Rotatable Antenna Enhanced Multicast Communication System

Abstract: Rotatable antenna (RA) provides additional spatial degrees of freedom (DoFs) for communication systems by enabling per-antenna dynamic boresight adjustment, which is attractive for fairness-oriented multicast transmission. This letter investigates an RA-enhanced downlink multi-group multicast system. Specifically, we aim to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among all users by jointly optimizing the multicast beamforming vectors and the RA boresight directions under transmit power and rotation constraints. To solve this non-convex problem, we first reformulate the max-min SINR objective via quadratic transform. Then, we develop an alternating optimization (AO) algorithm that iteratively updates the multicast beamforming and RA boresight directions. The beamforming vectors are obtained from a convex subproblem, while the boresight directions are refined using a successive convex approximation (SCA) procedure. Simulation results verify that the proposed RA-based scheme substantially enhances the fairness performance compared with fixed antenna-based and random-orientation benchmarks.

• The paper introduces the first rotatable-antenna framework for multi-group multicast, jointly optimizing beamforming and per-antenna 3D boresight directions to maximize the minimum user SINR.
• The proposed quadratic-transform and alternating-optimization algorithm combines convex beamforming updates with successive-convex-approximation orientation updates, converging in about 10 iterations with polynomial complexity.
• Simulations show up to 4.5 dB lower transmit power than fixed orientations, while performance depends on directivity, rotation limits, user angular spread, and the assumed near-field LoS channel model.

System overview and motivation

This letter studies a downlink multi-group multicast system in which a base station (BS) equipped with a uniform planar array (UPA) of $N$ rotatable antennas (RAs) serves $K$ single-antenna users partitioned into $M$ disjoint groups. The RA architecture provides per-antenna 3D boresight rotation with fixed element positions, distinguishing it from movable antenna and six-dimensional movable antenna designs that couple position and orientation reconfiguration. While prior RA work has addressed channel modeling, estimation, physical layer security, ISAC, and ISCC, all of it has focused on unicast transmission; this paper is, to the authors' knowledge, the first to consider RA-enhanced multi-group multicast. The motivation is that multicast rates are bottlenecked by the worst-channel user in each group, and per-antenna boresight adjustment can balance directional gains across users distributed heterogeneously in 3D space.

Each RA's orientation is parameterized by zenith and azimuth angles $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$, with a cosine-power gain pattern $G(\epsilon) = G_0\cos^{2p}(\epsilon)$ for incident angles within $\pi/2$, where $p > 0$ is the directivity factor and $G_0 = 2(2p+1)$ enforces power conservation. A near-field LoS-dominant channel model is adopted, so each channel coefficient depends on the pointing vector through $(\mathbf{f}_n^T \vec{\mathbf{u}}_{k,n})^p$. The design objective is to maximize the minimum user SINR over all $K$ users by jointly optimizing the multicast beamforming matrix $K$0 and the pointing matrix $K$1, subject to a total transmit power constraint $K$2 and a hardware-imposed zenith deflection limit $K$3, where $K$4 also mitigates mutual coupling between adjacent elements.

Algorithm design

Problem (P1) is non-convex due to the fractional SINR structure, the nonlinear dependence of the channels on the pointing vectors through the cosine-power pattern, and the intrinsic coupling between $K$5 and $K$6. The authors apply the quadratic transform from fractional programming to introduce auxiliary variables $K$7 and $K$8, yielding an equivalent epigraph formulation (P2) in which each SINR constraint becomes a surrogate function that is tight at the optimal closed-form $K$9.

An alternating optimization (AO) framework then updates the two variable blocks:

• Beamforming update: given $M$0 and $M$1, problem (P3) is a convex quadratically constrained program (QCP), since each constraint is a concave quadratic function of $M$2 lower-bounded by $M$3, solved via CVX.
• Boresight update: given $M$4 and $M$5, problem (P4) is handled by successive convex approximation (SCA). The desired term is lower-bounded by a second-order Taylor expansion with an explicit Lipschitz constant $M$6 derived in the appendix from the block-diagonal Hessian structure; the interference term is upper-bounded analogously using $M$7. The resulting convex subproblem (P5) relaxes the unit-norm constraint to $M$8, so its optimum is only an upper bound on (P4); the authors restore feasibility by post-hoc normalization of each pointing vector.

