Uniform Circular Arrays: Theory & Applications

• Uniform Circular Arrays (UCAs) are antenna configurations with elements evenly distributed along a circle, offering rotational symmetry and uniform spatial coverage.
• Their circulant structure enables DFT-diagonalization, achieving full spatial multiplexing in LoS MIMO and efficient OAM multiplexing through helical phasefronts.
• Advanced techniques like delay-phase precoding and precise calibration allow UCAs to maintain near-optimal performance in wideband and dense network scenarios.

A uniform circular array (UCA) consists of $N$ antenna elements distributed equidistantly along the circumference of a circle with radius $R$ in a plane, most commonly the $xy$-plane. Each element’s position can be described by a polar angle (azimuthal position) $\psi_n = 2\pi n/N$ for $n=0,1,\dots,N-1$, yielding a 2D spatial distribution with complete rotational symmetry. This geometry endows UCAs with key properties: identical array response for all azimuth angles, structure amenable to DFT-based diagonalization, and unique channel characteristics in LoS, near-field, wideband, and OAM-multiplexed communications.

1. Geometric Model, Array Manifold, and Channel Structure

Each element of a UCA lies at $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$. For plane wave incidence from azimuth angle $\theta$ (with elevation $\phi$), the array manifold (steering vector) is

$$\mathbf{a}(\theta, \phi) = \left[e^{j k R \cos(\theta-\psi_0)}, \dots, e^{j k R \cos(\theta-\psi_{N-1})}\right]^T$$

where $k=2\pi/\lambda$. For LoS MIMO systems utilizing transmit and receive UCAs separated by $R$0, the element-to-element distance under far-field $R$1 is

$R$2

with misalignment terms for rotation $R$3, tilting $R$4, and center-shift vector $R$5 included as per the generic model (Jeon et al., 2020).

The normalized LOS channel coefficient is

$R$6

with the channel matrix $R$7 factoring into circulant (DFT-diagonalizable) forms. Channel singular values depend only on the radii-product-to-distance ratio (RPDR) $R$8 and relative array rotation, remaining independent of tilting and center-shift (Jeon et al., 2020).

2. DFT-Diagonalization, Multiplexing, and Optimal Design

A core property, the circulant structure, allows $R$9 to be diagonalized by the DFT matrix $xy$0: $xy$1 which immediately yields singular values $xy$2 as explicit functions of $xy$3 and $xy$4: $xy$5 Thus, UCA-based LoS MIMO achieves full spatial multiplexing with $xy$6 streams per symbol, when $xy$7 is set optimally. Practically, $xy$8 is found by 1D search to maximize the sum capacity: $xy$9 with power allocation $\psi_n = 2\pi n/N$0. Selecting $\psi_n = 2\pi n/N$1 (offline for $\psi_n = 2\pi n/N$2), then choosing $\psi_n = 2\pi n/N$3 so that $\psi_n = 2\pi n/N$4, nearly achieves orthogonal channel conditions; ZF and water-filling receivers then deliver maximal throughput without CSI feedback (Jeon et al., 2020).

$\psi_n = 2\pi n/N$5	Optimal $\psi_n = 2\pi n/N$6 (SNR 15dB)	$\psi_n = 2\pi n/N$7 at $\psi_n = 2\pi n/N$8m
4	1.54	0.31 m
8	3.09	0.44 m
12	4.57	0.54 m
16	5.98	0.62 m

With optimal $\psi_n = 2\pi n/N$9, the channel matrix approaches unitarity, enabling robust spatial multiplexing with ZF (or ZF+SIC) processing (Jeon et al., 2020).

3. Channel-Independent Beamforming for UCA LoS MIMO

Channel-independent beamforming in UCA systems exploits the circularly symmetric geometry to enable fixed, DFT/IDFT-based precoding and combining that "decouples" the MIMO channel into parallel links. With parallel or aligned UCAs (with or without coaxiality), the fixed transmit matrix $n=0,1,\dots,N-1$0 and receive matrix $n=0,1,\dots,N-1$1 (where $n=0,1,\dots,N-1$2 is the DFT/IDFT, $n=0,1,\dots,N-1$3 are deterministic phase precompensation) reduce the effective channel $n=0,1,\dots,N-1$4 to a diagonal form, enabling symbol-wise ML detection at extremely reduced complexity: $n=0,1,\dots,N-1$5 Bit-error-rate performance matches that of full CSI-based MIMO processing, while computational cost drops by several orders of magnitude for moderate $n=0,1,\dots,N-1$6 (Jing et al., 2018, Jing et al., 2024). This approach extends to both coaxial and laterally shifted UCA pairs, provided far-field ($n=0,1,\dots,N-1$7) holds.

