Multi-user Massive Multiple-input Multiple-output Systems Research Articles

3D Antenna array for multi-user massive MIMO system to minimize unfavorable propagation

Unfavorable propagation in massive multiple input multiple output (MIMO) systems is an underlying channel condition that reduces the gains offered by the system in terms of parallel channels. This paper presents a study on different types of antenna array configurations at base station (BS) to minimize unfavorable propagation conditions. Unfavorable propagation results in increased correlation between channel vectors of two or more mobile terminals (MTs) which arises when the signals from two or more MTs have small angular separation and small angular spread. The study starts with the investigation of the conventional uniform linear array (ULA) under different propagation conditions using a geometrical channel model based on a single cluster of scatterers per MT to quantify the performance degradation in unfavorable propagation. Subsequently, the performance of other types of array geometries is investigated. A custom cluster-based geometrical channel model is used in this study which includes practical propagation aspects like multipath fading, shadow fading, and the effect of BS height. Further, the study considers two cases: micro-cell and macro-cell. Under space constraint settings in terms of the maximum dimension of the array, the proposed technique uses randomized antenna locations in the array to minimize the effect of unfavorable propagation. Based on the results on performance parameters like user correlation and capacity, the study reveals that an antenna array configuration comprising of elements distributed random-homogeneously in a spherical shell outperforms other configurations.

Performance analysis of multiuser massive MIMO with multi-antenna users: Asymptotic data rate and its application

Massive multiple-input multiple-output (MIMO) systems have become an essential feature in the fifth-generation (5G) wireless communication networks. Due to the commercialization of 5G mobile communication devices, the number of multi-antenna devices have increased over the years. Therefore, a precoding scheme based on multi-antenna users is an inevitable feature that needs to be analyzed in massive MIMO systems. The asymptotic ergodic sum-rate analysis of block diagonalization (BD) based multiuser MIMO systems is performed in this study. Based on the random matrix theory results derived from the massive base station antenna characteristics, the singular values of the block diagonalized channel are obtained asymptotically, and thereby, the closed-form expression for the BD based sum-rate is derived. The asymptotic sum-rate performance gap between the BD and the zero-forcing beamforming is then analyzed. Moreover, from the derived asymptotic sum-rate, the optimal number of users needed to maximize the ergodic sum-rate is proposed. Simulation results show that the derived asymptotic analyses are closely aligned to the sum-rate obtained by Monte Carlo simulations. In addition, the simulation results prove that the maximum ergodic sum-rate can be achieved by using the proposed number of users.

Multi-Stream Transmission in Massive MIMO Systems With Full-Duplex Bi-Directional Communication Links

This paper considers a full-duplex (FD) multi-user massive multiple-input multiple-output system where the base station (BS) and user equipment (UE) bi-directionally transmit and receive multiple independent data streams over the same frequency band. The BS and UEs are equipped with a large-scale antenna array. Accounting for imperfect channel state information, we derive the closed-form expressions for the achievable sum-rate and sum spectral efficiency (SE) for the proposed model using maximum-ratio combining and zero-forcing detection. The analytical solutions are verified with simulations. In addition, our analytical results highlight the benefits of multi-stream transmission and show an improved SE for fewer UEs. Moreover, the results show that increasing the antenna array size helps combat self-interference.

Joint CFO and Channel Estimation for RIS-Aided Multi-User Massive MIMO Systems

Accurate channel estimation is essential to achieve the performance gains promised by the use of reconfigurable intelligent surfaces (RISs) in wireless communications. In the uplink of multi-user orthogonal frequency division multiple access (OFDMA) systems, synchronization errors such as carrier frequency offsets (CFOs) can significantly degrade the channel estimation performance. This becomes more critical in RIS-aided communications, as the RIS phases are adjusted based on the channel estimates and even a small channel estimation error leads to a significant performance loss. Motivated by this, we propose a joint CFO and channel estimation method for RIS-aided multi-user massive multiple-input multiple-output (MIMO) systems. Our proposed pilot structure makes it possible to accurately estimate the CFOs without multi-user interference (MUI), using the same pilot resources for both CFO estimation and channel estimation. For optimization of the RIS phase shifts at the data transmission stage, we propose a projected gradient method (PGM) which achieves the same performance as a more computationally demanding grid search technique while having a significantly lower computational complexity. Simulation results demonstrate that the proposed method provides an improvement in the normalized mean-square error (NMSE) of channel es-timation as well as in the bit error rate (BER) performance. Moreover, analyzing the computational complexity and the pilot resource efficiency of the proposed method, we demonstrate that the proposed estimation approach requires low computational load and no extra cost in pilot overhead.

