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Joint Antenna Rotation and Polarforming for Satellite Communications

Xingxiang Peng, Qingqing Wu, Jingfeng Chen, Wei Feng, Wen Chen, Zan Li

arXiv:2610.35397v1eess.SP

TL;DR

Closely aligned satellite-user directions and finite array apertures can limit spatial discrimination, while polarization offers an additional channel-shaping degree of freedom. This paper jointly designs antenna rotation, polarforming, and receive filters with a WMMSE-based alternating method. Simulations report higher throughput for the joint design than for either single-technique benchmark, with antenna rotation and polarforming contributing complementary benefits.

  • Problem

    Closely aligned propagation directions and finite array apertures can limit spatial discrimination, while satellite geometry changes propagation directions and polarization projections.

    Source: §I · p. 1

  • Method

    A WMMSE-based alternating algorithm jointly optimizes RA orientation trajectories, element-wise polarformers, and digital receive filters, using semi-closed-form polarformer updates and feasible boresight-trajectory updates.

    Source: §I · p. 1, §III · p. 3, B. Polarforming Update · p. 4

  • Results

    About 1.04 Mbps at 23 dBm, with the joint design gaining 67.7% over polarforming only and 85.7% over RA only.

    Source: §IV · p. 6

  • Takeaways & Limitations

    Antenna rotation reallocates directional gains across clusters, while polarforming improves channel separability, and simulations show their benefits are complementary.

    Source: §V · p. 6

Abstract

from arXiv · show

This paper investigates joint antenna rotation and polarforming for low-Earth-orbit (LEO) communications, where a satellite equipped with rotatable dual-polarized antenna elements receives uplink signals from ground terminals (GTs) distributed across multiple clusters. In particular, antenna rotation redistributes directional gains across angularly separated clusters, while polarforming improves the separability of spatially correlated GT channels within each cluster. We formulate a weighted sum-rate maximization problem that jointly optimizes rotatable antenna (RA) orientation trajectories, element-wise polarformers, and digital receive filters under steering-range and inter-epoch slew constraints. To solve the resulting nonconvex problem, we develop a weighted minimum mean-square error (WMMSE)-based alternating algorithm, in which the optimal polarformer for each element is derived in semi-closed form, while an exact boresight parameterization yields convex feasible sets for RA-trajectory optimization, enabling Armijo-based gradient updates. Simulation results demonstrate that the proposed joint design outperforms benchmark schemes and reveal the complementary roles of antenna rotation in directional-gain allocation and polarforming in improving channel separability.

I. INTRODUCTION

Satellite antenna rotation and polarforming address different channel-shaping needs: rotation reallocates directional gain across clusters, while polarforming can separate spatially correlated users within clusters. The paper models their joint design for a moving satellite with mechanically constrained antenna trajectories.

I. INTRODUCTION

  • Polarforming complements spatial channel shaping where closely aligned propagation directions and finite array apertures limit user discrimination, a concern heightened by changing satellite geometry.The paper identifies satellite systems as a setting where combining spatial and polarization-domain channel shaping merits further investigation.Source: §I · p. 1
  • The proposed design jointly optimizes RA orientation trajectories, element-wise polarformers, and digital receive filters for multi-cluster GTs under steering-range and inter-epoch slew constraints.A WMMSE-based alternating algorithm uses semi-closed-form polarformer updates and Armijo-based gradient updates for RA trajectories.Source: §I · pp. 1–2
  • RA orientation redistributes directional gains across angularly separated clusters, while element-wise polarforming exploits polarization diversity to improve separability among spatially correlated GTs within a cluster.The geometry gives clusters different arrival directions while GTs in each cluster have similar propagation directions.Source: §I · p. 1

A. Two-Timescale Operation Protocol

  • The system uses a two-timescale protocol: RA boresights stay fixed within each control epoch, while polarforming and digital combining update per slot.Guard intervals precede epochs after the first for mechanical slewing.Source: A. Two-Timescale Operation Protocol · p. 2

B. Dynamic Satellite and Clustered-GT Geometry

  • The model places fixed GTs in Earth-centered coordinates and represents satellite position in a satellite-centric coordinate system to determine slant ranges and look directions.The satellite-centric axes point along-track, opposite the orbital normal, and toward the geocenter.Source: B. Dynamic Satellite and Clustered-GT… · p. 2

C. Satellite-Side RA and Polarforming Configuration

The satellite uses a planar array of rotatable elements with independently steered boresights and two orthogonal polarization ports. Each element coherently combines its port signals using a unit-norm polarformer.

