A Tensor-Structured Approach to Dynamic Channel Prediction for Massive MIMO Systems with Temporal Non-Stationarity

In moderate- to high-mobility scenarios, channel state information (CSI) varies rapidly and becomes temporally non-stationary, leading to significant performance degradation in channel reciprocity-dependent massive multiple-input multiple-output (MIMO) transmission. To address this challenge, we propose a tensor-structured approach to dynamic channel prediction (TS-DCP) for massive MIMO systems with temporal non-stationarity, leveraging dual-timescale and cross-domain correlations. Specifically, due to the inherent spatial consistency, non-stationary channels on long-timescales are treated as stationary on short-timescales, decoupling complicated correlations into more tractable dual-timescale ones. To exploit such property, we frame the pilot symbols, capturing short-timescale correlations within frames by Doppler domain modeling and long-timescale correlations across frames by Markov/autoregressive processes. Based on this, we develop the tensor-structured signal model in the spatial-frequency-temporal domain, incorporating correlated angle-delay-Doppler domain channels and Vandermonde-structured factor matrices. Furthermore, we model cross-domain correlations within each frame, arising from clustered scatterer distributions, using tensor-structured upgradations of Markov processes and coupled Gaussian distributions. Following these probabilistic models, we formulate the TS-DCP as the variational free energy (VFE) minimization problem, designing trial belief structures through online approximation and the Bethe method. This yields the online TS-DCP algorithm derived from a dual-layer VFE optimization process, where both outer and inner layers leverage the multilinear structure of channels to reduce computational complexity significantly. Numerical simulations demonstrate the significant superiority of the proposed algorithm over benchmarks in terms of channel prediction performance.

Polar-Coded Tensor-Based Unsourced Random Access with Soft Decoding

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 numer 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 Polarcoded 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.

Towards Unified AI Models for MU-MIMO Communications: A Tensor Equivariance Framework

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 demonstrate that the constructed precoding and user scheduling methods achieve near-optimal performance while exhibiting significantly lower computational complexity and generalization to inputs with varying sizes across multiple dimensions. This validates the superiority of TENN modules and the unified framework.

Joint Channel Estimation and Prediction for Massive MIMO with Frequency Hopping Sounding

In massive multiple-input multiple-output (MIMO) systems, the downlink transmission performance heavily relies on accurate channel state information (CSI). Constrained by the transmitted power, user equipment always transmits sounding reference signals (SRSs) to the base station through frequency hopping, which will be leveraged to estimate uplink CSI and subsequently predict downlink CSI. This paper aims to investigate joint channel estimation and prediction (JCEP) for massive MIMO with frequency hopping sounding (FHS). Specifically, we present a multiple-subband (MS) delay-angle-Doppler (DAD) domain channel model with off-grid basis to tackle the energy leakage problem. Furthermore, we formulate the JCEP problem with FHS as a multiple measurement vector (MMV) problem, facilitating the sharing of common CSI across different subbands. To solve this problem, we propose an efficient Off-Grid-MS hybrid message passing (HMP) algorithm under the constrained Bethe free energy (BFE) framework. Aiming to address the lack of prior CSI in practical scenarios, the proposed algorithm can adaptively learn the hyper-parameters of the channel by minimizing the corresponding terms in the BFE expression. To alleviate the complexity of channel hyper-parameter learning, we leverage the approximations of the off-grid matrices to simplify the off-grid hyper-parameter estimation. Numerical results illustrate that the proposed algorithm can effectively mitigate the energy leakage issue and exploit the common CSI across different subbands, acquiring more accurate CSI compared to state-of-the-art counterparts.

Robust Symbol-Level Precoding for Massive MIMO Communication Under Channel Aging

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 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 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.

Beam-Delay Domain Channel Estimation for mmWave XL-MIMO Systems

This paper investigates the uplink channel estimation of the millimeter-wave (mmWave) extremely large-scale multiple-input-multiple-output (XL-MIMO) communication system in the beam-delay domain, taking into account the near-field and beam-squint effects due to the transmission bandwidth and array aperture growth. Specifically, we model the sparsity in the delay domain to explore inter-subcarrier correlations and propose the beam-delay domain sparse representation of spatial-frequency domain channels. The independent and non-identically distributed Bernoulli-Gaussian models with unknown prior hyperparameters are employed to capture the sparsity in the beam-delay domain, posing a challenge for channel estimation. Under the constrained Bethe free energy minimization framework, we design different structures on the beliefs to develop hybrid message passing (HMP) algorithms, thus achieving efficient joint estimation of beam-delay domain channel and prior hyperparameters. To further improve the model accuracy, the multidimensional grid point perturbation (MDGPP)-based representation is presented, which assigns individual perturbation parameters to each multidimensional discrete grid. By treating the MDGPP parameters as unknown hyperparameters, we propose the two-stage HMP algorithm for MDGPP-based channel estimation, where the output of the initial estimation stage is pruned for the refinement stage for the computational complexity reduction. Numerical simulations demonstrate the significant superiority of the proposed algorithms over benchmarks with both near-field and beam-squint effects.

Soft Demodulator for Symbol-Level Precoding in Coded Multiuser MISO Systems

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) 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 soft demodulator, named pilot feature extraction network (PFEN), 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.

Symbol-Level Precoding for Average SER Minimization in Multiuser MISO Systems

This paper investigates symbol-level precoding (SLP) for high-order quadrature amplitude modulation (QAM) aimed at minimizing the average symbol error rate (SER), leveraging both constructive interference (CI) and noise power to gain superiority in full signal-to-noise ratio (SNR) ranges. We first construct the SER expression with respect to the transmitted signal and the rescaling factor, based on which the problem of average SER minimization subject to total transmit power constraint is further formulated. Given the non-convex nature of the objective, solving the above problem becomes challenging. Due to the differences in constraints between the transmit signal and the rescaling factor, we propose the double-space alternating optimization (DSAO) algorithm to optimize the two variables on orthogonal Stiefel manifold and Euclidean spaces, respectively. To facilitate QAM demodulation instead of affording impractical signaling overhead, we further develop a block transmission scheme to keep the rescaling factor constant within a block. Simulation results demonstrate that the proposed SLP scheme exhibits a significant performance advantage over existing state-of-the-art SLP schemes.