Rotatable Antenna Enabled Multi-Cell Mixed Near-Field and Far-Field Communications

Abstract: Prior studies on mixed near-field and far-field communications have focused exclusively on single-cell scenarios, where both near-field and far-field users are served by the same base station (BS), leading to intra-cell mixed-field interference. In this paper, we consider a more general and practical multi-cell mixed-field scenario consisting of multiple cells, each serving multiple users, thus resulting in more complex inter-cell mixed-field interference. To address this new challenge, we propose leveraging rotatable antenna (RA) technology to enhance multi-cell mixed-field communication performance by exploiting the additional spatial degree-of-freedom introduced by RA rotation to mitigate interference in an efficient way. Specifically, we study an RA-enabled multi-cell mixed-field communication system in which each BS is equipped with an RA array to serve its associated users. We formulate a network-wide sum-rate maximization problem that jointly optimizes the transmit beamforming and the rotation angles of the RA arrays, subject to per-BS power constraints and admissible array rotation limits. To gain useful insights into the role of RAs in multi-cell mixed-field communications, we first analyze a special case with a single user per cell. For this case, we obtain a closed-form expression for the rotation-aware inter-cell mixed-field interference using the Fresnel integrals and analytically show that RA rotation can effectively mitigate such interference, thereby substantially improving system performance. For the general case with multiple users per cell, we develop an efficient double-layer algorithm: the inner layer optimizes the transmit beamforming at each BS via semidefinite relaxation and successive convex approximation; while the outer layer determines the rotation angles of the RA arrays using particle swarm optimization.

• The paper extends mixed near-field and far-field communication research to multi-cell systems, showing that inter-cell interference is governed by the victim’s inter-cell angle and can be characterized using Fresnel integrals.
• The proposed design jointly optimizes hybrid beamforming and antenna rotations through an SDR/SCA inner loop and PSO outer loop, converging in simulations in about 15 and 30 iterations, respectively.
• Numerical results show consistent sum-rate gains over fixed-antenna and ZF-based benchmarks, especially at high transmit power and with large arrays, although perfect CSI, centralized control, LoS-dominant channels, and rotation energy costs remain limitations.

Motivation and problem setting

Extremely large-scale (XL) arrays push the Rayleigh distance far beyond typical cell radii: a 1 m aperture at 28 GHz yields an effective Rayleigh distance of roughly 187 m, so most users in a 200 m-radius cell lie in the near field of their serving BS while remaining in the far field of neighboring BSs. This motivates multi-cell mixed near-field and far-field communications, where each BS serves multiple near-field users via spherical wavefronts, and inter-cell links follow planar wavefronts. Prior work on mixed-field communications addressed only single-cell settings [zhang2023mixed], leaving the inter-cell mixed-field interference structure unexplored. This paper is the first to study rotatable antenna (RA)-enabled transceiver design for this multi-cell setting, exploiting the additional spatial degree-of-freedom provided by array rotation to suppress both intra-cell near-field interference and the newly characterized inter-cell mixed-field interference.

The system comprises $M$ cells, each with a BS equipped with an $N$-element uniform linear RA array ($N = 2\tilde{N}+1$, half-wavelength spacing) serving $K$ single-antenna users through a hybrid beamforming architecture with $K \ll N$ RF chains. Intra-cell channels use second-order Taylor-expanded spherical wavefronts; inter-cell channels use far-field steering vectors whose angles are computed geometrically from BS positions. The design objective (P1) maximizes network-wide sum-rate over analog/digital beamformers and rotation angles $\boldsymbol{\theta}$, subject to per-BS power constraints, unit-modulus constraints on the analog beamformer, and admissible rotation ranges $\mathcal{C}_{\theta_m}$. The paper assumes perfect CSI at all BSs—an assumption adopted to enable analytical tractability and to characterize performance upper bounds—and notes that mixed-field interference behavior persists even under fully near-field channel modeling, since users are effectively in the far field of neighboring BSs due to large inter-site distances.

