Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Ergodic Sum Rate Capacity Achieving Transmit Design for Massive MIMO LEO Satellite Uplink Transmission

Ke-Xin Li, Xiqi Gao, Xiang-Gen Xia

TL;DR

The paper tackles ESR capacity achieving uplink transmit design for massive MIMO LEO SATCOM under long-term sCSIT at UTs. It derives a UT-side rank bound and a lower-dimensional covariance representation, enabling efficient optimization of transmit strategies; it also characterizes when single-stream transmission suffices. A conditional gradient (CG) method and a simplified CG using a deterministic equivalent ESR are developed to compute the ESR-optimal covariances with guaranteed convergence and reduced complexity. The proposed approaches are validated by simulations, showing rapid convergence and near-optimal ESR performance across varying Rician factors and numbers of UTs. Collectively, the work provides practical, scalable design tools for next-generation LEO uplink systems with large UT deployments.

Abstract

In this paper, we investigate the ergodic sum rate (ESR) capacity achieving uplink (UL) transmit design for massive multiple-input multiple-output (MIMO) low-earth-orbit (LEO) satellite communications with statistical channel state information at the user terminals (UTs). The UL massive MIMO LEO satellite channel model with uniform planar array configurations at the satellite and UTs is presented. We prove that the rank of each UT's optimal transmit covariance matrix does not exceed that of its channel correlation matrix at the UT side, which reveals the maximum number of independent data streams transmitted from each UT to the satellite. We then prove that the transmit covariance matrix design can be transformed into the lower-dimensional matrix design without loss of optimality. We also obtain a necessary and sufficient condition when single data stream transmission from each UT to the satellite can achieve the ESR capacity. A conditional gradient (CG) method is developed to compute the ESR capacity achieving transmit covariance matrices. Furthermore, to avoid the exhaustive sample average, we utilize an asymptotic expression of the ESR and devise a simplified CG method to compute the transmit covariance matrices, which can approximate the ESR capacity. Simulations demonstrate the effectiveness of the proposed approaches.

Ergodic Sum Rate Capacity Achieving Transmit Design for Massive MIMO LEO Satellite Uplink Transmission

TL;DR

The paper tackles ESR capacity achieving uplink transmit design for massive MIMO LEO SATCOM under long-term sCSIT at UTs. It derives a UT-side rank bound and a lower-dimensional covariance representation, enabling efficient optimization of transmit strategies; it also characterizes when single-stream transmission suffices. A conditional gradient (CG) method and a simplified CG using a deterministic equivalent ESR are developed to compute the ESR-optimal covariances with guaranteed convergence and reduced complexity. The proposed approaches are validated by simulations, showing rapid convergence and near-optimal ESR performance across varying Rician factors and numbers of UTs. Collectively, the work provides practical, scalable design tools for next-generation LEO uplink systems with large UT deployments.

Abstract

In this paper, we investigate the ergodic sum rate (ESR) capacity achieving uplink (UL) transmit design for massive multiple-input multiple-output (MIMO) low-earth-orbit (LEO) satellite communications with statistical channel state information at the user terminals (UTs). The UL massive MIMO LEO satellite channel model with uniform planar array configurations at the satellite and UTs is presented. We prove that the rank of each UT's optimal transmit covariance matrix does not exceed that of its channel correlation matrix at the UT side, which reveals the maximum number of independent data streams transmitted from each UT to the satellite. We then prove that the transmit covariance matrix design can be transformed into the lower-dimensional matrix design without loss of optimality. We also obtain a necessary and sufficient condition when single data stream transmission from each UT to the satellite can achieve the ESR capacity. A conditional gradient (CG) method is developed to compute the ESR capacity achieving transmit covariance matrices. Furthermore, to avoid the exhaustive sample average, we utilize an asymptotic expression of the ESR and devise a simplified CG method to compute the transmit covariance matrices, which can approximate the ESR capacity. Simulations demonstrate the effectiveness of the proposed approaches.
Paper Structure (18 sections, 4 theorems, 76 equations, 5 figures, 1 table, 2 algorithms)

This paper contains 18 sections, 4 theorems, 76 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. System Configuration
  4. Signal and Channel Models
  5. Statistical Properties of Satellite Channels
  6. UL Transmit Design
  7. Rank Property of Transmit Covariance Matrices
  8. Low SNR Case
  9. High Rician Factor Case
  10. Lower-Dimensional Matrix Representation of Transmit Covariance Matrix
  11. CG Method for UL Transmit Design
  12. Simplified CG Method for UL Transmit Design
  13. Simulation Results
  14. Conclusion
  15. Proof of \ref{['Proposition_1']}
  16. ...and 3 more sections

Key Result

Theorem 1

The transmit covariance matrices $\{\mathbf{Q}_k\}_{k=1}^K$ that achieve the UL ESR capacity should satisfy

Figures (5)

  • Figure 1: A massive MIMO LEO SATCOM system.
  • Figure 2: Convergence of \ref{['algorithm_UL_sum_rate_Tk', 'algorithm_UL_sum_rate_Tk_DE']} at different transmit power.
  • Figure 3: Performance of \ref{['algorithm_UL_sum_rate_Tk', 'algorithm_UL_sum_rate_Tk_DE']} for different Rician factors.
  • Figure 4: Comparison of ESR capacity and ESR with optimal beamforming.
  • Figure 5: Performance of \ref{['algorithm_UL_sum_rate_Tk', 'algorithm_UL_sum_rate_Tk_DE']} for different numbers of UTs.

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4