ADMM Based Interference Exploitation Multi-User One-Bit Massive MIMO Precoding

In this paper, we focus on the 1-bit precoding design for a multi-user massive multiple-input multiple-output (MIMO) system, where the concept of constructive interference (CI) is employed to formulate the optimization problem. By adopting the symbol-scaling CI metric, the formulated optimization problem is transformed such that the alternating direction method of multipliers (ADMM) framework can be used to solve this problem. Furthermore, we obtain the closed-form solution to the subproblem in each step within the ADMM iteration, thus achieving lower complexity. We further provide the computational complexity analysis of the proposed algorithm. Numerical experiments verify the superior bit error rate (BER) performance of the proposed ADMM-based CI precoding (CI-ADMM) scheme over the state-of-the-art, with proper initialization.

Deep Learning-Based Rate-Splitting Multiple Access for Reconfigurable Intelligent Surface-Aided Tera-Hertz Massive MIMO

Reconfigurable intelligent surface (RIS) can significantly enhance the service coverage of Tera-Hertz massive multiple-input multiple-output (MIMO) communication systems. However, obtaining accurate high-dimensional channel state information (CSI) with limited pilot and feedback signaling overhead is challenging, severely degrading the performance of conventional spatial division multiple access. To improve the robustness against CSI imperfection, this paper proposes a deep learning (DL)-based rate-splitting multiple access (RSMA) scheme for RIS-aided Tera-Hertz multi-user MIMO systems. Specifically, we first propose a hybrid data-model driven DL-based RSMA precoding scheme, including the passive precoding at the RIS as well as the analog active precoding and the RSMA digital active precoding at the base station (BS). To realize the passive precoding at the RIS, we propose a Transformer-based data-driven RIS reflecting network (RRN). As for the analog active precoding at the BS, we propose a match-filter based analog precoding scheme considering that the BS and RIS adopt the LoS-MIMO antenna array architecture. As for the RSMA digital active precoding at the BS, we propose a low-complexity approximate weighted minimum mean square error (AWMMSE) digital precoding scheme, and further design a model-driven deep unfolding active precoding network (DFAPN) by combining the proposed AWMMSE scheme with DL. Then, to acquire accurate CSI at the BS for the investigated RSMA precoding scheme to achieve higher spectral efficiency, we propose a CSI acquisition network (CAN) with low pilot and feedback signaling overhead. The proposed DL-based RSMA scheme for RIS-aided Tera-Hertz multi-user MIMO systems can exploit the advantages of RSMA and DL to improve the robustness against CSI imperfection, thus achieving higher spectral efficiency with lower signaling overhead.

Design of bitstream-based adaptive-connected array architecture for mmWave Multiuser MIMO systems

We investigate a bitstream-based adaptive-connected massive multiple-input multiple-output (MIMO) architecture that trades off between high-power full-connected and low-performance sub-connected hybrid precoding architectures. The proposed adaptive-connected architecture which enables each data stream to be computed independently and in parallel, consists of fewer phase shifters (PS) and switches than the other adaptive-connected architectures. With smaller array groups, the proposed architecture uses fewer PS and switches, so that its power consumption gradually decreases in millimeter wave (mmWave) Multiuser MIMO (MU-MIMO) system. To fully demonstrate the performance of the proposed architecture in mmWave MU-MIMO system with practical constraints, we combine the connection-state matrix with the hybrid precoders and combiners to maximize energy efficiency (EE) of the system equipped with the proposed architecture. We then propose the hybrid precoding and combining (HPC) scheme suitable for multi-user and multi-data streams which utilizes the SCF algorithm to obtain the constant modulus of the analog precoder at convergence. In the digital precoding and combining stage, the digital precoder and combiner are designed to reduce the amount of computation by utilizing the singular value decomposition (SVD) of corresponding equivalent channel. In the mmWave MU-MIMO-OFDM system equipped with the proposed architecture, with the increase of the total number of data streams, simulation results demonstrate that we can exploit the proposed HPC scheme to achieve better EE than the traditional hybrid full-connected architecture exploiting some existing schemes.

