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

Near-Optimal Design for Hybrid Beamforming in mmWave Massive Multi-User MIMO Systems

Millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems can obtain sufficient beamforming gains to combat severe path loss in signal propagation. The hybrid (analog/digital) beamforming with multiple data streams can be utilized to further improve mmWave spectral efficiency. In this paper, we focus on the hybrid beamforming design of a downlink mmWave massive multi-user MIMO (MU-MIMO) system based on full-connected structure, and aim to maximize the sum rate of the overall system as an objective function. In the analog beamforming stage, a piecewise successive iterative approximation (PSIA) algorithm is proposed to design the analog beamformer and combiner. This algorithm not only has a linear property, but also can obtain closed-form solutions. In the digital beamforming stage, the piecewise successive approximation method is utilized to design the digital beamforming based on the criterion to avoid the loss of information, which can help reduce the computational complexity and is also implemented simply. The results show that the proposed scheme achieves good sum-rate performance in the mmWave massive MU-MIMO system, and outperforms the state-of-the art MIMO hybrid beamforming design schemes, even when the number of base station antennas is not very large.

BER Performance of Spatial Modulation Systems Under a Non-Stationary Massive MIMO Channel Model

In this paper, the bit error rate (BER) performance of spatial modulation (SM) systems is investigated both theoretically and by simulation in a non-stationary Kronecker-based massive multiple-input-multiple-output (MIMO) channel model in multi-user (MU) scenarios. Massive MIMO SM systems are considered in this paper using both a time-division multiple access (TDMA) scheme and a block diagonalization (BD) based precoding scheme, for different system settings. Their performance is compared with a vertical Bell labs layered space-time (V-BLAST) architecture based system and a conventional channel inversion system. It is observed that a higher cluster evolution factor can result in better BER performance of SM systems due to the low correlation among sub-channels. Compared with the BD-SM system, the SM system using the TDMA scheme obtains a better BER performance but with a much lower total system data rate. The BD-MU-SM system achieves the best trade-off between the data rate and the BER performance among all of the systems considered. When compared with the V-BLAST system and the channel inversion system, SM approaches offer advantages in performance for MU massive MIMO systems.

Clustering Based Hybrid Precoding Design for Multi-User Massive MIMO Systems

Hybrid precoding has been recognized as a promising technology to combat the path loss of millimeter-wave signals in massive multiple-input multiple-output (MIMO) systems. However, due to the joint optimization of the digital and analog precoding matrices as well as extra constraints for the analog part, the hybrid precoding design is still a tough issue in current research. In this paper, we adopt the thought of clustering in unsupervised learning and provide design schemes for fully-connected hybrid precoding (FHP) and adaptively-connected hybrid precoding (AHP) in multi-user massive MIMO systems. For FHP, we propose the hierarchical-agglomerative-clustering-based (HAC-based) scheme to explore the relevance among radio frequency (RF) chains in the optimal hybrid precoding design. The similar RF chains are merged into an individual when insufficient RF chains are available. For AHP, we propose the modified-K-means-based (MKM-based) scheme to explore the relevance among antennas. The similar antennas are supported by the same RF chain to make full use of the flexible connection in AHP. Particularly, in the proposed MKM-based AHP design, the clustering centers are updated by alternating-optimum-based (AO-based) scheme with a specific initialization method, which is capable to independently provide feasible sub-connected hybrid precoding (SHP) design with quick convergence. Simulation results highlight the superior spectrum efficiency of the proposed HAC-based FHP scheme, and the high power efficiency of the proposed MKM-based AHP scheme. Moreover, all the proposed schemes are clarified to effectively handle the inter-user interference and outperform the existing work.

