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

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).

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.

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.

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.

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.

Pilot power allocation for maximising the sum rate in massive MIMO systems

In this study, the authors investigate the issue of pilot power allocation in multi-cell multi-user massive multiple-inputmultiple-output (MIMO) systems to maximize the sum rate. In contrast to conventional scheme that assigns equal pilot power for all users in the system, they assume that different users can be assigned different pilot powers while the total pilot power per cell is fixed. They show that when the number of BS antennas goes to infinity, the signal-to-interference-and-noise ratio of a user only depends on the large-scale fading and pilot power of users who have the same pilot sequence. From that they derive an optimization problem to maximize the total uplink achievable rate of a target cell and prove that this problem is convex, which can be solved by the well-known Lagrange multiplier method. They also propose an extended optimization problem that solves the issue of zero-pilot power in the original problem. Eventually, two algorithms corresponding to the original and extended optimization problems are proposed to obtain the optimized pilot power set for all users in the systems. Numerical results show that the proposed algorithms outperform the existing methods relating to pilot power allocation problem as well as conventional scheme.

JOINT OPTIMIZATION OF COMPUTATION AND COMMUNICATION POWER IN MULTI-USER MASSIVE MIMO SYSTEMS.

With the growing interest in the deployment of massive multiple-input-multiple-output (MIMO) systems and millimeter wave technology for fifth generation (5G) wireless systems, the computation power to the total power consumption ratio is expected to increase rapidly due to high data traffic processing at the baseband unit. Therefore in this paper, a joint optimization problem of computation and communication power is formulated for multi-user massive MIMO systems with partially-connected structures of radio frequency (RF) transmission systems. When the computation power is considered for massiv MIMO systems, the results of this paper reveal that the energy efficiency of massive MIMO systems decreases with increasing the number of antennas and RF chains, which is contrary with the conventional energy efficiency analysis results of massive MIMO systems, i.e., only communication power is considered. To optimize the energy efficiency of multi-user massive MIMO systems, an upper bound on energy efficiency is derived. Considering the constraints on partially-connected structures, a suboptimal solution consisting of baseband and RF precoding matrices is proposed to approach the upper bound on energy efficiency of multi-user massive MIMO systems. Furthermore, an oPtimized Hybrid precOding with computation and commuNication powEr (PHONE) algorithm is developed to realize the joint optimization of computation and communication power. Simulation results indicate that the proposed algorithm improves energy and cost efficiencies and the maximum power saving is achieved by 76.59% for multi-user massive MIMO systems with partially-connected structures.

Frequency Reuse of Beam Allocation for Multiuser Massive MIMO Systems

Massive multiple-input-multiple-output (MIMO) has become a promising technique to provide high-data-rate communication in fifth-generation mobile systems, thanks to its ability to form narrow and high-gain beams. Among various massive MIMO beamforming techniques, the fixed-beam scheme has attracted considerable attention due to its simplicity. In this paper, we focus on a fixed-beam based multiuser massive MIMO system, where each user is served by a beam allocated to it. To maximize the sum data rate, a greedy beam allocation algorithm is proposed under the practical condition that the number of radio frequency chains is smaller than the number of users. Simulation results show that our proposed greedy algorithm achieves nearly optimal sum data rate. As only the sum data rate is optimized, there are some “worst-case” users, who could suffer from strong inter-beam interference and thus experience low data rate. To improve the individual data rates of the worst-case users while maintaining the sum data rate, an adaptive frequency reuse scheme is proposed. Simulation results corroborate that our proposed adaptive frequency reuse strategy can greatly improve the worst-case users’ data rates and the max-min fairness among served users without sacrificing the sum data rate.

A Novel Equivalent Baseband Channel of Hybrid Beamforming in Massive Multiuser MIMO Systems

The conventional full radio frequency (RF) configuration appears to be unfeasible in massive multiple-input-multiple-output (MIMO) systems due to the still-exorbitant energy consumption of RF chains at millimeter wave frequencies. In this letter, we address this challenge by proposing a novel two step hybrid beamforming scheme for the downlink massive multiuser MIMO systems. Our purpose is to maximize the overall spectral efficiency with limited RF chains. In the first step, we aim to find an equivalent baseband channel by maximizing its capacity through the analog RF processing. In the second step, the inter-user interference is eliminated by the block diagonalization (BD) technique. Simulation results demonstrate that the proposed scheme can achieve a higher capacity than the traditional BD scheme with much fewer number of RF chains.

