This paper investigates the design of distributed precoding for multi-satellite massive MIMO transmissions. We first conduct a detailed analysis of the transceiver model, in which delay and Doppler precompensation is introduced to ensure coherent transmission. In this analysis, we examine the impact of precompensation errors on the transmission model, emphasize the near-independence of inter-satellite interference, and ultimately derive the received signal model. Based on such signal model, we formulate an approximate expected rate maximization problem that considers both statistical channel state information (sCSI) and compensation errors. Unlike conventional approaches that recast such problems as weighted minimum mean square error (WMMSE) minimization, we demonstrate that this transformation fails to maintain equivalence in the considered scenario. To address this, we introduce an equivalent covariance decomposition-based WMMSE (CDWMMSE) formulation derived based on channel covariance matrix decomposition. By exploiting the channel characteristics, we develop a low-complexity decomposition method and propose an optimization algorithm. To further reduce computational complexity, we introduce a model-driven scalable deep learning (DL) approach that leverages the equivariance of the mapping from sCSI to the unknown variables in the optimal closed-form solution, enhancing performance through novel dense Transformer network and scaling-invariant loss function design. Simulation results validate the effectiveness and robustness of the proposed method in some practical scenarios. We also demonstrate that the DL approach can adapt to dynamic settings with varying numbers of users and satellites.

The upper mid-band balances coverage and capacity for the future cellular systems and also embraces extremely large-scale multiple-input multiple-output (XL-MIMO) systems, offering enhanced spectral and energy efficiency. However, these benefits are significantly degraded under mobility due to channel aging, and further exacerbated by the unique near-field (NF) and spatial non-stationarity (SnS) propagation in such systems. To address this challenge, we propose a novel channel prediction approach that incorporates dedicated channel modeling, probabilistic representations, and Bayesian inference algorithms for this emerging scenario. Specifically, we develop tensor-structured channel models in both the spatial-frequency-temporal (SFT) and beam-delay-Doppler (BDD) domains, which capture the NF and SnS propagation effects and leverage temporal correlations among multiple snapshots for channel prediction. In this model, the factor matrices of multi-linear transformations are parameterized by BDD domain grids and SnS factors, where beam domain grids are jointly determined by angles and slopes under spatial-chirp based NF representations. To enable tractable inference, we replace these environment-dependent BDD domain grids with uniformly sampled ones, and introduce perturbation parameters in each domain to mitigate grid mismatch.We further propose a hybrid beam domain strategy that integrates angle-only sampling with slope hyperparameterization to avoid the computational burden of explicit slope sampling. On this basis, we develop tensor-structured bi-layer inference (TS-BLI) algorithm under the expectation-maximization (EM) framework, which reduces the computational complexity by leveraging the inherent separation across different domains. In the E-step, we develop the bi-layer factor graph representation to isolate the bilinear mixing in the spatial domain induced by SnS propagation, thus facilitating bi-layer iterations using approximate inference techniques. In the M-step, we leverage an alternating strategy for hyperparameter learning, with closed-form rules derived by the quadratic approximation of objective functions. Numerical simulations based on a near-practical channel simulator developed upon QuaDRiGa with SnS extensions demonstrate the superior channel prediction performance of the proposed algorithm.

This paper investigates robust transmit (TX) beamforming from the satellite to user terminals (UTs), based on statistical channel state information (CSI). The proposed design specifically targets the mitigation of satellite-to-terrestrial interference in spectrum-sharing integrated terrestrial and satellite networks. By leveraging the distribution information of terrestrial UTs, we first establish an interference model from the satellite to terrestrial systems without shared CSI. Based on this, robust TX beamforming schemes are developed under both the interference threshold and the power budget. Two optimization criteria are considered: satellite weighted sum rate maximization and mean square error minimization. The former achieves a superior achievable rate performance through an iterative optimization framework, whereas the latter enables a low-complexity closed-form solution at the expense of reduced rate, with interference constraints satisfied via a bisection method. To avoid complex integral calculations and the dependence on user distribution information in inter-system interference evaluations, we propose a terrestrial base station position-aided approximation method, and the approximation errors are subsequently analyzed. Numerical simulations validate the effectiveness of our proposed schemes.