Enabling Ultrareliable and Low-Latency Communications Under Shadow Fading by Massive MU-MIMO

It is challenging to satisfy the critical requirements of ultrareliable and low-latency communications (URLLCs) in the Internet of Things (IoT) under severe channel fading. The emerging massive multiuser multiple-input–multiple-output (MU-MIMO) concept is applied in IoT networks under shadow fading, enabling URLLC with pilot-assisted channel estimation (PACE) and zero-forcing (ZF) detection. Assuming users are uniformly and randomly deployed under log-normal shadow fading, the probability density function (pdf) of postprocessing signal-to-noise ratios (SNRs) is derived for the uplink (UL) of massive MU-MIMO with perfect channel state information (CSI) and imperfect CSI obtained by PACE. Then, finite blocklength (FBL) information theory is utilized to derive the error probability of accessing users with a given latency, thereby evaluating the reliability of massive MU-MIMO for short-packet transmissions. Further, the length of pilots to minimize the error probability can be decided by the golden section search method (GSSM), which can converge rapidly. Numerical results verify that massive MU-MIMO can support a large number of UL URLLC users even when users are randomly deployed under shadow fading.

Efficient Nonlinear Precoding for Massive MIMO Downlink Systems With 1-Bit DACs

The power consumption of digital-to-analog converters (DACs) constitutes a significant proportion of the total power consumption in a massive multiuser multiple-input multiple-output (MU-MIMO) base station (BS). Using 1-bit DACs can significantly reduce the power consumption. This paper addresses the precoding problem for the massive narrow-band MU-MIMO downlink system equipped with 1-bit DACs at each BS. In such a system, the precoding problem plays a central role as the precoded symbols are affected by extra distortion introduced by 1-bit DACs. In this paper, we develop a highly efficient nonlinear precoding algorithm based on the alternative direction method framework. Unlike the classic algorithms, such as the semidefinite relaxation (SDR) and squared-infinity norm Douglas-Rachford splitting (SQUID) algorithms, which solve convex relaxed versions of the original precoding problem, the new algorithm solves the original nonconvex problem directly. The new algorithm is guaranteed to globally converge under some mild conditions. A sufficient condition for its convergence has been derived. The experimental results in various conditions demonstrated that the new algorithm can achieve the state-of-the-art performance comparable with the SDR algorithm while being much more efficient (e.g., more than 300 times faster than the SDR algorithm).

Eigen-Inference Precoding for Coarsely Quantized Massive MU-MIMO System With Imperfect CSI

This work considers the precoding problem in massive multiuser multiple-input multiple-output (MU-MIMO) systems equipped with low-resolution digital-to-analog converters (DACs). In previous literature on this topic, it is commonly assumed that the channel state information (CSI) is perfectly known. However, in practical applications the CSI is inevitably contaminated by noise. In this paper, we propose, for the first time, an eigen-inference (EI) precoding scheme to improve the error performance of the coarsely quantized massive MU-MIMO systems under imperfect CSI, which is mathematically modeled by a sum of two rectangular random matrices (RRMs). Instead of performing analysis based on the RRM, using Girko's Hermitization trick, the proposed method leverages the block random matrix theory by augmenting the RRM into a block symmetric channel matrix (BSCA). Specially, we derive the empirical distribution of the eigenvalues of the BSCA and establish the limiting spectra distribution connection between the true BSCA and its noisy observation. Then, based on these theoretical results, we propose an EI-based moments matching method for CSI-related noise level estimation and a rotation invariant estimation method for CSI reconstruction. Based on the cleaned CSI, the quantized precoding problem is tackled via the Bussgang theorem and the Lagrangian multiplier method. The prosed methods are lastly verified by numerical simulations and the results demonstrate the effectiveness of the proposed precoder.

