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Rotatable Antenna Enabled Multi-Satellite Communications: Joint Satellite Selection and Boresight Trajectory Optimization

Xingxiang Peng, Qingqing Wu, Haiying Hu, Wen Chen, Xin Lin

arXiv:2609.00929v1eess.SP

TL;DR

The paper addresses joint satellite selection and RA control for multi-satellite LEO reception under dynamic geometry, external interference, and mechanically constrained reconfiguration. It formulates a two-timescale optimization, combining submodular MM selection with slew-feasible Riemannian RA updates in a monotone alternating algorithm. Simulations show an optimal balance between channel strength and spatial separability, with selection more important under underloading or actuator limits and RA shaping more influential near full spatial loading.

  • Problem

    Joint reception depends on serving-set composition and RA-shaped channel gains, spatial separability, and interference, motivating their joint optimization under dynamic constraints.

  • Method

    The paper combines monotone-submodular satellite selection with an incumbent-tight modular MM surrogate and slew-feasible Riemannian RA trajectory updates in a two-color alternating framework.

  • Results

    Simulations consistently improve over benchmarks and reveal an optimal balance between channel strength and spatial separability across loading and actuator regimes.

  • Takeaways & Limitations

    Satellite selection is particularly important in underloaded and actuator-limited regimes, whereas RA shaping becomes more influential near full spatial loading.

Abstract

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This paper considers a satellite-to-ground communication system in which a ground station (GS) equipped with independently rotatable antenna (RA) elements jointly decodes independent streams from multiple low-Earth-orbit (LEO) satellites over a shared time--frequency resource. Specifically, we formulate a two-timescale throughput maximization problem under exogenous cochannel interference, capturing serving-set composition, RA-enabled channel shaping, time-varying satellite geometry, and mechanically constrained inter-epoch reconfiguration. We first characterize the joint effects of interference-whitened channel strength and spatial separability on multi-satellite reception, motivating the joint design of satellite selection and RA control. With the RA trajectory fixed, we establish the monotone submodularity of the epoch-level selection objective and construct an incumbent-tight modular lower-bound surrogate, leading to an efficient discrete Minorization-Maximization (MM) selection algorithm. For fixed serving sets, we develop slew-feasible RA updates based on Riemannian gradients and organize them into a two-color parallel update scheme. The two blocks are integrated into a monotone alternating algorithm with guaranteed objective convergence. Simulations demonstrate consistent gains over benchmark schemes and reveal an optimal balance between channel strength and spatial separability. The results further show that satellite selection is particularly important in underloaded and actuator-limited regimes, whereas RA shaping becomes more influential near full spatial loading.

I. INTRODUCTION

The paper jointly optimizes satellite selection and rotatable-antenna control for dynamic LEO reception under external interference, using a two-timescale architecture. Its analysis and simulations show that channel strength, spatial separability, loading, and actuator limits determine which design component matters most.

  • LEO integration offers low latency, wide coverage, and spatial diversity but introduces dynamic topology and intensive spectrum reuse.
  • RA steering reshapes effective gains, spatial separability, and interference exposure, while satellite selection determines the received multi-satellite channel composition.
  • The proposed two-timescale formulation jointly optimizes epoch-held serving sets and RA boresight trajectories under time-varying geometry, external interference, and mechanical reconfiguration constraints.
  • With fixed RA trajectories, the satellite-selection objective is monotone submodular because marginal capacity depends on effective strength and spatial complementarity.
  • Discrete MM selection uses an incumbent-tight modular surrogate, while slew-feasible Riemannian RA updates are organized in a parallel alternating framework with nondecreasing throughput and objective convergence.
  • Simulations identify an optimal strength–separability balance: selection matters most when underloaded or actuator-limited, whereas RA shaping matters more near full spatial loading.

C. RA Reconfiguration and Channel Model

The RA configuration model represents each element by an epoch-dependent boresight constrained to a spherical steering region and by finite-speed inter-epoch motion. A cosine-power directional pattern converts these orientations into direction-dependent receive gains.