In moderate- to high-mobility scenarios, channel state information (CSI) varies rapidly and becomes temporally non-stationary, leading to severe performance degradation in the massive multiple-input multiple-output (MIMO) transmissions. To address this issue, we propose a tensor-structured approach to dynamic channel prediction (TS-DCP) for massive MIMO systems with temporal non-stationarity, exploiting both dual-timescale and cross-domain correlations. Specifically, due to inherent spatial consistency, non-stationary channels over long-timescales can be approximated as stationary on short-timescales, decoupling complicated temporal correlations into more tractable dual-timescale ones. To exploit such property, we propose the sliding frame structure composed of multiple pilot orthogonal frequency-division multiplexing (OFDM) symbols, which capture short-timescale correlations within frames by Doppler domain modeling and long-timescale correlations across frames by Markov/autoregressive processes. Building on this, we develop the Tucker-based spatial-frequency-temporal domain channel model, incorporating angle-delay-Doppler (ADD) domain channels and factor matrices parameterized by ADD domain grids. Furthermore, we model cross-domain correlations of ADD domain channels within each frame, induced by clustered scattering, through the Markov random field and tensor-coupled Gaussian distribution that incorporates high-order neighborhood structures. Following these probabilistic models, we formulate the TS-DCP problem as variational free energy (VFE) minimization, and unify different inference rules through the structure design of trial beliefs. This formulation results in the dual-layer VFE optimization process and yields the online TS-DCP algorithm, where the computational complexity is reduced by exploiting tensor-structured operations. Numerical simulations demonstrate the significant superiority of the proposed algorithm over benchmarks in terms of channel prediction performance.

Large AI models (LAMs) offer new opportunities for wireless intelligence, but their deployment in latency- and resource-constrained systems remains challenging. To explore this in the context of channel state information (CSI) feedback for frequency-division duplex (FDD) massive multiple-input and multiple-output (MIMO) systems, we propose a novel framework, OLAMCF, that integrates LAMs via offline codebook optimization, thereby avoiding the need for real-time inference. Specifically, the large vision model (LVM) at the core of this framework is built upon a vision-based backbone, pre-trained on large-scale image datasets and fine-tuned with site-specific CSI. This strategy allows this framework to capture the structural similarity between CSI and image to refine codewords from the conventional codebook and generate customized codebooks tailored to the specific environments. Simulation results show that our approach significantly outperforms existing schemes in both reconstruction accuracy and system throughput, without introducing additional inference latency or computational overhead. This design philosophy—extracting the best offline and discarding the rest online—offers a practical perspective on integrating LAMs into communication systems.

This paper investigates robust transmit beamforming based on statistical channel state information (CSI), against satellite-to-terrestrial user terminal (UT) interference arising from spectrum sharing in the integrated terrestrial and satellite network. First, we develop an integral-form interference model free of shared CSI to characterize the interference from satellite to terrestrial UTs. Then, we propose a robust interference-avoidance transmit beamforming scheme under the interference threshold and power budget. We derive a closed-form solution based on the minimum mean square error criterion and apply a bisection method to satisfy interference thresholds. Furthermore, we introduce a base station position-aided approximation scheme to eliminate the complex integral calculations. Numerical simulations validate the proposed schemes.

With the burgeoning advancement of mega low earth orbit (LEO) satellite constellations, multi-antenna gateway station (MAGS) has emerged as a key enabler to support extremely high system capacity via massive feeder links. However, the densification of both space and ground segment will lead to reduced spatial separation between links, posing unprecedented challenges of interference exacerbation. This paper investigates graph coloring-based frequency allocation methods for interference mitigation (IM) of mega LEO satellite communication (SatCom) systems. We reveal the characteristics of MAGS interference pattern and formulate the IM problem of mega LEO systems into a K-coloring problem using an adaptive threshold method. Then, we propose a tailored graph coloring algorithm called Clique-Based Tabu Search (CTS), which leverages the unique clique structure brought by MAGSs to achieve outstanding IM performance. Simulation results demonstrate the superiority and effectiveness of the proposed methodology.