Enhanced CSI Acquisition for FDD Multi-User Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) is envisioned to meet the growing spectral efficiency (SE) requirement in next generation cellular systems. However, it has been recognized that the unaffordable channel state information reference signal (CSI-RS) overhead required for acquiring CSI is a major challenge in frequency division duplexing (FDD) massive MIMO systems. To tackle the challenge of this CSI-RS overhead limitation, certain attempts, which have been designed for the scenarios with dispersive locations of users and sparse nature of channels, suffer from inaccurate channel estimation when the nature of channels for different users becomes highly correlated and rich. In this paper, we propose an enhanced CSI acquisition scheme for FDD multi-user massive MIMO systems, which exploits beamformed CSI-RS transmission mechanism to reduce the CSI-RS overhead. We present two limited feedback algorithms which provide different tradeoffs between system performance and CSI feedback overhead, where the multistage CSI acquisition strategy is adopted to avoid prohibitive computational complexity and amount of feedback requirement. The simulation results show that our CSI acquisition scheme, without additional CSI-RS overhead and enormous CSI feedback overhead, achieves higher SE performance as compared to conventional scheme.

Disjoint Pilot Power and Data Power Allocation in Multi-Cell Multi-User Massive MIMO Systems

In this paper, we consider pilot and data power allocation in multi-cell multi-user massive multiple-input multiple-output (MIMO) systems to maximize the summation of spectral efficiency (sum SE). In conventional massive MIMO systems, equal pilot and data power is assigned to all users so the sum SE is not good. A common way to maximize sum SE is forming a maximization problem with the sum SE objective function containing both pilot and data power as variables. However, pilots are only used for channel estimation so pilot power should be allocated based on channel estimation quality instead of sum SE. Moreover, improving significantly channel estimation quality also helps to indirectly improve the sum SE. This motivated us to propose a disjoint pilot and data power allocation where pilot powers are optimized based on the sum normalized mean squared error (sum NMSE) channel estimation minimization problem and data powers are optimized based on sum SE maximization problem. We consider least squares (LS) and minimum mean squared error (MMSE) estimation methods which are commonly used in massive MIMO. In the first step, we formulate a minimization problem to minimize the summation of NMSE of the system under maximum pilot power per user constraint. Minimization problem for MMSE method is non-deterministic polynomial-time (NP) hard so we propose an algorithm to find the local optimum point. First step is only related to pilot powers and indirectly improves the sum SE by improving channel estimation quality. In second step, we further improve the sum SE by formulating a sum SE maximization problem with data powers as variables under maximum data power per user constraint. Since this problem is NP-hard, we derive a lower bound on the sum SE and maximize this bound instead Numerical results show the advantages of our proposed approach in comparison with existing schemes.

Compressed sensing-based structured joint channel estimation in a multi-user massive MIMO system

Acquisition of accurate channel state information (CSI) at transmitters results in a huge pilot overhead in massive multiple input multiple output (MIMO) systems due to the large number of antennas in the base station (BS). To reduce the overwhelming pilot overhead in such systems, a structured joint channel estimation scheme employing compressed sensing (CS) theory is proposed. Specifically, the channel sparsity in the angular domain due to the practical scattering environment is analyzed, where common sparsity and individual sparsity structures among geographically neighboring users exist in multi-user massive MIMO systems. Then, by equipping each user with multiple antennas, the pilot overhead can be alleviated in the framework of CS and the channel estimation quality can be improved. Moreover, a structured joint matching pursuit (SJMP) algorithm at the BS is proposed to jointly estimate the channel of users with reduced pilot overhead. Furthermore, the probability upper bound of common support recovery and the upper bound of channel estimation quality using the proposed SJMP algorithm are derived. Simulation results demonstrate that the proposed SJMP algorithm can achieve a higher system performance than those of existing algorithms in terms of pilot overhead and achievable rate.