An Iterative Semi-Blind Channel Estimation Scheme and Uplink Spectral Efficiency of Pilot Contaminated One-Bit Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) systems consist of a large number of antennas and radio frequency (RF) chains, which cause enormous circuit power consumption at the RF front ends. Since high-resolution analog-to-digital converters are the main contributor in the RF circuit power consumption, one-bit massive MIMO is considered as one of the potential solutions. The channel state information (CSI) acquisition in the presence of pilot contamination is a challenging task in such systems. In this paper, we present an iterative semi-blind-based channel estimation scheme for pilot contaminated one-bit multi-cell multi-user massive MIMO systems, which comprise of two stages: initialization and iteration. The initial channel estimate uses pilots in the initialization stage, which is further refined in the iteration stage with the help of both pilot and a few data symbols. We derive lower bounds on the uplink achievable rate with both perfect and imperfect CSI availability at the base station. Through simulations, we show that the proposed estimator achieves a considerable improvement in mean square error, bit-error-rate, power efficiency, and spectral efficiency from one-bit pilot-aided estimators at the cost of a nominal increase in computational complexity. Moreover, the proposed scheme in one-bit system achieves almost the same spectral efficiency as that of a pilot-aided estimator in an infinite-resolution-based massive MIMO system for lower values of signal-to-noise-ratio (SNR).

Decentralized Equalization With Feedforward Architectures for Massive MU-MIMO

Linear data-detection algorithms that build on zero forcing (ZF) or linear minimum mean-square error (L-MMSE) equalization achieve near-optimal spectral efficiency in massive multi-user multiple-input multiple-output (MU-MIMO) systems. Such algorithms, however, typically rely on centralized processing at the base-station (BS) which results in (i) excessive interconnect and chip input/output (I/O) data rates and (ii) high computational complexity. Decentralized baseband processing (DBP) partitions the BS antenna array into independent clusters that are associated with separate radio-frequency circuitry and computing fabrics in order to overcome the limitations of centralized processing. In this paper, we investigate decentralized equalization with feedforward architectures that minimize the latency bottlenecks of existing DBP solutions. We propose two distinct architectures with different interconnect and I/O bandwidth requirements that fuse the local equalization results of each cluster in a feedforward network. For both architectures, we consider maximum ratio combining, ZF, L-MMSE, and a nonlinear equalization algorithm that relies on approximate message passing, and we analyze the associated post-equalization signal-to-noise-and-interference-ratio (SINR). We provide reference implementation results on a multi graphics processing unit (GPU) system which demonstrate that decentralized equalization with feedforward architectures enables throughputs in the Gb/s regime and incurs no or only a small performance loss compared to centralized solutions.

Uplink Sum-Rate and Power Scaling Laws for Multi-User Massive MIMO-FBMC Systems

This paper analyses the performance of filter bank multicarrier (FBMC) signaling in conjunction with offset quadrature amplitude modulation (OQAM) in multi-user (MU) massive multiple-input multiple-output (MIMO) systems. Initially, closed form expressions are derived for tight lower bounds corresponding to the achievable uplink sum-rates for FBMC-based single-cell MU massive MIMO systems relying on maximum ratio combining (MRC), zero forcing (ZF) and minimum mean square error (MMSE) receiver processing with/without perfect channel state information (CSI) at the base station (BS). This is achieved by exploiting the statistical properties of the intrinsic interference that is characteristic of FBMC systems. Analytical results are also developed for power scaling in the uplink of MU massive MIMO-FBMC systems. The above analysis of the achievable sum-rates and corresponding power scaling laws is subsequently extended to multi-cell scenarios considering both perfect as well as imperfect CSI, and the effect of pilot contamination. The delay-spread-induced performance erosion imposed on the linear processing aided BS receiver is numerically quantified by simulations. Numerical results are presented to demonstrate the close match between our analysis and simulations, and to illustrate and compare the performance of FBMC and traditional orthogonal frequency division multiplexing (OFDM)-based MU massive MIMO systems.

