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.

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 precoder design for user-centric network (UCN) massive multiple-input multiple-output (mMIMO) downlink with matrix manifold optimization. In UCN mMIMO systems, each user terminal (UT) is served by a subset of the base stations (BSs) instead of all BSs, lowering the dimension of the precoders to be designed. Each BS in the system has a power constraint. By proving that the precoder set satisfying the constraints forms a Riemannian submanifold, we transform the constrained precoder design problem in Euclidean space as an unconstrained one on the Riemannian submanifold. Riemannian ingredients, including orthogonal projection, Riemannian gradient, retraction and vector transport, of the problem on the Riemannian submanifold are further derived, with which the Riemannian conjugate gradient (RCG) design method is proposed for solving the unconstrained problem. The proposed method avoids the inverses of large dimensional matrices. The complexity analyses show the high efficiency of RCG precoder design. Simulation results demonstrate the superiority of the proposed precoder design and the high efficiency of the UCN mMIMO system.

We investigate massive multiple-input multiple-output (MIMO) downlink (DL) transmission for multiple low-earth-orbit (LEO) 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 show 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 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. Simulation results validate the proposed approaches.

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.