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

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.

Hybrid precoding for multiuser massive MIMO systems based on MMSE-PSO

Hybrid Precoding has been adopted as a promising technology for 5th generation wireless communication systems. In this paper, we propose a hybrid precoding scheme based on minimum mean square error (MMSE) and particle swarm optimization (PSO) for multiuser massive multiple-input multiple-output systems. The closed-form solutions of baseband precoding and the combiner are solved by convex optimization method. Meanwhile, the MMSE between the transmitted signal and the received signal is considered as an objective function of PSO, and the radio frequency precoding is obtained by updating the global optimal positions of the particles. The simulation results show that the proposed hybrid MMSE-PSO precoding significantly improves achievable rate and the system reliability.

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.

GLSE Precoders for Massive MIMO Systems: Analysis and Applications

This paper proposes the class of generalized least-square-error (GLSE) precoders for multiuser massive multiple-input multiple-output (MIMO) systems. For a generic transmit constellation, the GLSE precoders minimize the interference at user terminals assuring that some given constraints on the transmit signals are satisfied. The general form of these precoders enables us to impose multiple restrictions at the transmit signal, such as limited peak power and restricted number of active transmit antennas. The performance of these precoders is analyzed in the large-system limit. It is shown that the output symbols are identically distributed, and their statistics are described with an equivalent scalar GLSE precoder. To demonstrate the applications of the proposed framework, we employ the GLSE precoding to form transmit signals over a discrete alphabet and to select an effective subset of transmit antennas. Our investigations show that a computationally efficient GLSE precoder requires 41% less active transmit antennas than the conventional selection protocols in order to achieve a given level of input–output distortion.

A low-complexity algorithm for the joint antenna selection and user scheduling in multi-cell multi-user downlink massive MIMO systems

The massive MIMO (multiple-input multiple-output) technology plays a key role in the next-generation (5G) wireless communication systems, which are equipped with a large number of antennas at the base station (BS) of a network to improve cell capacity for network communication systems. However, activating a large number of BS antennas needs a large number of radio-frequency (RF) chains that introduce the high cost of the hardware and high power consumption. Our objective is to achieve the optimal combination subset of BS antennas and users to approach the maximum cell capacity, simultaneously. However, the optimal solution to this problem can be achieved by using an exhaustive search (ES) algorithm by considering all possible combinations of BS antennas and users, which leads to the exponential growth of the combinatorial complexity with the increasing of the number of BS antennas and active users. Thus, the ES algorithm cannot be used in massive MIMO systems because of its high computational complexity. Hence, considering the trade-off between network performance and computational complexity, we proposed a low-complexity joint antenna selection and user scheduling (JASUS) method based on Adaptive Markov Chain Monte Carlo (AMCMC) algorithm for multi-cell multi-user massive MIMO downlink systems. AMCMC algorithm is helpful for selecting combination subset of antennas and users to approach the maximum cell capacity with consideration of the multi-cell interference. Performance analysis and simulation results show that AMCMC algorithm performs extremely closely to ES-based JASUS algorithm. Compared with other algorithms in our experiments, the higher cell capacity and near-optimal system performance can be obtained by using the AMCMC algorithm. At the same time, the computational complexity is reduced significantly by combining with AMCMC.

Hybrid Analog-Digital Beamforming Design for SE and EE Maximization in Massive MIMO Networks

Hybrid analog-digital (HAD) beamforming architectures have been proposed to facilitate the practical implementation of massive multiple-input multiple-output (MIMO) systems by reducing the number of employed radio frequency chains. While most prior studies have aimed to maximize spectral efficiency (SE), the present paper proposes a two-stage HAD beamforming design for multi-user MIMO systems that can be used to maximize either the system's overall energy efficiency (EE) or SE. This problem is nonconvex and NP-hard due to the joint optimization between the analog and digital domains and the constant modulus constraints required by the analog domain. To address this problem, we propose a decoupled two-stage design wherein the first stage, the analog beamforming parts are updated, which are then taken into account in the second stage to design the digital beamforming parts to maximize the system's EE or SE. We consider two widely-used HAD beamforming techniques that utilize either fully-connected (FC) or partially-connected (PC) architectures employing variable phase-shifters. Using the most recently available data for the circuitry power consumption of the components, we compare the performance of these two HAD architectures with that of the fully-digital (FD) architecture in terms of the total circuitry power consumption, and achieved SE and EE. We find that there is a certain number of users above which the FC architecture has higher circuitry power consumption than the FD counterpart, in contrast to the PC architecture that always has lower circuitry power consumption. More importantly, our results reveal, contrary to the common opinion, that depending on the circuitry parameters the FD architecture may achieve not only higher SE, but also higher EE than the HAD architectures.

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).