Low-Complexity Semiblind Channel Estimation in Massive MU-MIMO Systems

Massive multi-user multiple-input multiple-output (MU-MIMO) systems are a promising solution for achieving high throughput and robust transmission in next generation mobile communications. Achieving the optimal transceiver design in such systems requires an accurate knowledge of the channel state information. However, in massive MU-MIMO systems, the quality of the channel estimates is often degraded by pilot contamination. In this paper, we propose a low-complexity semiblind channel estimation algorithm to mitigate the ill effects of pilot contamination. In the proposed approach, the received signals are first projected onto the subspace with minimal interference, where the bases of this subspace are determined recursively via a low-complexity modified power method. An initial estimate of the projected channel coefficients is then made based on a small number of pilot symbols. Finally, data symbols are detected and the channel estimation is refined alternatively. Compared with existing channel estimation methods, the proposed algorithm has lower complexity due to the subspace projection and innovation process. An asymptotic analysis reveals that the mean square error of the channel estimates is inversely proportional to the length of the data symbols. Simulation results demonstrate that the proposed algorithm outperforms the existing works and alleviates the pilot contamination effects effectively.

Impact of pilot sequence contamination in massive MIMO systems

Time-division duplex (TDD) is the most efficient technique for acquiring channel state information in massive multiple-input multiple-output (MIMO) systems where the reciprocity between the uplink and downlink channels is utilised by the pilot signals to extract the channel parameters. In this study, the authors consider the pilot contamination problem in TDD multicell multiuser massive MIMO systems and examine two different pilot signal allocation schemes for which they derive the lower bounds on the achievable rate on the uplink for the cases of maximum-ratio combining (MRC) and zero-forcing (ZF) detectors. To achieve further performance enhancements, they propose a new algorithm for pilot sequences allocation in which the multiplicity of the pilot sequences over the number of users in each cell is exploited. The authors' results show that when pilot contamination is severe, allocating more system resources for channel estimation results in a better system performance especially in limited mobility environments. Moreover, they show that when the signal-to-interference plus noise ratio is low, MRC is superior to ZF, and vice versa. Finally, they demonstrate that their proposed allocation algorithm can significantly improve the spectral efficiency of the network compared to the conventional pilot allocation method.

Massive MIMO Performance With Imperfect Channel Reciprocity and Channel Estimation Error

Channel reciprocity in time-division duplexing (TDD) massive multiple-input multiple-output (MIMO) systems can be exploited to reduce the overhead required for the acquisition of channel state information (CSI). However, perfect reciprocity is unrealistic in practical systems due to random radio-frequency (RF) circuit mismatches in uplink and downlink channels. This can result in a significant degradation in the performance of linear precoding schemes, which are sensitive to the accuracy of the CSI. In this paper, we model and analyse the impact of RF mismatches on the performance of linear precoding in a TDD multi-user massive MIMO system, by taking the channel estimation error into considerations. We use the truncated Gaussian distribution to model the RF mismatch, and derive closed-form expressions of the output signal-to-interference-plus-noise ratio for maximum ratio transmission and zero forcing precoders. We further investigate the asymptotic performance of the derived expressions, to provide valuable insights into the practical system designs, including useful guidelines for the selection of the effective precoding schemes. Simulation results are presented to demonstrate the validity and accuracy of the proposed analytical results.

Performance Analysis and Scaling Law of MRC/MRT Relaying With CSI Error in Multi-Pair Massive MIMO Systems

This paper provides a comprehensive scaling law and performance analysis for multi-user massive multiple-input-multiple-output (MIMO) relay networks, where the relay is equipped with a massive antenna array and uses maximal-ratio combining/maximal-ratio transmission (MRC/MRT) for low-complexity processing. Imperfect channel state information (CSI) is considered for both source-relay and relay-destination channels. First, a sum-rate lower bound is derived, which manifests the effect of system parameters, including the numbers of relay antennas and users, the CSI quality, and the transmit powers of the sources and the relay. Via a general scaling model on the parameters with respect to the relay antenna number, the asymptotic scaling law of the signal-to-interference-plus-noise-ratio (SINR) is obtained, which shows quantitatively the tradeoff of the network parameters. In addition, a sufficient condition on the parameter scalings for the SINR to be asymptotically deterministic is given, which covers existing results on such analysis as special cases. Then, the scenario where the SINR increases linearly with the relay antenna number is studied. The sufficient and necessary condition on the parameter scaling for this scenario is proved. It is shown that in this case, the interference power is not asymptotically deterministic, and then, the average bit error rate is analyzed.