  • Each RA element has an epoch-dependent boresight in the GS-centered ENU frame, with feasible orientations restricted to a spherical cap around the array normal.
  • The maximum steering angle from the nominal array normal limits the feasible RA steering region.
  • Finite actuation speed limits angular displacement between consecutive epoch boresights during each guard interval.
  • Epoch-1 boresights are pre-positioned before observation and therefore avoid an initial slew constraint.
  • The front-side cosine-power pattern models direction-dependent receive gain; increasing the directivity exponent narrows the main lobe and raises peak gain.

2) Satellite-to-GS Channel Model:

The channel model combines transmit directivity, propagation, array phase, and RA-dependent receive gains for time-varying satellite links. It then incorporates independently generated external interference and slot-level MMSE-SIC reception into the sum-capacity model.

  • Satellite-to-GS channels combine RA response, transmit directivity, large-scale propagation, and array-induced phase differences.
  • Time-varying satellite geometry controls propagation gain and array phase, while RA boresights provide element-wise control of directional gains.
  • External interferers are independently operated, uncontrolled satellites whose effective channels depend on geometry, link parameters, and RA-dependent receive gains.
  • The GS selects at most Kmax serving satellites per epoch and uses one RF chain per RA element with fully digital reception.
  • MMSE-SIC computes slot sum capacity from instantaneous CSI, while satellite selection and RA control use epoch-level predicted geometry and large-scale channel and interference information.
  • Scheduling more than M satellites can still increase sum capacity, but streams beyond M add no spatial degrees of freedom and increase acquisition and decoding overhead.

E. Problem Formulation

The paper formulates a two-timescale mixed discrete–continuous throughput problem that jointly selects satellite serving sets and controls mechanically constrained RA trajectories. Its geometric analysis shows that effective strength and spatial separability jointly determine multi-satellite capacity.

  • E. Problem Formulation: The effective-throughput problem jointly optimizes epoch-level serving sets and the complete RA trajectory over time-varying intra-epoch geometry.Serving sets and boresights remain fixed within epochs, while effective channels vary across constituent slots.
  • E. Problem Formulation: The formulation is mixed discrete–continuous and nonconvex because satellite selection, RA-dependent channel gains, and inter-epoch slew constraints are coupled.Boresights must remain within feasible steering regions, and consecutive configurations are limited by available reconfiguration time.
  • E. Problem Formulation: Transmit powers are fixed at their maximum values because jointly decoded sum capacity is monotonically nondecreasing in each satellite’s transmit power.The resulting focus is satellite selection and RA control rather than power optimization.
  • A. Geometric Insights for Multi-Satellite Reception: Interference whitening converts interference-plus-noise covariance to identity, making whitened channel norms and mutual alignment interference-aware strength and separability measures.The representation is equivalent because the whitening transformation is invertible.
  • A. Geometric Insights for Multi-Satellite Reception: For two satellites, capacity contains individual strengths α1 and α2 plus a complementarity term α1α2(1 −¯ρ^2) that decreases with channel coherence.Fully aligned channels lose the complementarity contribution, whereas orthogonal channels provide two separable spatial modes.
  • A. Geometric Insights for Multi-Satellite Reception: At low SNR, individual channel strengths dominate first-order capacity, while at high SNR spatial separability becomes inseparable from channel strength.Thus, individually strong satellites may still yield limited sum capacity when their whitened channels are highly aligned.
  • A. Geometric Insights for Multi-Satellite Reception: The paper therefore jointly designs satellite selection and RA control to balance effective channel strength, spatial orientations, and interference susceptibility.Selection determines the channel set, while RA steering modifies directional gains and relative channel orientations.
  • A. Geometric Insights for Multi-Satellite Reception: Clustered arrival directions facilitate simultaneous directional-gain alignment but reduce separability, whereas widely separated directions improve separability but hinder simultaneous high-gain alignment.RA steering can partially alleviate this tradeoff by reshaping directional gains.

B. Optimization for Satellite Selection

With the RA trajectory fixed, the satellite-selection objective separates across epochs and becomes a cardinality-constrained set optimization problem. The proposed discrete MM method uses an incumbent-tight modular lower-bound surrogate to address its NP-hard structure.