Semi-Probabilistic Repetition Schemes for Sporadic URLLC Traffic in Multiuser Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) assisted grant-free access is a compelling approach to support uplink ultra-reliable low-latency communications (URLLCs). It is a natural idea to combine massive MIMO and repetition transmission to further improve the reliability. However, excessive repetitions may increase the collision probability in multiuser scenarios and thus limit the reliability improvement. In this paper, we propose a novel semi-probabilistic repetition (SPRe) scheme for the massive multiuser MIMO (MU-MIMO) systems with grant-free access. By introducing a transmission probability for the replicas, the SPRe is more flexible than the popular repetition scheme, i.e., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -repetition, and covers the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -repetition as a special case. Considering practical MU-MIMO systems with finite block-length coding, channel estimation errors, pilot collisions and the sporadic arrivals of URLLC traffic, the reliability of the proposed SPRe is thoroughly analyzed and derived in closed form. Through further asymptotic analysis, the optimal transmission probability to maximize the reliability of MU-MIMO is derived for the high-SNR regime and low-load scenarios. Moreover, the diversity gain of the proposed SPRe is also analyzed and it is proved that the optimal SPRe is superior to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -repetition in terms of reliability. The analysis and superiority of the SPRe are finally verified through computer simulations.

Secure Communication for Spatially Correlated RIS-Aided Multiuser Massive MIMO Systems: Analysis and Optimization

This letter investigates the secure communication in a reconfigurable intelligent surface (RIS)-aided multiuser massive multiple-input multiple-output (MIMO) system exploiting artificial noise (AN). We first derive a closed-form expression of the ergodic secrecy rate under spatially correlated MIMO channels. By using this derived result, we further optimize the power fraction of AN in closed form and the RIS phase shifts by developing a gradient-based algorithm, which requires only statistical channel state information (CSI). Our analysis shows that spatial correlation at the RIS provides an additional dimension for optimizing the RIS phase shifts. Numerical simulations validate the analytical results which show the insightful interplay among the system parameters and the degradation of secrecy performance due to high spatial correlation at the RIS.

Rethinking WMMSE: Can Its Complexity Scale Linearly With the Number of BS Antennas?

Precoding design for maximizing weighted sum-rate (WSR) is a fundamental problem for downlink of massive multi-user multiple-input multiple-output (MU-MIMO) systems. It is well-known that this problem is generally NP-hard due to the presence of multi-user interference. The weighted minimum mean-square error (WMMSE) algorithm is a popular approach for WSR maximization. However, its computational complexity is cubic in the number of base station (BS) antennas, which is unaffordable when the BS is equipped with a large antenna array. In this paper, we consider the WSR maximization problem with either a sum-power constraint (SPC) or per-antenna power constraints (PAPCs). For the former, we prove that any nontrivial stationary point must have a low-dimensional subspace structure, and then propose a reduced-WMMSE (R-WMMSE) with linear complexity by exploiting the solution structure. For the latter, we propose a linear-complexity WMMSE approach, named PAPC-WMMSE, by using a novel recursive design of the algorithm. Both R-WMMSE and PAPC-WMMSE have simple closed-form updates and guaranteed convergence to stationary points. Simulation results verify the efficacy of the proposed designs, especially the much lower complexity as compared to the state-of-the-art approaches for massive MU-MIMO systems.

Second-Order Statistics-Aided Channel Estimation for Multipath Massive MIMO-OFDM Systems

This paper develops an efficient channel estimation algorithm based on second-order statistics of time division duplex (TDD) multiuser massive multiple-input multiple-output (MIMO) systems. The algorithm uses the received signal correlation to determine the most significant lags (MSLs) of the received signal. We first employ these MSLs to propose a novel set containing the channel’s four most significant taps (MSTs). Then, by using them, we propose an efficient semi-blind iterative algorithm called enhanced modified-subspace pursuit (EM-SP). It uses the set mentioned above and two theoretical results ( <xref ref-type="lemma" rid="lemma1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lemma 1</xref> and <xref ref-type="theorem" rid="theorem1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Theorem 1</xref> ) to estimate an arbitrary number of MSTs efficiently. Simulation results show that the normalized mean square error (NMSE) of the proposed EM-SP algorithm is much smaller than that of the subspace pursuit (SP) and orthogonal matching pursuit (OMP) algorithms at the cost of 0.3 % and 2 % more computational complexity for the channels with three and six nonzero paths, respectively. Moreover, the NMSE of it is very close to that of the optimal genie-aided least square algorithm.