C. Satellite-Side RA and Polarforming Configuration

  • The fixed UPA lies in the x–y plane, with element positions indexed by the array's two dimensions.The element index is formed from the x- and y-direction indices and the x-dimension size.Source: C. Satellite-Side RA and Polarforming… · p. 2
  • The unit boresight of each element is constrained to a maximum tilt from the satellite-facing z-axis and to a maximum rotation between epochs.The inter-epoch limit is the maximum mechanical angular speed multiplied by the guard interval.Source: C. Satellite-Side RA and Polarforming… · p. 2
  • Each UPA element has two co-located orthogonal polarization ports whose signals are coherently combined by a unit-norm polarformer.The polarization basis is well defined for maximum boresight tilt below π/2.Source: C. Satellite-Side RA and Polarforming… · p. 2

D. Polarization-Aware Uplink Channel Model

The channel model combines propagation loss, directional gain, polarization response, and array phase for each GT-to-element link. It accounts for polarization projections as the satellite geometry and antenna orientations change.

D. Polarization-Aware Uplink Channel Model

  • The GT–satellite links are modeled as far-field, polarization-preserving line-of-sight channels, with directional receive gain and free-space path gain.The antenna directivity is controlled by the cosine-power parameter p.Source: D. Polarization-Aware Uplink Channel… · p. 2
  • GT polarization is represented in the local east–north basis by a Jones vector whose orientation is independently drawn and fixed over the observation interval.The orientation angle is uniformly distributed on [0, π).Source: D. Polarization-Aware Uplink Channel… · pp. 2–3
  • The model combines propagation loss, directional gain, polarization response, and array-induced phase into element-wise channels, then stacks them into each GT's uplink channel vector.The resulting channel captures satellite geometry, RA boresight steering, and receive polarforming; the polarization response is independent of the chosen transverse-plane basis.Source: D. Polarization-Aware Uplink Channel… · p. 3

E. Multiuser Uplink Reception and Problem Formulation

The receiver estimates each GT's symbol from the shared uplink signal using a linear receive filter, and the weighted effective sum rate accounts for achievable rates and guard overhead. The paper jointly optimizes receive filters, polarformers, and RA boresights under the stated constraints.

E. Multiuser Uplink Reception and Problem Formulation

  • The received uplink signal combines all GT transmissions with noise, and each GT's symbol estimate is formed using its linear receive filter.The GT symbols have unit power and each GT has a fixed transmit power.Source: E. Multiuser Uplink Reception and… · p. 3
  • The weighted effective sum rate uses each GT's achievable rate, positive GT weights, and guard-interval overhead.The achievable rate is B log2(1 + γ_k[n]).Source: E. Multiuser Uplink Reception and… · p. 3
  • The joint problem optimizes the boresights, polarformers, and receive filters, but is highly nonconvex because of channel coupling, unit-norm constraints, and inter-epoch slew coupling.Boresight constraints impose steering-range and slew limits, while polarformers must have unit norm.Source: E. Multiuser Uplink Reception and… · p. 3

III. THE PROPOSED SOLUTION

The proposed solution reformulates weighted sum-rate maximization as an equivalent WMMSE problem, exposing block-wise updates for receive filters, polarformers, and RA boresights. This structure supports an alternating optimization framework.

III. THE PROPOSED SOLUTION

  • The weighted sum-rate problem is reformulated as an equivalent WMMSE problem, exposing tractable block-wise optimization of receive filters, polarformers, and RA boresights.The formulation follows the standard rate–MSE relationship.Source: §III · p. 3, A. WMMSE Reformulation · p. 3

A. WMMSE Reformulation

B. Polarforming Update

With receive filters and MSE weights fixed, polarforming is optimized slot by slot. Within a slot, element polarformers remain coupled, so the algorithm updates them cyclically using a globally optimal element-wise solution.