  • B. Optimization for Satellite Selection: With the RA trajectory fixed, effective throughput decomposes into independent epoch-level selection objectives.Each epoch objective is defined over candidate serving sets for that epoch.
  • B. Optimization for Satellite Selection: Because both the objective and constraints are separable across epochs, all epoch-level satellite-selection problems can be solved independently and in parallel.Each resulting problem is a cardinality-constrained set optimization.
  • B. Optimization for Satellite Selection: The epoch-level selection problem is generally NP-hard, so the method derives conditional marginal gains and establishes monotone submodularity before constructing a modular surrogate.The surrogate is optimized within a discrete Minorization-Maximization framework.

1) Marginal-Gain Characterization and Submodularity:

The selection objective’s conditional gains reflect both candidate strength and spatial separation from already selected channels. This structure yields monotonicity and submodularity, supporting capacity-aware selection and modular MM updates.

  • 1) Marginal-Gain Characterization and Submodularity:: Adding a candidate satellite contributes a rank-one term to the current received covariance, defining its conditional marginal throughput gain.The marginal gain is the objective difference between the enlarged and current serving sets.
  • 1) Marginal-Gain Characterization and Submodularity:: The marginal-gain expression separates candidate interference-whitened strength from overlap with the selected-channel subspace and its associated separability loss.Large gains favor satellites that are both strong and spatially complementary to the current set.
  • 1) Marginal-Gain Characterization and Submodularity:: The epoch-level throughput function Fℓ(S) is monotone and submodular on the candidate satellite set.Monotonicity gives nonnegative marginal gains, while submodularity means marginal contributions diminish as the serving set grows.
  • 1) Marginal-Gain Characterization and Submodularity:: The proof establishes diminishing returns by comparing received covariance matrices for nested serving sets and applying positive-definite order reversal under inversion.This relation is substituted into the marginal-gain expression to prove submodularity.
  • 1) Marginal-Gain Characterization and Submodularity:: Monotonicity implies selecting all candidates when their number is within the limit, or a set of cardinality Kmax otherwise.Submodularity additionally makes each candidate’s value dependent on the satellites already selected.

2) Modular Surrogate Construction and Discrete MM Optimization:

The paper converts set-dependent satellite-selection gains into an incumbent-tight modular surrogate, enabling exact cardinality-constrained updates within a discrete MM algorithm.

  • The incumbent elements are ordered greedily by conditional marginal gains relative to the current chain prefix.
  • Each chain weight is an exact conditional marginal gain evaluated along the permutation and lower-bounds the corresponding gain for any subset of preceding elements.
  • The resulting modular surrogate is a lower bound on the selection objective and is tight at the incumbent set.
  • Maximizing the surrogate under the cardinality constraint selects the Kmax candidates with the largest chain weights.
  • The discrete MM algorithm produces a nondecreasing epoch-throughput sequence whose objective values are guaranteed to converge.

C. Optimization for RA Trajectory

With serving sets fixed, the paper optimizes RA boresight trajectories while accounting for slew constraints that couple adjacent epochs.

  • The RA update reshapes effective channel strengths and spatial relationships after satellite serving sets are fixed.
  • Although the objective separates across epochs, inter-epoch slew constraints create chain-structured coupling.
  • The coupled updates are organized into a two-color parallel scheme with neighboring epochs held fixed.

1) Epoch-Level RA Gradient:

The RA trajectory method derives Euclidean and Riemannian gradients for boresight updates, then restricts directions to locally feasible sets under neighboring configurations.

  • The channel coefficient of each source is first expressed in terms of the RA element orientation.
  • The Euclidean gradient of effective throughput is derived using d ln det X = tr(X^-1dX).
  • The gradient accounts for scheduled channels and orientation-dependent external interference, with the interference term vanishing under specified conditions.
  • Projection onto the unit-sphere tangent space yields the Riemannian gradient.
  • With neighboring boresights fixed, a local feasible set and linear oracle determine the update direction.

I (AIAT

The paper combines feasible RA updates with discrete MM satellite selection in an alternating procedure that preserves constraints and guarantees nondecreasing throughput.

