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.

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.

The increasing demands for spectral resources in emerging massive machine-type communication applications necessitate the implementation of massive grant-free transmission in the millimeter-wave (mmWave) band. This paper proposes two efficient receive analog beamforming design algorithms for mmWave massive grant-free transmission under hybrid beamforming architectures, intending to optimize spectral efficiency and access probability, respectively. Specifically, we first express the spectral efficiency of mmWave massive grant-free transmission systems and then derive an analytically tractable approximation using the random matrix theory. Following this, an alternating optimization method is employed to design the receive beamforming matrix efficiently. Additionally, we provide the formulation of access probability for mmWave massive grant-free transmission, whose explicit expression is approximately derived through the Gaussian approximation. Building upon this, we utilize a convex hull relaxation-based optimization method to optimize the beamforming matrix. The effectiveness of our proposed beamforming design algorithms in improving spectral efficiency and access probability is validated through extensive simulation experiments.

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.

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.

To meet the escalating demand on spectral resource in massive machine-type communication (mMTC) applications, a critical solution is applying massive grant-free transmission to the millimeter-wave (mmWave) band. In this paper, to maximize the ergodic rate, we propose an efficient hybrid analog/digital beamforming (HBF) design algorithm for the massive grant-free transmission in uplink mmWave systems. Specifically, to make the HBF design problem tractable, we first leverage the deterministic equivalent method to derive an approximate expression of the ergodic rate for the mMTC in the mmWave system. Since the ergodic rate maximization-based HBF design problem is nonconvex, we leverage the alternating optimization strategy and propose a semidefinite relaxation-based HBF algorithm to improve the ergodic rate. Simulation results verify the superior performance of the proposed HBF design algorithm in improving the ergodic rate.

In massive grant-free transmission, joint user activity detection (UAD) and channel estimation (CE) is essential for data recovery at the receiver, which has been extensively researched in frequency-flat fading scenarios. However, in practical orthogonal frequency division multiplexing (OFDM)-based systems, frequency-selective fading leads to a significant increase in the number of channel coefficients to be estimated, imposing new challenges for the design of joint UAD and CE algorithms. Therefore, this paper investigates joint UAD and CE for OFDM-based massive grant-free transmission over frequency-selective fading channels. Firstly, the discrete cosine transform (DCT) is employed to reformulate the compressed sensing (CS) problem with the reduced dimension of the DCT domain channel response vector. Then, we develop a hybrid message passing (HMP) algorithm under the framework of the constrained Bethe free energy (BFE) minimization to achieve efficient joint UAD and CE. Numerical results confirm the superior joint estimation performance of the proposed algorithm over frequency-selective fading channels.

In massive grant-free transmission, joint user activity detection (UAD) and channel estimation (CE) is essential for data recovery at the receiver, which has been extensively researched in frequency-flat fading scenarios. However, in practical orthogonal frequency division multiplexing (OFDM)-based systems, frequency-selective fading (FSF) leads to a significant increase in the number of channel coefficients to be estimated, imposing new challenges for the design of joint UAD and CE algorithms. Therefore, this paper investigates joint UAD and CE for OFDM-based massive grant-free transmission over FSF channels. Firstly, by employing the discrete cosine transform (DCT), the joint estimation problem is formulated as the compressed sensing (CS) problem with the reduced dimension of the DCT-domain channel response vector. Then, based on the low-dimension sparse channel model, we develop a hybrid message passing (HMP) algorithm under the constrained Bethe free energy (BFE) minimization framework to achieve efficient joint UAD and CE. To deal with the lack of the DCT-domain prior information in practical scenarios, we parameterize it as the Cauchy distribution or the Laplacian distribution and learn their parameters by the proposed HMP algorithm. Numerical results confirm the superior joint UAD and CE performance of the proposed algorithm over FSF channels.

In the massive grant-free orthogonal frequency division multiple access (OFDMA), the timing and frequency offsets between users impose new challenges on joint active user detection (AUD) and channel estimation (CE) for the subsequent data recovery. In the asynchronous OFDMA, the timing and frequency offset effects can be modeled as the phase-shifting on the pilot matrix. As such, by constructing the measurement matrix with timing and frequency offsets, the joint estimation problem can be formulated as a multiple measurement vector (MMV) recovery problem with structured sparsity. However, such structured sparsity cannot be tackled by the existing compressed sensing (CS) techniques. To address this issue, we develop an efficient structured generalized approximate message passing (S-GAMP) algorithm, which includes the parallel AMP-MMV algorithm as a particular case. To deal with the high dimensionality of the measurement matrix, we propose the dynamic S-GAMP algorithm with a dynamic measurement matrix to reduce the computational complexity. Simulation results confirm the superiority of the proposed algorithms in grant-free OFDMA with both timing and frequency offsets.