Time-Varying Channel Estimation Scheme for Uplink MU-MIMO in 6G Systems

Channel estimation is a challenging issue for millimeter wave (mmWave) and massive multiple-input multiple-output (MIMO) in the future sixth generation (6G) wireless systems, where the conventional estimation schemes may fail to track the fast varying channels, especially in high-speed mobile scenarios. In this paper, a novel tensor-based uplink channel estimation scheme is proposed for multi-user MIMO (MU-MIMO) systems over time-varying channels. In the proposed scheme, a low-overhead pilot transmission scheme is designed to track the varying channel. The received uplink signal at the base station (BS) is formulated as a third-order tensor which admits a CANDECOMP/PARAFAC (CP) model. The CP decomposition issue is then solved using blind matrix decomposition, in which the special structures of signals in the time dimension and the matrix subspace are utilized. By exploiting low-rank structure of the signal tensor, the channel parameters (angles of arrival/departure, path gains, and Doppler shifts) are estimated from the factor matrices. Moreover, the proposed scheme is theoretically analyzed and it is guaranteed with low pilot overhead. Simulation results verify that the proposed scheme can outperform the compressed sensing (CS) based scheme and the iteration-based scheme in terms of accuracy and stability. The uniqueness of the proposed scheme is also verified in our simulation.

Two‐timescale design for RIS‐aided full‐duplex MIMO systems with transceiver hardware impairments

This paper focuses on a reconfigurable intelligent surface (RIS)-aided full-duplex multi-user massive multiple-input multiple-output system with transceiver hardware impairments (THWIs). Different from the existing works, the two-timescale design scheme is considered. The phase shift at the RIS is designed only based on the statistical channel state information. Firstly, the closed-form expression of the uplink and downlink achievable rate is derived. Then, the power scaling laws are revealed. Finally, the impact of THWIs on the system performance is analysed and genetic algorithm to maximize the achievable rate is used.

Autoencoder‐based deep learning for massive multiple‐input multiple‐output uplink under high‐power amplifier non‐linearities

In this paper, the authors study the compensation of high-power amplifier (HPA) non-linear distortion in the multi-user (MU) massive multiple-input multiple-output (MIMO) systems and focus on uplink transmission, where the base station (BS) uses a large antenna array. First, the authors present a non-linear distortion iterative cancellation (NDIC) algorithm-based MMSE and approximate message passing (AMP) at the receiver level, in order to estimate and mitigate jointly a non-linear distortion and the channel noise. Second, the authors propose a novel distortion cancellation technique based on deep learning. At this level, the authors first introduce a multilayer neural network, trained in the Levenberg–Marquardt algorithm by eliminating HPA non-linearities on the ‘Pre distortion’ transmitter and ‘Post distortion’ receiver side. Next, the authors developed a novel end-to-end (E2E) learning approach for the joint transmitter and non-coherent receiver in the Rayleigh fading channel. The basic idea lies in the use of deep neural networks (DNNs), auto encoder (AE) for unknown channels, where DNNs are applied to perform several functions and modules existing in the transmission chain. The simulation results demonstrate the strong potential of the proposed approach E2E in terms of improving the link quality and symbol error rate (SER) compared to other compensation techniques presented in this work.

A Joint Hybrid Precoding/Combining Scheme Based on Equivalent Channel for Massive MIMO Systems

Due to its inherent ability in reducing hardware cost and power consumption while maintaining high system capacity, hybrid precoding is deemed as one of the key technologies in the upcoming 5G/6G millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, it is challenging to design high performance hybrid precoders/combiners with low computational complexity. In this paper, based on the singular value decomposition (SVD) technique and the concept of equivalent channel, joint hybrid precoding strategies with high spectral-efficiency and low complexity are proposed for both single-user and multi-user massive MIMO systems. Specifically, for single-user massive MIMO scenarios, after transforming the design of hybrid beamforming into the problem of maximizing the square of sum eigenvalues for an equivalent channel, a two-stage successive method is conceived to design the analog precoder and combiner jointly, and the corresponding equivalent channel is constructed. Then, the digital precoding and combining operations are realized directly by applying the SVD technique to the matrix of equivalent channel. Meanwhile, the hybrid precoding strategy is extended to the multi-user scenario for achieving high performance resultant from multi-user diversity. Extensive simulations are conducted to verify the effectiveness of the precoding/combing schemes. The results show that our proposed schemes can achieve superior performance with lower complexity compared to the existing ones.

Spectral-efficient hybrid precoding for multi-antenna multi-user mmWave massive MIMO systems with low complexity

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems allow for a data transmission rate of gigabits per second owing to the large bandwidth available in the mmWave spectrum and the antenna gains provided by the massive MIMO system. However, hybrid precoding with high complexity and low spectral efficiency cannot address the challenge of high cost and power consumption of RF chains of multi-user systems. In this paper, we propose a low-complexity hybrid precoding scheme for downlink multi-antenna multi-user mmWave massive MIMO systems, aiming to enhance the sum spectral efficiency (SSE) performance. We first extend the dimension of the analog precoding matrix into a square matrix and find the optimal analog combiner by selecting some of the discrete Fourier transform (DFT) bases, which enhances the equivalent baseband channel matrix gain. Then, we directly aggregate the channel gain through the equal gain transmission (EGT) method to ensure the frequency efficiency performance. Finally, we propose an improved BD scheme to design the digital precoder and combiner to reduce the inter-user interference. We consider both the mmWave channel and the Rayleigh channel to evaluate the performance of the proposed algorithm. The simulation results verify that the proposed scheme enjoys near-optimal achievable sum spectrum efficiency and BER performance in both the mmWave channel and Rayleigh channel and performs even better in Rayleigh channel than in the mmWave channel.