Data-Aided Secure Massive MIMO Transmission Under the Pilot Contamination Attack

In this paper, we study the design of secure communication for time division duplex multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with active eavesdropping. We assume that the eavesdropper actively attacks the uplink pilot transmission and the uplink data transmission before eavesdropping the downlink data transmission of the users. We exploit both the received pilots and the received data signals for uplink channel estimation. We show analytically that when the number of transmit antennas and the length of the data vector both tend to infinity, the signals of the desired user and the eavesdropper lie in different eigenspaces of the received signal matrix at the base station provided that their signal powers are different. This finding reveals that decreasing (instead of increasing) the desired user's signal power might be an effective approach to combat a strong active attack from an eavesdropper. Inspired by this observation, we propose a data-aided secure downlink transmission scheme and derive an asymptotic achievable secrecy sum-rate expression for the proposed design. For the special case of a single-cell single-user system with independent and identically distributed fading, the obtained expression reveals that the secrecy rate scales logarithmically with the number of transmit antennas. This is the same scaling law as for the achievable rate of a single-user massive MIMO system in the absence of eavesdroppers. Numerical results indicate that the proposed scheme achieves significant secrecy rate gains compared to alternative approaches based on matched filter precoding with artificial noise generation and null space transmission.

Interference Exploitation-Based Hybrid Precoding With Robustness Against Phase Errors

Hybrid analog-digital precoding significantly reduces the hardware costs in massive multiple-input multiple-output (MIMO) transceivers when compared with fully digital precoding at the expense of increased transmit power. In order to mitigate the above-mentioned shortfall, we use the concept of constructive interference-based precoding, which has been shown to offer significant transmit power savings when compared with the conventional interference suppression-based precoding in fully digital multiuser MIMO systems. Moreover, in order to circumvent the potential quality-of-service degradation at the users due to the hardware impairments in the transmitters, we judiciously incorporate robustness against such vulnerabilities in the precoder design. Since the undertaken constructive interference-based robust hybrid precoding problem is nonconvex with infinite constraints and thus difficult to solve optimally, we decompose the problem into two subtasks, namely, analog precoding and digital precoding. In this paper, we propose an algorithm to compute the optimal constructive interference-based robust digital precoders. Furthermore, we devise a scheme to facilitate the implementation of the proposed algorithm in a low-complexity and distributed manner. We also discuss the block-level analog precoding techniques. The simulation results demonstrate the superiority of the proposed algorithm and its implementation scheme over the state-of-the-art methods.

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.

Impact of imperfect channel estimation and antenna correlation on quantised massive multiple‐input multiple‐output systems

This study examines the uplink performance of large-constellation multi-user massive multiple-input multiple-output systems with low-resolution analogue-to-digital converters (ADCs) in the presence of channel correlation and imperfect channel state information (CSI). The base station (BS) employs a large number of antennas for multiplexing and demultiplexing co-channel users with each antenna element having a dedicated radio frequency chain and two low-resolution ADCs. While such ADCs cause data loss due to coarse quantisation, the large number of antennas can be exploited not only to alleviate such a problem but also to make it possible to utilise large-constellation modulation schemes. The results provide an insight into the trade-off between various performance metrics and the number of quantisation bits under a wide range of realistic conditions. It will be shown that 1-bit quantisation provides sufficient resolution with 100 BS antennas to communicate with ten user equipments using quadrature phase shift keying, but the number of quantisation bits must be increased for larger constellations particularly to overcome CSI mismatch and channel correlation. The results also consider the trade-off between average mutual information and power consumption of the low-resolution ADCs. It will be shown that 16-quantum amplitude modulation with 2-bit quantisation may provide a good compromise between energy efficiency and average mutual information.

Reverse TDD-Based Massive MIMO Systems With Underlay Spectrum Sharing

Multi-cell multi-user underlay spectrum-sharing massive multiple-input multiple-output systems operating with reverse time division duplexing (R-TDD) are investigated. By primarily aiming at fully mitigating intra-cell pilot contamination and coherent interference, in the proposed R-TDD scheme, the primary/secondary systems are allowed to operate only in the opposite transmission directions. In order to establish fundamental performance limits, the secondary transmit power constraints and achievable rates are derived in the presence of training-based channel estimation. Thereby, the joint detrimental effects of spatial correlation, beamforming uncertainty, and inter-/intra-cell coherence interference due to pilot contamination are quantified and compared against the conventional TDD (C-TDD) counterpart. A max–min optimal power control policy is designed, and thereby, the common achievable rates and power control coefficients are derived. It is shown that by invoking R-TDD, the secondary power constraints and sum rates can be made to become asymptotically independent of primary interference threshold. Thus, the secondary system can be operated with its maximum average transmit power, independent of the primary system without hindering its asymptotically achievable rates by the virtue of the inherent intra-cell coherent interference mitigation benefit of the R-TDD. By exploiting the pilot decontamination feature of R-TDD, the achievable rates of primary/secondary systems can be significantly boosted, compared to the underlay spectrum sharing with C-TDD.