Effects of Pilot Contamination Attacks in Multi-Cell Multi-User Massive MIMO Relay Networks

The detrimental effects of pilot contamination attacks by active eavesdroppers are investigated for multi-cell multi-user massive multiple-input multiple-output (MIMO) relay networks. To this end, secure transmission strategies are designed for both users-to-relay and relay-to-destination channels in the presence of active pilot attacks with imperfect legitimate user channel state information (CSI) and with no eavesdropper CSI knowledge at the relay. The excess degrees-of-freedom offered by the massive MIMO relay are exploited to mitigate detrimental effects of cooperative jamming (CJ) signals and to generate artificial noise (AN) during the first and second time-slots, respectively. Thereby, the achievable secrecy rate lower bounds for active attacks are derived in the finite/infinite relay antenna regimes. The secrecy rates for passive eavesdropping are deduced and compared to that of active attacks. A joint optimal power allocation scheme for the pilot, payload data, and AN and CJ signals is formulated and solved by using geometric programming techniques. Rigorous numerical and simulation results are provided to obtain valuable insights, which are useful in designing secure physical layer transmission strategies for multi-cell multi-user massive MIMO relay networks.

Novel Detectors for Massive MU-MIMO Communications

The massive multi-user multiple-input multiple-output (MU-MIMO) can be adapted to meet the increasing requirement of data throughput services in wireless transmission systems. The combination of the Single Carrier Frequency Division Multiple Access (SC-FDMA) with the massive MU-MIMO technology can be employed for the uplink transmission to meet the requirement of data rates and error performance. In this paper, for practical implementation, we integrate multi-user detection, Kalman channel estimation and turbo equalization and propose turbo detectors to solve the problem of huge computation load of matrix inversion at receiver side. The proposed low-complexity detectors are based on Neumann series expansion, successive over-relaxation (SOR), and symmetric successive over-relaxation (SSOR) principles. Simulation examples in the uplink scenario are given for the proposed low-complexity turbo detectors to demonstrate the comparisons and effectiveness of the proposed schemes.

Information-Theoretic Pilot Design for Downlink Channel Estimation in FDD Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) is one of the most promising techniques for next generation wireless communications due to its superior capability to provide high spectrum and energy efficiency. Considering the very large number of antennas employed at the base station, however, the pilot overhead for downlink channel estimation becomes unaffordable in frequency division duplex (FDD) multiuser massive MIMO systems. In this paper, we propose an information-theoretic metric to design the pilot for downlink channel estimation in FDD multiuser massive MIMO systems. By exploiting the low-rank nature of the channel covariance matrix, we first derive the minimum number of pilot symbols required to ensure perfect channel recovery, which is much less than the number of antennas at the base station. Further, under a general channel model that the channel vector of each user follows a Gaussian mixture distribution, the pilot symbols are designed by maximizing the weighted sum of the Shannon mutual information between the measurements of the users and their corresponding channel vectors on the complex Grassmannian manifold. Simulation results demonstrate the effectiveness of the proposed information-theoretic pilot design for the downlink channel estimation in FDD massive MIMO systems.

Blind downlink channel estimation for TDD‐based multiuser massive MIMO in the presence of nonlinear HPA

In time division duplex (TDD)‐based multiuser massive multiple input multiple output (MIMO) systems, the uplink channel is estimated and the results are used in downlink for signal detection. Owing to noisy uplink channel estimation, the downlink channel should also be estimated for accurate signal detection. Therefore, recently, a blind method was developed, which assumes the use of a linear high‐power amplifier (HPA) in the base station (BS). In this study, we extend this method to a scenario with a nonlinear HPA in the BS, where the Bussgang decomposition is used for HPA modeling. In the proposed method, the average power of the received signal for each user is a function of channel gain, large‐scale fading, and nonlinear distortion variance. Therefore, the channel gain is estimated, which is required for signal detection. The performance of the proposed method is analyzed theoretically. The simulation results show superior performance of the proposed method compared to that of the other methods in the literature.