Massive MIMO Precoding and Spectral Shaping With Low Resolution Phase-Only DACs and Active Constellation Extension

Nonlinear precoding and pulse shaping are jointly considered in multi-user massive multiple-input multiple-output (MIMO) systems with low resolution D/A-converters (DACs) in terms of algorithmic approach as well as large system performance. Two design criteria are investigated: the mean squared error (MSE) with active constellation extension (ACE) and the symbol error rate (SER). Both formulations are solved based on a modified version of the generalized approximate message passing (GAMP) algorithm. Furthermore, theoretical performance results are derived based on the state evolution analysis of the GAMP algorithm. The MSE based technique is extended to jointly perform over-the-air (OTA) spectral shaping and precoding for frequency-selective channels, in which the spectral performance is characterized at the transmitter and at the receiver. Simulation and analytical results demonstrate that the MSE based approach yields the same performance as the SER based formulation in terms of uncoded SER. The analytical results provide good performance predictions up to medium SNR. Substantial improvements in detection, as well as spectral performance, are obtained from the proposed combined pulse shaping and precoding approach compared to standard linear methods.

3-D Antenna Array Structures for Millimeter Wave Multi-User Massive MIMO Hybrid Precoder Design: A Performance Comparison

In this letter, we investigate the performance of various three-dimensional (3D) array structures in the design of hybrid precoder (HP) for millimeter wave (mmWave) multi-user massive multiple-input multiple-output (MU-mMIMO) systems. The proposed HP scheme involves two stages: (i) RF beamforming based on singular value decomposition (SVD) of channel matrix, and baseband MU precoding based on the instantaneous effective baseband channel to mitigate MU-interference by a regularized zero-forcing (RZF) technique. Illustrative results show that, in comparison to two-dimensional (2D) arrays, 3D array structures can provide high spectral and energy efficiencies as well as non-varying achievable rate independent from the user angular location.

Exponentially-Weighted Based Dynamic Pilot Power Allocation in Massive MIMO Systems

In this paper, we propose a distinctive pilot power allocation algorithm to maximize the sum rate in a multi-cell multi-user massive multiple-input multiple-output (MIMO) system. The algorithm optimizes pilot powers by polarizing the corresponding SINR values. In order to polarize SINRs, the difference between average SINR per cell and individual SINR is calculated for each user of the whole cells. The exponential form of the difference is used in the calculations of the weights for power allocation. New power values are obtained in proportion to these weights. Therefore, the power budget is utilized more efficiently thanks to these optimized power values. The efficiency of the algorithm is measured using the cumulative average SINR of the simulation system. Furthermore, equal pilot power allocation (EPPA) and water-filling pilot power allocation (WF-PPA) schemes are also implemented to compare the performances under the same simulation environments. A vast number of simulations results prove that our proposed heuristic approach is more efficient than EPPA and WF-PPA methods.

One-bit DACs precoding for massive MU-MIMO systems based on antenna selection architecture

In massive multi-user multiple-input multiple-output (MU-MIMO) communication systems, the utilization of one-bit digital-to-analog converters (DACs) in the base station (BS) radio frequency (RF) chains can significantly reduce the power consumption of the system. This study proposes a low-cost precoding architecture for massive MU-MIMO systems to alleviate multi-user interference (MUI). By including a selection structure, the architecture decreases the power consumption of typical one-bit precoding architecture. Based on this structure, we investigate the antenna selection-aided one-bit DACs precoding problem. However, jointly identifying the precoding factor and the precoding vector of the proposed precoding architectures is intractable because they are coupled together. We address this issue by utilizing an alternating direction multiplication method (ADMM) framework. The antenna selection strategy and the implementation of the non-convex approximate projection operator are given in detail. In addition, the power consumption of the proposed system architecture is analyzed. Simulation results reveal that the proposed precoding algorithm can successfully activate the antenna subset and ensure the performance of the system. Moreover, the hardware complexity and power consumption of the proposed precoding architectures are considerably lower than those of previous one-bit DACs precoding architectures.