We investigate massive multiple-input multiple-output (MIMO) downlink (DL) transmission for multiple low-earth-orbit satellite communication systems. We establish the signal and channel models, and reveal that the signals received by each user terminal (UT) are typically asynchronous in time and frequency. We propose a spatial linear receive processing for signal extraction and perform time and frequency compensations at each UT to achieve synchronized signal. We prove that the single data stream transmission from each satellite to each UT is optimal to maximize the ergodic sum rate. Therefore, without loss of optimality, we can reduce the joint design of the transmit covariance matrices and receive vectors for spatial linear processing to that of the precoding vectors and receive vectors, which we refer to as joint precoder and receiver design (JPRD). We devise a weighted minimum mean-square error (WMMSE) based JPRD algorithm by using the statistical channel state information. Further, we approximate the optimal design with an ergodic sum rate upper bound, for which the optimality of single data stream transmission still holds. We derive a condition under which the inter-satellite interference can be eliminated, and develop a low-complexity WMMSE based JPRD algorithm with the upper bound. Simulation results validate the proposed approaches.

We investigate massive multiple-input multiple-output (MIMO) uplink (UL) transmission for multiple low-earth-orbit (LEO) satellite communication (SATCOM). The signal and channel models are established for the UL massive MIMO multi-satellite system. We reveal that the signals transmitted from the user terminals (UTs), which are intended for different satellites, are typically asynchronous at each satellite. We propose linear precoding with frequency and time pre-compensations at each UT for each satellite, so that the signals intended for a specific satellite from different UTs can be synchronized. We formulate the ergodic sum rate maximization problem by considering the minimum mean square error successive interference cancellation (MMSE-SIC) receiver at each satellite with perfect instantaneous channel state information (iCSI). We propose a Riemannian conjugate gradient (RCG) based precoding vector design algorithm within the manifold optimization framework, which does not include any matrix inversion. Then, in order to reduce the complexity in implementation at satellites, we reformulate the UL ergodic sum rate maximization problem by considering the linear receiving at each satellite with statistical CSI (sCSI) only. We devise an RCG based joint precoding and receiving vector design (JPRVD) to maximize the sum rate, which avoids any matrix inversion, thereby reducing the computational complexity. Simulation results indicate the effectiveness of our proposed approaches.

With the rapid development of low-Earth-orbit (LEO) satellite communications, multi-beam precoding has emerged as a key technology for improving spectrum efficiency. However, the long propagation delay and large Doppler frequency offset pose significant challenges to existing precoding techniques. To address this issue, this paper investigates downlink precoding design for multi-beam LEO satellite communications. First, the downlink channel and signal models are established. Then, we reveal that traditional zero-forcing (ZF), regularized zero-forcing (RZF), and minimum mean square error (MMSE) precoding schemes all require the satellite transmitter to acquire the instantaneous channel state information (iCSI) of all users, which is challenging to obtain in satellite communication systems. Subsequently, we propose a downlink precoding design based on statistical channel state information (sCSI) and derive closed-form solutions for statistical-ZF, statistical-RZF, and statistical-MMSE precoding. Furthermore, we propose that sCSI can be computed using the positions of the satellite and users, which reduces the system overhead and complexity of sCSI acquisition. Monte Carlo simulations under the 3GPP non-terrestrial network (NTN) channel model are employed to verify the performance of the proposed method. The simulation results show that the proposed method achieves sum-rate performance comparable to that of iCSI-based schemes and the optimal transmission performance based on sum-rate maximization. In addition, the proposed method significantly reduces the computational complexity of the satellite payload and the system feedback overhead.

In this paper, we investigate the decoupled designs of precoders and receivers for both downlink (DL) and uplink (UL) in massive multiple-input multiple-output (MIMO) multiple low earth orbit (LEO) satellite communication systems. We first establish the beam based satellite channel model, where the beam matrix is constructed with sampled steering vectors. Then, we propose a decoupled precoder and receiver design for both DL and UL, which allows precoders and receivers to be designed independently at each satellite and user terminal (UT), respectively, with only local statistical channel state information (sCSI). Moreover, with the established beam based channel model, the design of space domain DL precoder and UL receiver can be converted into that of lower-dimensional beam domain vectors with only local sCSI, and the resulting space domain precoder and receiver are beam structured. Furthermore, we propose a low-complexity design and implementation for the beam structured DL precoder and UL receiver by exploiting properties of the beam matrix, significantly reducing the computational complexity. Simulation results validate the proposed approaches.

In this paper, we investigate the downlink (DL) precoder design for massive multiple-input multiple-output (MIMO) multiple low earth orbit (LEO) satellite communication (SATCOM). We first establish the DL beam based channel model for massive MIMO multiple LEO SATCOM systems by using sampled array response vectors. We propose a closed-form statistical channel state information (sCSI) based space domain DL precoder design for multi-satellite systems by maximizing the average signal-to-leakage-plus-noise ratio (ASLNR). Then, with the proposed beam based channel model, we transform the design of space domain DL precoder into that of lower-dimensional beam domain vector and the resulting space domain precoder is beam structured. Moreover, by leveraging the properties of the beam matrix, we propose a low-complexity design and implementation for the beam structured DL precoder. Simulation results demonstrate that the proposed beam structured DL precoder can achieve near performance to the space domain approach with significantly reduced computational complexity.