This paper presents a dual transformer-based robust precoding scheme for massive multiple-input multiple-output systems with low computational complexity. By utilizing the a posteriori channel model, the imperfect channel state information (CSI) is modeled as the statistical CSI that incorporates channel mean and channel variance information with spatial correlation. Based on this, we formulate a robust precoding problem aimed at maximizing the expected sum rate and subsequently transform it into a robust weighted minimum mean square error problem. We prove the permutation equivariance and invariance satisfied by the mapping from the available CSI to the low-dimensional variables in the optimal closed-form solution. To fully exploit such properties, we design a dual transformer block with residual connection and introduce an invariant transformer module to construct a neural network, which is trained to approximate the mapping for precoding computation. Simulation results demonstrate that this method exhibits strong robustness, lower computational complexity, and high scalability in dynamic user/antenna scenarios compared to other approaches.

This paper studies the distributed precoding design for multi-satellite massive MIMO transmission. We first conduct a detailed analysis of the transceiver process, examining the effects of delay and Doppler compensation errors and emphasizing the nearly independent nature of inter-satellite interference. Based on the derived signal model, an approximate expected sum rate maximization problem is formulated, incorporating statistical channel state information and compensation errors. Unlike conventional approaches that recast such problems as weighted minimum mean square error (WMMSE) minimization, we demonstrate that this transformation cannot hold equivalence in the considered scenario. To address this, we propose a modified WMMSE formulation leveraging channel covariance matrix decomposition. By exploiting channel characteristics, a low-complexity decomposition method is then developed, accompanied by an efficient algorithm. Simulation results validate the effectiveness and robustness of the proposed method in some practical simulated scenarios.

The unsourced random access (URA) has emerged as a viable scheme for supporting the massive machine-type communications (mMTC) in the sixth generation (6G) wireless networks. Notably, the tensor-based URA (TURA), with its inherent tensor structure, stands out by simultaneously enhancing performance and reducing computational complexity for the multi-user separation, especially in mMTC networks with a large number of active devices. However, current TURA scheme lacks the soft decoder, thus precluding the incorporation of existing advanced coding techniques. In order to fully explore the potential of the TURA, this paper investigates the Polar-coded TURA (PTURA) scheme and develops the corresponding iterative Bayesian receiver with feedback (IBR-FB). Specifically, in the IBR-FB, we propose the Grassmannian modulation-aided Bayesian tensor decomposition (GM-BTD) algorithm under the variational Bayesian learning (VBL) framework, which leverages the property of the Grassmannian modulation to facilitate the convergence of the VBL process, and has the ability to generate the required soft information without the knowledge of the number of active devices. Furthermore, based on the soft information produced by the GM-BTD, we design the soft Grassmannian demodulator in the IBR-FB. Extensive simulation results demonstrate that the proposed PTURA in conjunction with the IBR-FB surpasses the existing state-of-the-art unsourced random access scheme in terms of accuracy and computational complexity.

In this paper, we propose a unified framework based on equivariance for the design of artificial intelligence (AI)-assisted technologies in multi-user multiple-input-multiple-output (MU-MIMO) systems. We first provide definitions of multidimensional equivariance, high-order equivariance, and multidimensional invariance (referred to collectively as tensor equivariance). On this basis, by investigating the design of precoding and user scheduling, which are key techniques in MU-MIMO systems, we delve deeper into revealing tensor equivariance of the mappings from channel information to optimal precoding tensors, precoding auxiliary tensors, and scheduling indicators, respectively. To model mappings with tensor equivariance, we propose a series of plug-and-play tensor equivariant neural network (TENN) modules, where the computation involving intricate parameter sharing patterns is transformed into concise tensor operations. Building upon TENN modules, we propose the unified tensor equivariance framework that can be applicable to various communication tasks, based on which we easily accomplish the design of corresponding AI-assisted precoding and user scheduling schemes. Simulation results show that the proposed methods achieve near-optimal performance with significantly lower complexity and strong generalization across multiple dimensions. For instance, the NN trained for precoding with 8 users provides satisfactory performance in a 10-user scenario. This validates the superiority of TENN modules and the unified framework.