Multiuser Massive MIMO Systems With Time-Offset Pilots and Successive Interference Cancellation

This paper proposes time-offset pilots for a single-cell multiuser massive multiple-input multiple-output (MIMO) system and studies its performance under the minimum mean-squared error channel estimator and successive interference cancellation. With the proposed time-offset pilots, users are divided into two groups and the uplink pilots from one group are transmitted simultaneously with the uplink data of the other group, which allows the system to accommodate more users for a given number of pilots. Successive interference cancellation is developed to ease the effect of pilot contamination and enhance data detection. Closed-form expressions for lower bounds of the uplink spectral efficiencies in both the training and data phases are derived when the maximum-ratio combining receiver is used at the base station. The power control problem is formulated with the objective of either maximizing the quality of service that can be equally provided to all users, or minimizing the total transmit power. Since the original power control problems are NP-hard, we also propose algorithms based on the bisection method to solve the problems separately in training and data phases. Analysis and numerical results show that the effect of pilot contamination can be mitigated by successive interference cancellation and proper power control.

Multicell multiuser massive MIMO channel estimation and MPSK signal block detection applying two-dimensional compressed sensing

For the uplink multicell massive multiple-input multiple-output (MIMO) block fading systems, a two-dimensional smoothed l0 channel estimation method (2D-SL0-CE) with the aid of virtual channel representation is firstly exploited in this paper, which can jointly estimate the desired multiuser channels of the target cell and the interference links from neighbor cells without inducing pilot contamination. Then, a 2D-SL0 signal detection method (2D-SL0-SD) with the aid of sparse decomposing and the modified 2D sl0 recovery algorithm is proposed, which can jointly decode M-ary phase-shift keying (MPSK) signal block for whole desired users. Moreover, an improved 2D-SL0-SD is also proposed to remove multiuser interference of neighbor cells in high SNR scenario. Simulation results show that the 2D-SL0-CE method can remove performance floor induced by pilot contamination and need less pilot overhead than the conventional least square (LS) method. When detecting QPSK signal blocks at 12 dB SNR, the 2D-SL0-SD method with perfect channel state information (CSI) can obtain 10−2 BER. Moreover, in the case of 8PSK signals, the 2D-SL0-SD joining with the 2D-SL0-CE can obtain 10−2 BER at 20 dB SNR.

Downlink Channel Estimation in Multiuser Massive MIMO With Hidden Markovian Sparsity

Recently, compressive sensing based massive multiple input multiple output (MIMO) channel estimation (CE) has attracted intensive research interest. By exploiting the structured sparsity of massive MIMO channels, it is possible to design structured sparse channel estimation (SSCE) algorithms to significantly reduce the pilot/feedback overheads in massive MIMO downlink CE. However, most existing SSCE algorithms are designed based on oversimplified channel models with restrictive assumptions, and thus perform poorly under realistic channels. In this paper, we propose a Hidden-Markov-Model (HMM) to capture the structured sparsity of multiuser massive MIMO channels. The HMM has the flexibility to model different propagation environments that occur in practice. We derive an efficient approximate message passing algorithm called Turbo-orthogonal approximate message passing (OAMP) to solve the resulting sparse CE problem with an HMM prior . The proposed Turbo-OAMP does not require knowledge of the HMM channel parameters, which is automatically learned based on the expectation maximization framework. As a result, the proposed Turbo-OAMP algorithm derived from the HMM works well for realistic channels with complicated propagation environments and unknown channel parameters. Extensive simulations verify that the proposed Turbo-OAMP can achieve significant gains over the existing SSCE algorithms under realistic channels.