4. Orbital Angular Momentum (OAM) Multiplexing with UCAs

UCAs are the canonical structure for generating and detecting radio OAM modes, where feeding element $n=0,1,\dots,N-1$8 with phase $n=0,1,\dots,N-1$9 realizes helical phasefronts indexed by integer $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$0. The array factor for OAM mode $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$1 is

$\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$2

where $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$3 is the Bessel function of order $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$4, yielding a doughnut-shaped beam with central null for $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$5 (Gaffoglio et al., 2015, Chen et al., 2020). The link budget for OAM transmission acquires an extra decay $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$6 with distance. Mode isolation is high—mode sorters and precise alignment (mechanical tolerance $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$7) achieve $\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$8 dB inter-mode isolation in field experiments. For high-order OAM modes, divergence and attenuation grow rapidly; concentric UCAs (multiple rings) enable capacity-optimized multiplexing using several parallel low-order modes, with water-filling power allocation across rings and modes (Jing et al., 2024, Jing et al., 2024).

5. Wideband Beamforming, Spatial Effects, and Delay-Phase Precoding

UCA hybrid precoding architectures for mmWave/THz operate under spatial-wideband impairments. Unlike ULAs (which suffer beam split), UCAs manifest a "beam defocus" effect: analog phase shifters cannot maintain constructive interference across ultra-large bandwidths, so the main-lobe gain drops at frequencies away from the carrier. The frequency-domain beam pattern is analytically

$\mathbf{p}_n = [R\cos\psi_n,\, R\sin\psi_n,\,0]^T$9

where $\theta$0. Delay-phase-precoding (DPP) schemes remedy defocus by integrating true-time-delay (TTD) devices per element or subarray, producing frequency-dependent phase shifts and restoring constructive summation over wideband. Analytical and simulation results show DPP with $\theta$1 TTD taps recovers $\theta$2 of the optimum gain and achieves near-ideal spectral efficiency across multi-GHz bandwidths; narrowband PS-only architectures suffer bandwidth-dependent loss (Wu et al., 2023).

6. Near-Field, XL-MIMO, and Localization

UCAs, due to their rotational symmetry, support angle-independent and omnidirectional near-field beamforming and localization. Key metrics such as effective Rayleigh distance (ERD) quantify the spatial region for beamfocusing; for UCAs,

$\theta$3

is angle-invariant, in contrast to ULAs, whose ERD shrinks at off-broadside angles (Wu et al., 2022). In radiative near-field, closed-form expressions for beamdepth and EBRD enable analytic trade-off of coverage versus capacity under element-count or fixed-aperture constraints (Hussain et al., 16 Nov 2025). FFT-accelerated backprojection on sectored UCAs achieves ML-consistent localization with nearly linear complexity, and exact angle quantization with massive UCAs yields real-time 2D-DOA estimation robust to nonuniform noise (Liu et al., 2024, Gong, 17 Jul 2025).

7. Design Guidelines, Implementation, and Calibration

Optimal UCA LoS MIMO mandates setting the RPDR near $\theta$4 for orthogonalizable channels; this tunes $\theta$5 for a given $\theta$6 (Jeon et al., 2020). When mechanical constraints limit $\theta$7, codebook-based phase precoding with a small feedback overhead (6–10 bits) can recover most capacity loss incurred by sub-optimal $\theta$8.

Odd-element UCAs, particularly $\theta$9, facilitate wideband decoupling and matching with compact DMNs; advanced microstrip designs (two-stage or star-triangle) extend matching/decoupling bandwidth to several percent RF BW, outperforming simple neutralization-line DMNs (Kornprobst et al., 2021). Calibration—including mutual coupling—can be performed via sparse recovery with an integrated wideband dictionary, combining subspace SVD projection, iterative LASSO, and non-numerical atomic construction (Bozorgasl et al., 2024).

In massive MIMO, UCAs guarantee "favorable propagation": inter-user interference decays as $\phi$0 for fixed spacing $\phi$1 in pure-LoS, an asymptotic property derived via Bessel expansion. Stacking UCAs vertically (cylindrical arrays) achieves double-sided FP for distinct elevation and azimuth (Anarakifirooz et al., 2021).

8. Beamforming, User-Dense Networks, and Concentric UCAs

Concentric UCAs (UCCAs) with multiple rings enable sharper beams, higher beam-packing gains, and enhanced spatial multiplexing. Large-aperture arrays with spacing $\phi$2 yield narrower HPBW and up to $\phi$3 higher angular packing capacity than conventional planar arrays. SINR and spectral efficiency for UCCAs in dense 5G scenarios exceed planar arrays by up to $\phi$4; moderate sidelobe levels and high efficiency are retained provided amplitude tapering and calibration are implemented (Hasan et al., 2022).

Conclusion

Uniform circular arrays represent a highly symmetric, analytically tractable transceiver architecture offering unique advantages in LoS MIMO, OAM multiplexing, wideband beamforming, and near-field spatial sensing. Their channel structure, when properly exploited (by RPDR tuning or DFT-based beamforming), achieves maximal multiplexing rate and computational efficiency. UCA’s omnidirectional symmetry underpins angle-invariant coverage, favorable propagation, and simplified calibration. Next-generation enhancements—multi-ring concentric architectures, delay-phase precoding, and sparse calibration—continue expanding UCA's practical relevance in ultra-dense, bandwidth-rich communication paradigms.