This paper investigates the joint beam alignment and Doppler estimation (BADE) for fast time-varying wideband millimeter-wave channels, which is essential for subsequent data transmission. In such scenarios, the non-negligible Doppler frequencies significantly impact the beam alignment performance and reference signal overhead, calling for accurate time variation modeling and efficient transceiver design. Toward this end, we leverage the angle, Doppler frequency, and delay sparsity, thus formulating the joint BADE problem as a sparse signal recovery problem in the angle-Doppler-delay domain. The feasibility of the formulated problem strongly depends on the transmitter codebook and the receiver algorithm, which motivates our design. For the transmitter codebook, we characterize the design criterion aiming at maximal identifiable paths, which facilitates precise path parameter estimations and is not satisfied by existing deterministic codebooks. Following this, we provide a new deterministic codebook generation algorithm to meet the necessary conditions of the proposed criterion. For the receiver algorithm, we propose the greedy-based multi-path parameter extraction algorithm. In the proposed algorithm, the hierarchical refinement dictionaries with extended refinement range are employed, balancing the BADE performance and computational complexity. The numerical simulations demonstrate the superiority of the proposed transceiver over benchmarks on the joint BADE problem.

In this paper, we consider symbol-level precoding (SLP) in channel-coded multiuser multi-input single-output (MISO) systems. It is observed that the received SLP signals do not always follow Gaussian distribution, rendering the conventional soft demodulation with the Gaussian assumption unsuitable for the coded SLP systems. It, therefore, calls for novel soft demodulator designs for non-Gaussian distributed SLP signals with accurate log-likelihood ratio (LLR) calculation. To this end, we first investigate the non-Gaussian characteristics of both phase-shift keying (PSK) and quadrature amplitude modulation (QAM) received signals with existing SLP schemes and categorize the signals into two distinct types. The first type exhibits an approximate-Gaussian distribution with the outliers extending along the constructive interference region (CIR). In contrast, the second type follows some distribution that significantly deviates from the Gaussian distribution. To obtain accurate LLR, we propose the modified Gaussian soft demodulator and Gaussian mixture model (GMM)-expectation-maximization (EM) soft demodulators to deal with two types of signals respectively. Subsequently, to further reduce the computational complexity and pilot overhead, we put forward a novel neural network named pilot feature extraction network (PFEN) to replace the EM algorithm, leveraging the transformer mechanism in deep learning. Simulation results show that the proposed soft demodulators dramatically improve the throughput of existing SLPs for both PSK and QAM transmission in coded systems.

This paper investigates the robust design of symbol-level precoding (SLP) for multiuser multiple-input multiple-output (MIMO) downlink transmission with imperfect channel state information (CSI) caused by channel aging. By utilizing thea posteriorichannel model based on the widely adopted jointly correlated channel model, the imperfect CSI is modeled as the statistical CSI incorporating the channel mean and channel variance information with spatial correlation. With the signal model in the presence of channel aging, we formulate the signal-to-noise-plus-interference ratio (SINR) balancing and minimum mean square error (MMSE) problems for robust SLP design. The former targets to maximize the minimum SINR across users, while the latter minimizes the mean square error between the received signal and the target constellation point. When it comes to massive MIMO scenarios, the increment in the number of antennas poses a computational complexity challenge, limiting the deployment of SLP schemes. To address such a challenge, we simplify the objective function of the SINR balancing problem and further derive a closed-form SLP scheme. Besides, by approximating the matrix involved in the computation, we modify the proposed algorithm and develop an MMSE-based SLP scheme with lower computation complexity. Simulation results confirm the superiority of the proposed schemes over the state-of-the-art SLP schemes.