Closed-form characterization of rotation-aware interference

For the special case of two cells with one user per cell, using MRT-based analog beamforming toward each served user, the sum-rate reduces to two terms governed by normalized cross-correlations $$\rho(\psi_{i,k}, \vartheta_{i,m}, r_{i,m}, \theta_i)$$ between the far-field steering vector of the victim user and the near-field beamformer of the interfering BS. The central analytical result expresses this interference in closed form via Fresnel integrals:

$$\rho(\psi_{i,k}, \vartheta_{i,m}, r_{i,m}, \theta_i) \approx G(\gamma^{(1)}_{i,k,m}, \gamma^{(2)}_{i,m}) = \left| \frac{\widehat{C}(\gamma^{(1)}, \gamma^{(2)}) + j\widehat{S}(\gamma^{(1)}, \gamma^{(2)})}{2\gamma^{(2)}} \right|,$$

where $\widehat{C}$ and $N$0 are differences of Fresnel cosine/sine integrals evaluated at $N$1, with

$N$2

The function $N$3 decreases monotonically in both $N$4 and $N$5, attaining its maximum of one when either argument vanishes. Two structural properties carry design significance. First, the interference inflicted by BS $N$6's transmission depends only on that BS's own rotation angle $N$7—not on the victim's serving BS angle—so the analysis decouples across cells. Second, the governing geometry differs fundamentally from the single-cell case: inter-cell mixed-field interference is determined by the inter-cell angle $N$8 of the victim relative to the interferer's BS, together with the interfered user's intra-cell angle and range, rather than by shared intra-cell angles as in single-cell mixed-field systems. Numerically, the lowest victim rate occurs when the interferer's intra-cell angle coincides with the victim's inter-cell angle—not when the two users share an intra-cell angle—confirming this distinction.

Corollaries quantify when rotation helps. When the victim's inter-cell angle equals the interferer's intra-cell angle but neither is boresight ($N$9), the suboptimal rotation rotates the array toward $N = 2\tilde{N}+1$0 relative to that common direction, clipped to the admissible range; when the two angles differ, there always exists a feasible rotation strictly reducing the interference below the fixed-antenna value. Conversely, when the angles coincide, increasing the interferer's range raises the interference and erodes the benefit of rotation—consistent with the interferer transitioning to far-field behavior—so rotation gains become marginal at large ranges. A notable limitation case: when both users sit at boresight ($N = 2\tilde{N}+1$1), the optimal rotation is zero and RA provides no interference suppression benefit.

Trade-off between near-field and mixed-field suppression

Because a single rotation angle must serve both purposes, the paper identifies a trade-off between mitigating intra-cell near-field interference and inter-cell mixed-field interference, illustrated by adding a second user to one cell. When the additional user's range is small (below roughly $N = 2\tilde{N}+1$2 in the studied configuration), near-field interference dominates and ignoring it causes severe loss; at larger ranges, mixed-field interference dominates instead. In the angular dimension, misalignment with the served user's intra-cell angle hurts more than misalignment with the inter-cell angle, so the "mixed-field-only" benchmark performs better across varying angles. The practical prescription is that rotation should prioritize whichever interference source is currently moderate, balancing against the dominant one. The paper also discusses implementation feasibility: MEMS-based mechanical RAs respond within microseconds to milliseconds, electronic RAs from nanoseconds to milliseconds, and achievable angular accuracy is on the order of hundredths to thousandths of a wavelength; a two-timescale design using statistical CSI for rotation would make the instantaneous-CSI design presented here an upper bound.

Double-layer algorithm for the general multi-user case

For $N = 2\tilde{N}+1$3 users per cell, the joint problem is non-convex with tightly coupled variables. The proposed solution alternates between two layers:

• Inner layer (beamforming): For fixed rotations, the analog beamformer aligns each column with the near-field steering vector of its target user; the digital beamformers are then optimized by lifting $N = 2\tilde{N}+1$4, expressing the negative sum-rate as a difference of convex functions, applying SCA via first-order Taylor lower bounds on the concave component, and dropping the rank-one constraint via SDR. The resulting convex problem (P5) is solved with interior-point methods; rank-one solutions are reported to be consistently attainable based on established SDR tightness results.
• Outer layer (rotation): With beamformers fixed, rotation angles are optimized by PSO with inertia weight annealed between 0.4 and 0.9, learning factors $N = 2\tilde{N}+1$5, population $N = 2\tilde{N}+1$6, and $N = 2\tilde{N}+1$7 iterations, with infeasible angles projected back onto $N = 2\tilde{N}+1$8.

