massive antennas, we are entering the "Near-Field." In this zone, signals travel like expanding bubbles or spheres.

Because the signal is a "bubble," we can do something amazing: Beamfocusing. Instead of just pointing the light in a certain direction, we can point it at a specific spot (like a specific person standing 10 feet away).

However, there is a catch. Even if you aim perfectly, the light isn't a laser; it has a certain "thickness" or "depth." If your light beam is too "thick," you’ll accidentally hit the person standing behind your friend, causing interference (like shouting a message to one person but accidentally being heard by five others).

The Comparison: Who wins?

The researchers looked at two ways to build these antennas:

Scenario A: You have a limited number of lights (Fixed Element Count)

The Line (ULA) wins easily. Because the lights are in a long line, they can create a very "thin" and precise beam. It’s like having a long, narrow spotlight.
The Ring (UCA) struggles. Because the lights are wrapped in a circle, they don't spread out as far. Their "spotlight" ends up being much "fatter" and blurrier. This means they accidentally hit too many people, causing a mess of interference.

Scenario B: You have a limited amount of space (Fixed Aperture Length)

The Ring (UCA) gets a tiny boost. If you are only allowed a 1-meter wide space to build your antenna, the Ring can actually create a slightly "thinner" beam than the Line.
But the Square (URA) is the King. The researchers also tested a "Square" grid (like a checkerboard of lights). The square wins here because it can pack way more lights into that same 1-meter space, making the beam incredibly sharp and powerful.

The "Aha!" Moment (The Conclusion)

For a long time, people thought the Ring (UCA) would be better because it can "see" in every direction (360 degrees) equally.

But this paper reveals a surprising truth: Coverage doesn't equal Capacity.

Just because the Ring can point its light in any direction doesn't mean it can handle a lot of people at once. Because its beam is "fatter" and "blurrier" than the Line, it creates too much "noise" for the people standing nearby.

The takeaway: If you want to serve a huge crowd of people with high-speed data, a long line or a dense square of antennas is much better at "focusing" on individuals than a ring is. The Ring is great for seeing everything, but the Line is better at talking to someone without bothering everyone else.

Technical Summary: Uniform Circular Arrays in Near-Field: Omnidirectional Coverage with Limited Capacity

1. Problem Statement

As wireless networks transition toward Ultra-Massive MIMO (UM-MIMO), communication is increasingly expected to occur in the radiative near-field. Unlike the far-field, where signals are modeled as planar waves, the near-field involves spherical wavefronts, allowing for "beamfocusing"—the ability to separate users not just by angle, but also by distance (depth).

While Uniform Circular Arrays (UCAs) are known to provide omnidirectional angular coverage (unlike the boresight-dependent Uniform Linear Arrays (ULAs)), it remains unclear whether this enhanced angular coverage translates into superior spatial multiplexing (capacity) performance. The core research question is: Does the UCA's ability to cover all angles compensate for its potential limitations in beamfocusing precision and spatial correlation?

2. Methodology

The authors conduct a rigorous comparative analysis between ULAs and UCAs using two distinct design constraints: fixed antenna element count and fixed aperture length.

New Metric Introduction: To accurately define the boundaries of effective beamfocusing, the authors introduce the Effective Beamfocusing Rayleigh Distance (EBRD). This metric defines the maximum distance at which a beam can be effectively focused in the distance domain.
Mathematical Modeling:
- They derive closed-form expressions for beamdepth ( $r_{BD}$ )—the distance interval where the array gain remains within 3 dB of its maximum.
- They model the array gain of the UCA using the Zero-Order Bessel Function ( $J_0(\zeta)$ ), whereas the ULA is modeled using Fresnel integrals.
System Model: A downlink multi-user UM-MIMO system is assumed, employing Maximum Ratio Transmission (MRT) under a Rician fading channel model (incorporating both LoS and NLoS paths).
Simulation Setup: Monte Carlo simulations are performed at 30 GHz, comparing ULA, UCA, and various Uniform Rectangular Array (URA) configurations.

3. Key Contributions

Derivation of EBRD for UCAs: The paper provides the first formal derivation of the EBRD for circular geometries, establishing the limit for effective near-field beamfocusing.
Analytical Comparison of Beam Characteristics: The authors mathematically prove how array geometry affects beamdepth and EBRD. They show that while UCAs offer rotational symmetry in azimuth, their beamfocusing performance is highly dependent on the elevation angle ( $\theta$ ).
Asymptotic Orthogonality Analysis: The study characterizes how the array gain functions decay. They demonstrate that ULA (sinc/Fresnel) decays faster ( $1/x$ ) than UCA (Bessel, $1/\sqrt{x}$ ), implying that ULAs achieve better spatial separation (lower correlation) in both angular and distance domains.

4. Results and Findings

The performance of the arrays depends heavily on the hardware constraints:

Constraint: Fixed Number of Antenna Elements ( $N_{BS}$ ):
- ULA wins significantly. Because a ULA spreads its elements over a longer linear distance, it achieves a much larger Rayleigh distance and a narrower beamdepth.
- UCA suffers from wider beamdepth and higher forelobe levels (8–10 dB higher than ULA), leading to higher inter-user interference and lower sum-rates.
Constraint: Fixed Aperture Length ( $D$ ):
- Performance gap narrows. When the physical size is fixed, the UCA requires many more elements to match the ULA's aperture, which helps its performance.
- UCA shows marginal gains in high-user-loading scenarios due to a slightly narrower beamdepth compared to the ULA under this specific constraint.
Spatial Correlation: The UCA exhibits higher spatial correlation between users due to its oscillatory Bessel-function-based gain pattern, which limits its ability to multiplex users effectively compared to the ULA.

5. Significance

This paper provides a critical reality check for the deployment of UCAs in near-field communications. While UCAs are attractive for their omnidirectional coverage, they are not a "silver bullet" for capacity. The study reveals a fundamental trade-off: the geometric symmetry of the UCA comes at the cost of higher spatial correlation and less precise beamfocusing compared to the ULA. This work is essential for engineers designing UM-MIMO systems, as it highlights that array geometry choice must be driven by whether the priority is coverage area (UCA) or spatial multiplexing capacity (ULA/URA).