Toward Multi-Satellite Cooperative Transmission: A Joint Framework for CSI Acquisition, Feedback, and Phase Synchronization

Abstract: The stringent link budget, caused by long propagation distances and payload constraints, poses a fundamental bottleneck for single-satellite transmission. Although LEO mega-constellations make multi-satellite cooperative transmission (MSCT), such as distributed precoding (DP), increasingly feasible, its cooperative gains critically rely on stringent time-frequency-phase synchronization (TFP-Sync), which is difficult to maintain under rapid channel variation and feedback latency. To address this issue, this paper proposes a joint CSI acquisition, feedback, and phase-level synchronization (JCAFPS) framework for MSCT. Specifically, to enable reliable, overhead-efficient CSI acquisition, we design a beam-domain adjustable phase-shift tracking reference signal (TRS) transmission scheme, along with criteria for the TRS and CSI-feedback periods. Then, exploiting deterministic orbital motion and dominant LoS propagation, we establish a polynomial model for the temporal evolution of delay and Doppler shift, and derive an OFDM-based multi-satellite signal model under non-ideal synchronization. The analysis reveals that, unlike the single-satellite case, the composite multi-satellite channel exhibits nonlinear time-frequency-varying phase behavior, necessitating symbol- and subcarrier-wise phase precompensation for coherent transmission. Based on these results, we develop a practical closed-loop realization integrating single-TRS-based channel parameter estimation, multi-TRS-based channel prediction, predictive CSI feedback, and user-specific TFP precompensation. Numerical results demonstrate that the proposed framework achieves accurate CSI acquisition and precise TFP-Sync, enabling DP-based dual-satellite cooperative transmission to approach the theoretical 6 dB power gain over single-satellite transmission, while remaining robust under extended prediction durations and enlarged TRS periods.

• The paper presents the JCAFPS framework that jointly acquires CSI, feedback, and phase synchronization, enabling near-theoretical 6 dB power gains in multi-satellite DP systems.
• It introduces a predictive channel model using polynomial estimation and adjustable phase-shift TRSs to overcome Doppler effects, propagation latency, and synchronization challenges.
• Simulation results confirm that closed-loop precompensation with ESPRIT-based parameter extraction significantly outperforms conventional methods in NMSE and synchronization metrics.

Toward Multi-Satellite Cooperative Transmission: A Joint Framework for CSI Acquisition, Feedback, and Phase Synchronization

Introduction and Motivation

The proliferation of LEO mega-constellations is catalyzing a paradigm shift in satellite communications architectures toward multi-satellite cooperative transmission (MSCT), which holds the potential to address long-standing limitations in link budget, antenna aperture, and interference management that constrain single-satellite systems. However, the realization of distributed precoding (DP) gains in MSCT is intrinsically constrained by the challenges of time-frequency-phase synchronization (TFP-Sync) as well as robust acquisition and timely feedback of channel state information (CSI). The compounding impact of rapid satellite motion, severe Doppler effects, propagation latency, and feedback delays impede both coherent cooperative transmission and preclude the straightforward extension of terrestrial distributed MIMO techniques to satellite domains.

This work rigorously addresses the joint CSI acquisition, feedback, and phase-level synchronization problem, formulating the JCAFPS (Joint CSI Acquisition, Feedback, and Phase Synchronization) framework for MSCT. The approach systematically exploits orbital determinism and the dominant LoS propagation in satellite-to-ground (S2G) channels, to design a tightly coupled closed-loop system for predictive channel modeling, pilot configuration, and synchronization. The framework incorporates a beam-domain, adjustable phase-shift tracking reference signal (APS-TRS), polynomial-based predictive channel tracking, and subcarrier-wise phase precompensation.

System Model and Problem Formulation

An FDD OFDM-based multi-satellite system is considered, where $S$ cooperating LEO satellites, each equipped with a uniform planar array, concurrently serve $U$ single-antenna user equipments (UEs) using space-division multiple access over common frequency resources. The system is partitioned spatially into pre-defined service beams (BPs) and finer-grained tracking broadcast areas (TBAs), managed via beam hopping strategies to balance coverage and manage inter-beam interference under hardware and power restrictions.

The principal challenge is the accurate and efficient acquisition of reliable CSI and phase tracking information for all satellite-UE links, under severe propagation loss, stringent payload constraints, high mobility, and asynchronous satellite clocks. Unlike terrestrial MU-MIMO, S2G channels are quasi-deterministic and heavily LoS-dominated, leading to both opportunities (for parametric channel modeling) and unique difficulties (nonlinear time/frequency-varying behavior, acute sensitivity to synchronization errors).