Convergence is argued constructively: the inner-layer objective is monotonically non-increasing and bounded, and PSO's global best is non-decreasing, so the overall algorithm converges to a stationary value. Total complexity scales as $N = 2\tilde{N}+1$9, dominated by the interior-point solves; the authors note that parallel evaluation of PSO particles and lower-complexity inner-layer substitutes (fractional programming, ZF) can mitigate this, though real-time deployment remains open. Scalability concerns are acknowledged candidly: the centralized design requires global CSI, and distributed alternatives (two-timescale coordination, block-coordinate rotation updates) are deferred to future work.

Numerical findings

Simulations use $K$0-cell deployments with $K$1, $K$2, $K$3 GHz, $K$4 dBm, noise floor $K$5 dBm, three NLoS paths per link, and rotation limits $K$6. Key observations:

• Convergence: the SCA beamforming loop stabilizes in about 15 iterations; PSO in about 30.
• Transmit power sweep: the joint design outperforms all benchmarks, with the gap widening for $K$7 dBm because ZF-based and fixed-antenna baselines saturate—the former sacrifices array gain and cannot suppress inter-cell mixed-field interference, the latter lacks the rotational DoF entirely. Notably, RA+ZF beats FA+BF below 20 dBm but falls behind above it, indicating that sophisticated digital beamforming becomes essential once mixed-field interference intensifies. RA+ZF matches exhaustive discrete rotation search (100 quantization points per angle), validating the continuous PSO optimizer.
• User count sweep: all schemes improve with $K$8, since near-field user rates dominate the sum-rate, but the proposed scheme and FA+BF grow substantially faster than ZF-based schemes, demonstrating stronger resilience to escalating intra-cell and inter-cell interference.
• Antenna count sweep: FA+BF initially outperforms RA+ZF, but the ordering reverses once $K$9, as finer spatial resolution lets ZF suppress intra-cell interference cheaply enough that rotation-assisted ZF prevails.

The simulations exclude the energy cost of array rotation itself; the authors state plainly that no validated power-consumption model for RA hardware exists and that energy-efficiency analysis is left open.

Limitations and open questions

Several assumptions bound the applicability of the results. The analytical section relies on LoS-dominant channels and MRT-based analog beamforming; scenarios with blocked LoS or rich scattering are explicitly not covered. Perfect CSI is assumed throughout, and the rotation-dependent parametric channel estimation needed for the outer-layer search is more demanding than conventional pilot-based estimation, with only an iterative estimation-and-adjustment procedure sketched as a remedy. The closed-form corollaries provide suboptimal rather than globally optimal rotation angles, and no optimality guarantee exists for the PSO outer layer beyond empirical convergence. Finally, the centralized architecture, the omitted rotation energy consumption, and real-time low-complexity implementations all remain unresolved questions raised by this work.

Conclusion

This paper extends mixed near-field/far-field communication theory from single-cell to multi-cell systems and establishes, via Fresnel-integral analysis, that inter-cell mixed-field interference obeys geometric rules distinct from its single-cell counterpart—governed by inter-cell rather than intra-cell angles—and that RA rotation offers a tractable, effective lever against it, except in degenerate boresight or large-range configurations. The double-layer SDR/SCA-plus-PSO design delivers consistent sum-rate gains over fixed-antenna and partially optimized benchmarks, with the advantage growing in high-power and interference-limited regimes. The main caveats—LoS-dominant analysis, perfect CSI, centralized optimization, and unmodeled rotation energy—define the immediate open problems for making RA-enabled multi-cell mixed-field systems practically deployable.