  • The linear oracle selects the feasible candidate with the largest linear objective before the boresight is updated toward it.
  • The normalized update preserves steering-cap and neighboring slew constraints under the stated parameter conditions.
  • An Armijo search accepts a feasible step when the epoch oracle gap is positive.
  • Odd and even epochs are updated in parallel, reducing serial depth from L updates to two color rounds while preserving feasibility and monotonic ascent.
  • The alternating algorithm repeatedly updates RA trajectories and serving sets until effective-throughput improvement falls below a prescribed tolerance.
  • The integrated algorithm generates a feasible, nondecreasing effective-throughput sequence through surrogate maximization and Armijo-based RA updates.
  • Both optimization blocks have polynomial per-iteration complexity and substantial epoch-level parallelism.

IV. SIMULATION RESULTS AND DISCUSSION

Simulations show that joint satellite selection and RA trajectory optimization improves effective throughput across changing loading, interference, temporal, and actuator conditions. The results also reveal when selection or RA shaping contributes most and confirm the proposed algorithm’s monotone convergence.

  • Simulation setup: The default evaluation uses a 550-km Starlink Walker–Delta shell, a 3 × 3 UPA, Kmax = 6, 18.2 GHz carrier frequency, and 100 MHz bandwidth.The GS is located at (50°N, 120°E), and orbital parameters are randomized across realizations.
  • Strength–separability tradeoff: At ψ = 25°, throughput reaches 5.005 Gbps as effective rank rises to 4.72 despite normalized channel strength falling to 0.339.The intermediate optimum shows that spatial-separability gains can outweigh channel-strength loss.
  • Strength–separability tradeoff: At ψ = 0°, co-directional channels yield rank one and 1.297 Gbps, while at ψ = 60° throughput falls to 3.646 Gbps after separation benefits diminish.The optimized-RA sweep therefore produces a unimodal throughput curve rather than favoring either extreme.
  • Algorithm validation: Across 3 × 3, 4 × 4, and 5 × 5 UPAs, average throughput increases monotonically and stabilizes after approximately 15 iterations.The results are averaged over 200 orbital realizations under the default 10-dB reference INR, and larger arrays achieve higher throughput.
  • Loading and component contributions: RA + MM consistently achieves the highest throughput, with satellite selection more influential when underloaded and RA reconfiguration increasingly important near full spatial loading.RA + Gain-TopK surpasses Fixed UPA + MM as Kmax approaches M, while the joint scheme benefits from both mechanisms.
  • Interference robustness: Under stronger interference, RA + MM degrades more gradually and its gaps over single-component schemes widen because selection and RA shaping jointly account for interference exposure.With more interferers, interference becomes more diffuse and the gaps between joint and single-component schemes gradually narrow.
  • Scheduling timescale: A moderate number of scheduling epochs balances temporal adaptation against guard-interval overhead, whereas overly frequent updates reduce effective throughput.RA updates track changing geometry and interference, but additional guard intervals reduce payload duty factor.
  • Actuator limitations: RA-enabled schemes improve monotonically with maximum angular velocity and largely saturate beyond approximately 20°/s.At low angular velocities, interference-aware selection can outperform slowly reconfigurable RAs paired with strength-only selection, showing that the mechanisms are complementary.

V. CONCLUSION

The paper jointly optimizes satellite selection and RA boresight trajectories for multi-satellite LEO reception, combining discrete MM selection with slew-feasible RA updates in a convergent alternating framework.

  • The two-timescale framework accounts for epoch-held serving sets and RA configurations, time-varying satellite geometry, exogenous cochannel interference, and inter-epoch slew constraints.
  • Interference-whitened marginal-capacity analysis reveals that effective channel strength and spatial separability jointly shape multi-satellite reception.
  • With fixed RA trajectories, the monotone submodular satellite-selection objective enables a discrete MM method based on an incumbent-tight modular lower-bound surrogate.
  • Slew-feasible RA updates use Riemannian gradients and a two-color parallel update scheme, while the integrated alternating algorithm preserves feasibility and guarantees monotonic objective improvement and convergence.
  • Simulations show consistent gains from joint design and an optimal balance between channel strength and spatial separability.
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