The AO algorithm produces monotonically non-decreasing objective values and converges to a suboptimal (Karush–Kuhn–Tucker-type local) solution within roughly 10 iterations in simulations. The overall complexity is $M$9, dominated by the beamforming QCP for larger $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$0.

Two caveats deserve emphasis: convergence guarantees are only to a local optimum, and the norm relaxation plus normalization step means the boresight subproblem solutions are feasible but not necessarily optimal for (P4). Additionally, the entire formulation rests on a LoS-dominant near-field channel model; performance under rich multipath scattering is not analyzed.

Numerical results

Simulations use a 2.4 GHz carrier, noise power $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$1 dBm, half-wavelength spacing, users on a circular arc at radius $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$2 m below a BS at height $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$3 m, and defaults of $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$4, $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$5, group size 2, $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$6, $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$7, and $$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$8 dBm. Three benchmarks—fixed directional antennas ($$\boldsymbol{\theta}_n = [\theta_{z,n}, \theta_{a,n}]^T$$9), random orientations averaged over 100 realizations, and isotropic antennas—are evaluated with the same optimal beamforming.

The key quantitative finding is that the RA-based scheme achieves the same max-min SINR as the fixed-orientation scheme with approximately 4.5 dB less transmit power, and it outperforms all benchmarks across the entire power range. Notably, the random-orientation scheme performs worst, underscoring that the gains stem from optimization of the boresight directions rather than mere reconfigurability. Max-min SINR improves monotonically with the directivity factor $G(\epsilon) = G_0\cos^{2p}(\epsilon)$0, since narrower beams combined with rotational freedom better balance intra-group gains while suppressing inter-group interference.

With respect to the user distribution angle $G(\epsilon) = G_0\cos^{2p}(\epsilon)$1, RA schemes remain superior for moderate spreads, but a trade-off emerges: beyond $G(\epsilon) = G_0\cos^{2p}(\epsilon)$2, RA performance declines as user separation complicates boresight alignment, and the isotropic benchmark overtakes the non-RA directional schemes at large angles (e.g., $G(\epsilon) = G_0\cos^{2p}(\epsilon)$3 and $G(\epsilon) = G_0\cos^{2p}(\epsilon)$4). Larger rotation limits consistently help—the $G(\epsilon) = G_0\cos^{2p}(\epsilon)$5 setting is most robust to increasing $G(\epsilon) = G_0\cos^{2p}(\epsilon)$6—and even limited ranges such as $G(\epsilon) = G_0\cos^{2p}(\epsilon)$7 yield meaningful gains over fixed orientations. When scaling to $G(\epsilon) = G_0\cos^{2p}(\epsilon)$8 groups of 4 users, the RA scheme with $G(\epsilon) = G_0\cos^{2p}(\epsilon)$9 antennas already exceeds every benchmark across the full antenna range shown, though diminishing returns appear as $\pi/2$0 grows under the fixed power constraint.

Limitations and open questions

Several limitations are acknowledged or implicit in the study. First, the LoS-only channel model excludes NLoS multipath, so the reported gains may not transfer to scattering-rich environments where directional gain alignment is less decisive. Second, the SCA-based boresight update and the norm relaxation guarantee only local optimality, and no global optimality gap is quantified. Third, the model assumes perfect channel state information and instantaneous boresight control; the mechanical latency and energy cost of rotating elements are not modeled. Finally, the evaluation considers a single-ring user geometry, leaving open how the approach performs for arbitrary 3D user distributions and whether the observed crossover against isotropic antennas at large angular spreads persists in denser deployments.

Conclusion

This letter extends rotatable antenna design from unicast to multi-group multicast transmission, formulating a max-min SINR problem jointly over multicast beamformers and per-antenna boresight directions. A quadratic-transform reformulation combined with alternating optimization—convex QCP beamforming and SCA-based orientation refinement—yields a provably convergent algorithm with polynomial complexity. Simulations demonstrate substantial fairness gains, including a 4.5 dB power saving over fixed orientations, while revealing sensitivity to wide angular user spreads and dependence on LoS-dominated propagation conditions.