This paper investigates the robust design of symbollevel precoding (SLP) for multiuser multiple-input multipleoutput (MIMO) downlink transmission with imperfect channel state information (CSI) caused by channel aging. By utilizing the a posteriori channel model based on the widely adopted jointly correlated channel model, the imperfect CSI is modeled as the statistical CSI incorporating the channel mean and channel variance information with spatial correlation. With the signal model in the presence of channel aging, we formulate the signal-to-noise-plus-interference ratio (SINR) balancing problem for robust SLP design, which targets to maximize the minimum SINR and can be transformed into a typical max-min fractional programming (MMFP). In the scenario of massive MIMO, we simplify the objective function of the SINR balancing problem and further derive a low-complexity SLP scheme. Simulation results confirm the superiority of the proposed schemes over the state-of-the-art SLP schemes.

This paper focuses on energy efficiency (EE) pre-coding design and computational-efficient precoding updating strategy for low earth orbit (LEO) satellite communications. Firstly, we formulate the EE precoding problem, which aims to maximize the EE metric under the quality of service (QoS) constraint and per-antenna power constraint (PAPC). By intro-ducing semidefinite relaxation, first-order Taylor approximation, and quadratic transformation, the problem is transferred into a convex one that can be efficiently solved. Moreover, due to the continuous movement of LEO satellites, precoding is performed frequently to maintain the high EE performance, leading to high computational complexity. Consequently, we consider prolonging precoding intervals to reduce complexity while alleviating severe performance degradation during the intervals. To this end, a computational-efficient beam direction change (BDC) algorithm is proposed to update pre coding vectors, which makes the main lobes of beams always point toward users. Furthermore, an adaptive method is proposed to adjust the precoding interval flexibly. Simulation results have indicated the effectiveness of the EE precoding algorithm and the BDC algorithm.

Abstract With the increasing number of user terminals (UTs), the interference among UTs might significantly decrease the throughput of the low earth orbit satellite communication system. In this paper, the user scheduling method is investigated to suppress user interference. Specifically, leveraging the strong spatial directivity of satellite channels, a low‐complexity angle‐based orthogonal user selection (AOUS) algorithm is proposed, which selects UTs with nearly orthogonal channels via angle information of UTs. A rate‐based proportionally fair (PF)‐AOUS algorithm is further proposed to ensure fairness among UTs, which combines the AOUS with the PF criterion. To reduce complexity, an improved angle‐based PF‐AOUS algorithm that schedules UTs according to their pitch angles rather than their rates is proposed. In addition, efficient precoding schemes for orthogonal UTs are designed by combining the steering vector and power allocation matrix, and it is shown that precoding can be converted into power allocation problems that further balance fairness and throughput. The numerical results indicate that the AOUS achieves a near‐optimal sum rate performance, and the angle‐based PF‐AOUS has the similar performance to the rate‐based PF‐AOUS, which achieves a high fairness index with the proposed precoding scheme.

This paper studies low-complexity robust beamforming in mobile massive multiple-input multiple-output (MIMO) wireless communication systems, which introduces a robustness factor and deep learning (DL)-based framework to mitigate the impact of imperfect channel state information (CSI). By incorporating the estimation uncertainty, we aim to design transceivers to minimize outage probability subject to a total transmit power constraint. However, due to the probabilistic constraints, the optimization problem is difficult to solve. Therefore, we introduce a robustness factor to the quality of service (QoS) constraints by maximizing a zero-outage region, based on an extension of the offset maximization method. Then, we convert the problem into a convex problem and get a quasi-closed-form solution. Besides, iterating the fixed point equation of the Lagrange multipliers in the inequality optimization introduces enormous computational complexity. To this end, we present a novel DL-based algorithm to predict the multipliers directly from imperfect CSI, which includes a column convolutional layer elaborately designed for channel input. Comprehensive experimental comparisons demonstrate the proposed robust transceiver can improve the outage probability significantly over conventional baselines, and the DL-based algorithm can further reduce the running time.