B. Polarforming Update

  • For fixed receive filters and MSE weights, polarforming optimization decouples across slots, and the slot index can be omitted because each subproblem has the same structure.Source: B. Polarforming Update · p. 4
  • The channel is rewritten to expose each polarformer’s dependence, and the resulting symbol-estimation MSE couples the antenna elements’ polarformers.Source: B. Polarforming Update · p. 4
  • The algorithm cyclically optimizes one element’s polarformer while holding the others fixed, globally solving each element-wise subproblem.The optimality conditions parameterize the polarformer for a given Lagrange multiplier; a one-dimensional search determines the optimal multiplier.Source: B. Polarforming Update · p. 4

C. Boresight-Trajectory Update

The boresight trajectory is represented by two-dimensional coordinates that preserve steering and slew feasibility through a convex feasible set. Because the trajectory objective remains nonconvex, the algorithm uses feasible first-order updates and an Armijo line search.

C. Boresight-Trajectory Update

  • An exact two-dimensional boresight parameterization makes the steering and inter-epoch slew constraints define a convex feasible set.The coordinates collect the first two SCCS components of each boresight; the resulting set supports a reformulation of the trajectory problem.Source: C. Boresight-Trajectory Update · pp. 4–5
  • The trajectory objective remains nonconvex, so the update linearizes it at the current trajectory and solves a convex subproblem.Source: C. Boresight-Trajectory Update · p. 5
  • The convex trajectory subproblem separates across antenna elements and can be solved in parallel.Source: C. Boresight-Trajectory Update · p. 5
  • An Armijo line search selects a feasible update that preserves the original steering-range and slew constraints.The algorithm recovers the physical boresights from the parameterized coordinates after the update.Source: C. Boresight-Trajectory Update · p. 5

D. Overall Algorithm and Convergence Analysis

Each block update does not increase the WMMSE objective, and the objective sequence converges because it is bounded below.

D. Overall Algorithm and Convergence Analysis

  • The WMMSE objective sequence is nonincreasing and converges because it is bounded below.Polarforming subproblems are globally solved, boresight updates ensure feasible descent through Armijo line search, and receive filters and MSE weights are updated in closed form.Source: D. Overall Algorithm and Convergence… · p. 5

IV. SIMULATION RESULTS AND DISCUSSION

Simulations compare joint design, RA-only, polarforming-only, and fixed benchmarks across transmit powers and user-clustering patterns. Joint design leads overall, while the relative value of antenna rotation and polarforming changes with operating conditions and cluster density.

IV. SIMULATION RESULTS AND DISCUSSION

  • At low transmit powers, RA steering improves directional-gain allocation across clusters, while polarforming becomes increasingly effective as interference grows and eventually outperforms RA-only optimization.Polarforming exploits polarization diversity to improve separability of spatially correlated user channels.Source: §IV · pp. 5–6
  • The joint design consistently achieves the highest throughput, reaching about 1.04 Mbps at 23 dBm, with gains of 67.7% and 85.7% over polarforming-only and RA-only optimization, respectively.Source: §IV · p. 6
  • As the fraction of GTs per cluster increases, effective sum rate generally decreases because users become more spatially concentrated and harder to separate spatially.The comparison fixes K = 12 while varying cluster count and GTs per cluster.Source: §IV · p. 6
  • RA-only optimization performs better when users are spread across many clusters, whereas polarforming becomes relatively more effective when users concentrate in fewer clusters.Joint design consistently achieves the highest throughput across the clustering patterns.Source: §IV · p. 6

V. CONCLUSION

The paper concludes that joint antenna rotation and polarforming offer complementary channel-shaping benefits for satellite communications. It reports a WMMSE-based alternating algorithm and simulation gains over benchmark schemes.

V. CONCLUSION

  • The proposed WMMSE-based alternating algorithm uses semi-closed-form polarforming updates and exact boresight parameterization for feasible RA-trajectory optimization.The conclusion also describes substantial gains over benchmark schemes.Source: §V · p. 6
  • Antenna rotation redistributes directional gains across user clusters and is particularly beneficial at low transmit powers, while polarforming improves channel separability under stronger multiuser interference.Together, they provide complementary directional and polarization-domain channel shaping.Source: §V · p. 6
  • Fig. 3 plots effective sum rate against the fraction of GTs per cluster.Source: Figure 3 · p. 6
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