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.

Figures (7)

• Figure 1: Flow chart of JCAFPS framework.
• Figure 2: TRS configuration with $N_{\rm sym}^{\rm trs} = 4$, $N_{\rm slot}^{\rm trs} = 2$, and $N_{\rm tc} = 4$38.214.
• Figure 3: Satellite-to-UE distance modeling error based on Taylor series expansion with $f_{\rm c} = 2$ GHz, $r_{\rm sat} = 6721$ km, $\theta_{\rm inc} = 53^{\circ}$, $\beta_{\rm max} = 90^{\circ}$.
• Figure 4: Characteristic analysis of equivalent TF-domain channels: (a) ICI power of single-satellite channel; (b) phase and magnitude variations of single-satellite channel (left) and dual-satellite composite channel (right); (c) equalization results over single-satellite channel (left) and dual-satellite composite channel (right). Parameters: $f_{\rm c}\!=\!2$ GHz, $N\!=\!2048$, $\Delta f\!=\!15$ kHz, $\nu_{00}\!=\!27$ kHz, $\nu_{10}\!=\!-20$ kHz, $\tilde{\nu}_{00}^{\rm res}\!=\!180$ Hz, $\tilde{\nu}_{10}^{\rm res}\!=\!-260$ Hz, $\alpha_{00}^{\rm res}\!=\!1$, and $\alpha_{10}^{\rm res}\!=\!0.92$.
• Figure 5: Per-beam power $P_{\rm beam}$ vs (a) NMSE, (b) TEE, (c) FEE, (d) PEE, and (e) SINR. $T_{\rm pred} = 80$ ms, $M = 12$, $T_{\rm period}^{\rm trs} = 20$ ms.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4