Multi-Satellite Multi-Stream Beamspace Massive MIMO Transmission
Abstract
This paper studies multi-satellite multi-stream (MSMS) beamspace transmission, where multiple satellites cooperate to form a distributed multiple-input multiple-output (MIMO) system and jointly deliver multiple data streams to multi-antenna user terminals (UTs), and beamspace transmission combines earth-moving beamforming with beam-domain precoding. For the first time, we formulate the signal model for MSMS beamspace MIMO transmission. Under synchronization errors, multi-antenna UTs enable the distributed MIMO channel to exhibit higher rank, supporting multiple data streams. Beamspace MIMO retains conventional codebook based beamforming while providing the performance gains of precoding. Based on the signal model, we propose statistical channel state information (sCSI)-based optimization of satellite clustering, beam selection, and transmit precoding, using a sum-rate upper-bound approximation. With given satellite clustering and beam selection, we cast precoder design as an equivalent covariance decomposition-based weighted minimum mean square error (CDWMMSE) problem. To obtain tractable algorithms, we develop a closed-form covariance decomposition required by CDWMMSE and derive an iterative MSMS beam-domain precoder under sCSI. Following this, we further propose several heuristic closed-form precoders to avoid iterative cost. For satellite clustering, we enhance a competition-based algorithm by introducing a mechanism to regulate the number of satellites serving certain UT. Furthermore, we design a two-stage low-complexity beam selection algorithm focused on enhancing the effective channel power. Simulations under practical configurations validate the proposed methods across the number of data streams, receive antennas, serving satellites, and active beams, and show that beamspace transmission approaches conventional MIMO performance at lower complexity.
Summary
** This paper tackles the challenge of achieving ubiquitous connectivity in 6G satellite communication (SatCom) by proposing a novel multi-satellite multi-stream (MSMS) beamspace MIMO transmission framework. The core problem is how to effectively design multi-satellite distributed MIMO systems that can support multiple data streams to multi-antenna user terminals (UTs) while being practical and compliant with existing standards, particularly considering the limitations in acquiring instantaneous channel state information (CSI) and the presence of synchronization errors. The authors address this by integrating satellite clustering, beam selection, and beam-domain transmit precoding within a coherent joint transmission (CJT) framework. The approach involves formulating a signal model for MSMS beamspace MIMO transmission under synchronization errors and proposing statistical CSI (sCSI)-based optimization of satellite clustering, beam selection, and transmit precoding. The precoder design is cast as a covariance decomposition-based weighted minimum mean square error (CDWMMSE) problem. To obtain tractable algorithms, the paper develops a closed-form covariance decomposition and derives an iterative MSMS beam-domain precoder under sCSI. Heuristic closed-form precoders are also proposed to avoid iterative costs. For satellite clustering, a competition-based algorithm is enhanced, and a two-stage low-complexity beam selection algorithm is designed to enhance effective channel power. Simulations using practical configurations are used to validate the proposed methods. The key findings demonstrate that the proposed beamspace transmission approach can achieve performance close to conventional MIMO but with significantly lower complexity. This matters to the field because it offers a practical solution for enhancing spectral efficiency and capacity in SatCom systems, addressing the limitations of single-satellite systems and the high complexity of traditional MIMO precoding. The work contributes a new channel model, optimization framework, and a set of algorithms for MSMS beamspace MIMO transmission, advancing the development of ubiquitous connectivity in 6G. **
Key Insights
- •Novel Signal Model: The paper introduces a multi-satellite distributed MU-MIMO channel model under OFDM modulation that accounts for inter-satellite synchronization errors with multi-antenna UTs. This model extends existing work by considering multi-antenna UTs and exploiting the multi-rank structure of the multi-satellite channel.
- •CDWMMSE Formulation: The authors reformulate the precoder design problem as an equivalent covariance decomposition-based weighted minimum mean square error (CDWMMSE) problem. This allows for the development of tractable algorithms using sCSI.
- •Upper-Bound Approximation: The work utilizes a sum-rate upper-bound approximation for optimization. This avoids the underestimation of effective signal power that can occur with lower-bound approximations, leading to improved performance.
- •Low-Complexity Beam Selection: A two-stage low-complexity beam selection algorithm is designed, focusing on enhancing the effective channel power. Critically, its computational complexity is independent of the number of antennas, making it scalable to massive MIMO scenarios.
- •Iterative and Closed-Form Precoders: Both iterative (MS2CDWM) and closed-form (MS2CDM, Location Information Based) precoding algorithms are developed. The iterative algorithm offers improved performance, while the closed-form algorithms provide a better performance-complexity tradeoff.
- •Complexity Reduction: Beamspace MIMO transmission significantly reduces computational complexity compared to conventional MIMO, scaling approximately as (̃B/NT)^3, where ̃B is the number of active beams and NT is the number of transmit antennas. For example, the paper notes a reduction to approximately 0.7% with Bs = 48 and NT = 256.
- •Synchronization Error Modeling: The paper explicitly incorporates synchronization errors, modeling them as a random phase distribution. This is a crucial consideration for practical multi-satellite systems.
Practical Implications
- •6G SatCom Deployment: The research provides a practical framework for designing multi-satellite distributed MIMO systems for 6G SatCom networks, enabling higher data rates and improved coverage.
- •Satellite Operators: Satellite operators can benefit from these results by implementing the proposed algorithms to enhance the capacity and efficiency of their satellite networks. Specifically, the algorithms for satellite clustering, beam selection, and precoding provide tools for optimizing resource allocation.
- •Hardware Design: The beamspace MIMO architecture allows for retaining existing codebook-based beamforming hardware while introducing precoding in the beam domain. This provides a good performance-complexity tradeoff and compatibility with existing systems.
- •Future Research: The work opens up avenues for future research, including:
- •Investigating the impact of different beam codebook designs on system performance.
- •Developing more sophisticated satellite clustering algorithms that consider factors beyond channel power, such as feeder link capacity.
- •Exploring the use of machine learning techniques for optimizing beam selection and precoding.
- •Analyzing the performance of the proposed algorithms under different channel conditions and synchronization error models.