JCAFPS Framework Design

Tracking Reference Signal (TRS) Design

To facilitate overhead-efficient CSI estimation across asynchronous multi-satellite links, the framework implements APS-TRSs. These are constructed such that all satellites employ identical TF resources but individual links are identified via orthogonal frequency-specific phase shifts (frequency-domain linear phase shifts, corresponding to unique delay-domain signatures). This architecture avoids excessive pilot overhead associated with fully orthogonal or UE-specific pilot allocations and leverages the sparsity in S2G delay profiles. TRS transmissions are mapped to the beam domain for power efficiency and are fine-grained to TBA centers to account for spatial non-uniformities in Doppler and delay.

Polynomial Channel Evolution Modeling

Central to predictive synchronization is the representation of temporal evolution in propagation delay and Doppler shift as low-order polynomials, parameterized by orbital mechanics and deterministic trajectories. The framework employs Taylor expansion of S2G path distances, with model order tuned to the target prediction interval (first-order for millisecond scales, higher orders for longer windows). This parametric model dramatically reduces feedback overhead and facilitates reliable prediction of future channel states, critical to mitigating the impact of feedback latency in LEO settings.

Closed-Loop Synchronization and Precompensation

CSI acquisition is followed by compact, model-based feedback from UE to satellites, consisting of polynomial coefficients for each link's delay, Doppler, and phase evolution. Satellites use this predictive CSI to apply UE-specific precompensation in all time, frequency, and phase dimensions—pre-aligning the outgoing data such that residual asynchrony and nonlinear composite-channel phase evolution across satellites are effectively neutralized. The framework analytically establishes that, in contrast to single-satellite or terrestrial MIMO settings, MSCT requires symbol- and subcarrier-wise phase precompensation due to the inherently nonlinear TF evolution inherent to the composite channel.

ESPRIT-Poly-PU Algorithmic Realization

A pipeline is developed whereby channel parameters are extracted from each TRS using spatial-smoothing ESPRIT super-resolution techniques, providing robust estimators for delay, gain, and phase. Successive TRS estimates are fused via polynomial regression, with Doppler-assisted cross-TRS phase unwrapping to resolve ambiguities induced by phase cycling. Predictive feedback and closed-loop TFP precompensation complete the cycle, realizing distributed coherent transmission with minimal pilot and feedback load.

Numerical Results

Simulation studies use 3GPP-compliant, geometry-based S2G models (QuaDRiGa) under realistic LEO orbital dynamics. Key findings include:

• The JCAFPS framework enables dual-satellite DP to approach the theoretical 6 dB power gain over single-satellite links (as seen in SINR comparisons), even for extended prediction durations ($T_{\mathrm{pred}} \approx 160$ ms) and large TRS periods ($\approx 40$ ms).
• The polynomial channel model remains robust for sub-second time scales, ensuring that the performance degradation due to prediction horizon and pilot overhead is contained.
• Cross-TRS phase unwrapping is essential; omitting it degrades phase estimation and nullifies the benefits of predictive modeling.
• The proposed compressed feedback (reporting polynomial coefficients rather than full sequences) achieves high accuracy with low signaling load.
• The ESPRIT-based parameter extraction substantially outperforms OMP-based and AR-model-based baselines in both NMSE (for CSI) and TFP-Sync metrics (timing, frequency, and phase errors).

Theoretical and Practical Implications

This study demonstrates that the interplay between TRS design, polynomial-based predictive modeling, and closed-loop synchronization is critical for scalable MSCT. The work clarifies that offsetting nonlinear, asynchronous TF phase behavior across satellites cannot be effectively handled by receiver-side processing or simple reference signal interpolation; transmitter-side, predictive precompensation is fundamentally required. The effective closed-loop strategy is robust to realistic imperfections, e.g., time-varying Doppler, feedback delays, and uneven UE spatial distribution.

Practically, this unlocks the feasibility of high-order multi-satellite cooperation in LEO mega-constellations, allowing actual realization of the theoretical power/spectral efficiency scaling of DP systems. It also offers a template for the broader unification of terrestrial and space communications systems as envisioned in 6G architectures, where interoperability and synchronization resilience are crucial. The polynomial tracking approach, which leverages deterministic satellite motion, is expected to be extensible to higher-mobility NTN scenarios and can be synergistically combined with deep-learning-based channel prediction [zhang2022deep2], [ying2024deep].

Future Directions

• Extension to massive-MIMO satellite payloads and ultra-dense multi-satellite clusters.
• Co-design of uplink feedback channels using robust coding and random access, considering feedback latency and unreliability.
• Integration of learning-based long-horizon prediction models to augment the polynomial model for multi-path or severe dynamic environments.
• Study of the trade-offs between synchronization overhead and throughput under varying service requirements and user distributions.

Conclusion

This work establishes a complete technical framework for joint CSI acquisition, predictive feedback, and synchronization in multi-satellite cooperative transmission systems. By combining pilot-efficient TRS design with polynomial-based channel prediction and closed-loop fine-grained precompensation, the proposed JCAFPS enables coherent multi-satellite DP transmission at near-theoretical efficiency with practical robustness, fundamentally advancing the viability of large-scale non-terrestrial network deployment (2603.28195).