Hybrid preprocessing aided spatial modulation in multi‐user massive MIMO systems

Massive multiple-input multiple-output (MIMO) as a promising technology to achieve high spectral efficiency encounters the problem of high cost and complexity of hardware implementation for digital signal processing. One proposed solution is hybrid analogue–digital processing to reduce the number of radio-frequency (RF) chains required at massive antenna arrays. In this study, hybrid analogue–digital preprocessing aided spatial modulation is introduced to the downlink of multi-user massive MIMO systems. Linear zero-forcing (ZF) and regularised ZF preprocessors which are near-optimal in massive MIMO systems and a low-complexity two-stage preprocessing scheme based on block-diagonalisation are proposed. These full-digital schemes are implemented in hybrid RF-baseband domain through a low-dimensional processor based on the baseband effective channel and phase controllers at the RF domain. The spatially correlated and sparsely scattered millimetre wave channels are adopted to consider the proposed preprocessing schemes. Under an imperfect channel state information at the transmitter, the robust design of full digital and hybrid analogue-digital preprocessors is presented using stochastic robust approximation. Furthermore, the hybrid RF-baseband preprocessors are realised using heavily quantised angles and the preprocessing schemes are investigated from the data rate point of view. The simulation results show desirable performance and close to that of full digital preprocessing is achieved by proper configuration of system.

Energy and spectral efficiency tradeoff in massive MIMO systems with multi-objective adaptive genetic algorithm

Spectral efficiency (SE) and energy efficiency (EE) are both important metrics in massive multiple-input multiple-output (MIMO) systems. However, maximizing EE and SE is always conflicting with each other, and they can hardly be achieved simultaneously. In this paper, we focus on the tradeoff optimization between EE and SE in multiuser massive MIMO systems in terms of the number of transmit antennas and the transmit power. Different from the previous EE-oriented or SE-oriented method, the EE–SE tradeoff problem is formulated into a multi-objective optimization problem. To efficiently attain the Pareto optimal front (POF) of EE–SE tradeoff, a multi-objective adaptive genetic algorithm, inspired by the non-dominated sorting genetic algorithm (NSGA-II), is proposed to improve the convergence speed. Experimental comparisons against several well-known multi-objective algorithms show that the proposed algorithm can quickly adapt to the true POF of EE–SE tradeoff and maintain good performance on benchmark functions in terms of the adopted performance metrics.

A projected fast ISTA algorithm for joint beam forming and antenna selection in massive MIMO

The joint beam-forming and antenna selection problem encountered in modern multi-user massive multiple input multiple output (MIMO) communication systems is solved using the projected fast iterative shrinkage–thresholding algorithm (ISTA). The algorithm aim is to find the suboptimal set of transmitting antennas and to calculate the suboptimal beamforming weights which maximize the users’ achievable data rates. These requirements should be achieved quickly to maintain the system quality and reliability. The numerical analysis shows that the same rates are achieved using projected ISTA and projected fast ISTA. It also shows that the convergence rates for projected fast ISTA are much better than that of projected ISTA, and these rates are independent of the problem size. The paper concluded that the projected fast ISTA is suitable for multiuser massive MIMO systems due to the fast convergence rates and the implementation simplicity even for large system dimensions.

Finite-Alphabet Precoding for Massive MU-MIMO With Low-Resolution DACs

Massive multiuser multiple-input multiple-output (MU-MIMO) systems are expected to be the core technology in fifth-generation wireless systems because they significantly improve spectral efficiency. However, the requirement for a large number of radio frequency (RF) chains results in high hardware costs and power consumption, which obstruct the commercial deployment of massive MIMO systems. A potential solution is to use low-resolution digital-to-analog converters (DAC)/analog-to-digital converters for each antenna and RF chain. However, using low-resolution DACs at the transmit side directly limits the degree of freedom of output signals and thus poses a challenge to the precoding design. In this study, we develop efficient and universal algorithms for a downlink massive MU-MIMO system with finite-alphabet precodings. Our algorithms are developed based on the alternating direction method of multipliers (ADMM) framework. The original ADMM does not converge in a nonlinear discrete optimization problem. The primary cause of this problem is that the alternating (update) directions in ADMM on one side are biased, and those on the other side are unbiased. By making the two updates consistent in an unbiased manner, we develop two algorithms called iterative discrete estimation (IDE) and IDE2: IDE demonstrates excellent performance and IDE2 possesses a significantly low computational complexity. Compared with state-of-the-art techniques, the proposed precoding algorithms present significant advantages in performance and computational complexity.