Energy and spectral efficiency of secure massive MIMO downlink systems

Spectral efficiency, energy efficiency, and security are cornerstones for the upcoming 5G systems. In this study, the issue of how the energy and spectral efficiency of multiuser massive multiple-input multiple-output (Ma-MIMO) systems are affected in the presence of a secrecy constraint is addressed. The performance of the two most prominent linear precoding techniques, the matched filter (MF) and zero-forcing (ZF) precoders, for secure downlink multiuser Ma-MIMO in the presence of multi-antenna passive eavesdropper is investigated. The authors consider three performance metrics, namely, the achievable ergodic secrecy rate, the secrecy spectral efficiency (SSE), and the secrecy energy efficiency (SEE), assuming perfect and imperfect channel state information. The tradeoff between SSE and SEE is also studied. Moreover, the authors derive tight lower bounds on the achievable ergodic secrecy rate for MF and ZF precoding techniques. The derived lower bounds provide insights on the tradeoff between the SSE and SEE. It is shown that ZF precoder outperforms MF precoder at high transmit power, whereas at very low transmit power, MF outperforms ZF. Moreover, it is shown that using large number of transmit antennas can improve the SSE and the SEE with orders of magnitude compared to a single-input single-output system.

Fully Decentralized Approximate Zero-Forcing Precoding for Massive MIMO Systems

We analyze the downlink of a massive multiuser multiple input, multiple output (MIMO) system where antenna units at the base station are connected in a daisy chain without a central processing unit and only possess local channel knowledge. For this setup, we develop and analyze a linear precoding algorithm for suppressing interuser interference. It is demonstrated that the algorithm is close to zero-forcing precoding in terms of performance for a large number of antennas. Moreover, we show that with careful scheduling of processing across antennas, requirements for interconnection throughput are reduced compared with the fully centralized solution. Favorable tradeoff between performance and interconnection throughput makes the daisy chain a viable candidate topology for real-life implementations of base stations in MIMO systems where the number of antennas is very large.

A Robust Semi-Blind Receiver for Joint Symbol and Channel Parameter Estimation in Multiple-Antenna Systems

For multiple-antenna systems, the technologies of joint symbol and channel parameter estimation have been developed in recent works. However, existing technologies have a number of problems, such as performance degradation and the large cost of prior information. In this paper, a tensor space-time coding scheme in multiple-antenna systems was considered. This scheme allowed spreading, multiplexing, and allocating information symbols associated with multiple transmitted data streams. We showed that the received signal was formulated as a third-order tensor satisfying a Tucker-2 model, and then a robust semi-blind receiver was developed based on the optimized Levenberg–Marquardt (LM) algorithm. Under the assumption that the instantaneous channel state information (CSI) is unknown at the receiving end, the proposed semi-blind receiver jointly estimates the information symbol and channel parameters efficiently. The proposed receiver had a better estimation performance compared with existing semi-blind receivers, and still performed well when the channel became strongly correlated. Moreover, the proposed semi-blind receiver could be extended to the multi-user massive multiple-input multiple-output (MIMO) system for joint symbol and channel estimation. Computer simulation results were shown to demonstrate the effectiveness of the proposed receiver.

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.

Efficient Constant Envelope Precoding With Quantized Phases for Massive MU-MIMO Downlink Systems

This study considers a generalized constant envelope-based precoding design problem in massive multiuser multiple-input multiple-output systems, in which the output signals of digital-to-analog converters are restricted to $M$ -ary phase-shift keying signaling to facilitate the use of low-cost and power-efficient power amplifiers at a base station. We aim to jointly optimize the precoding vector and the precoding factor to minimize the mean-squared error between the transmitted and the estimated symbols. However, the considered precoding problem is nonconvex and challenging to solve because the precoding vector and the precoding factor are coupled together. To address this problem, we apply the alternating minimization (AltMin) framework to decouple the considered problem into two problems: the precoding factor design problem and the precoding vector design problem. The former has an analytical solution, while the latter requires solving a difficult combinatorial problem, which we address by proposing a simple yet efficient gradient projection (GP)-based algorithm to find an approximate precoding vector. Simulation results demonstrate that the proposed GP-based AltMin algorithm achieves the same or higher BER performance than state-of-the-art algorithms while requiring lower complexity. In addition, when higher order modulations are employed, the error floor experienced by the existing algorithms can be substantially mitigated by the proposed GP-AltMin algorithm through increasing the number of phase bits.

Receive Spatial Modulation in Correlated Massive MIMO With Partial CSI

Spatial modulation is emerging as a promising signal transmission paradigm for future wireless communications relying on massive multiple-input multiple-output (MIMO) technology. In this paper, the receive spatial modulation (RSM) is applied to the downlink of multi-user MIMO systems with the base station equipped with a massive array of antennas. Due to the significant overhead associated with acquiring channel state information at the transmitter (CSIT) of frequency-division-duplex massive MIMO systems, herein we propose a preprocessing scheme for correlated channels that reduces the channel estimation overheads. The proposed preprocessing method relies on the partial CSIT and consists of two stages of beamforming and precoding. The beamforming is accomplished via block-diagonalization to combat multi-user interference while the precoding matrix is designed by formulating optimization problems aiming to eliminate inter-antenna interference and enhancing RSM transmission performance. The design criteria of the problems include bit-error-rate minimization and discrete-input continuous-output (DCMC) capacity maximization with a transmit power constraint. The arising non-convex problems are cast as semi-definite and second-order cone programs that can be solved efficiently. The proposed schemes are readily extended to generalized RSM as the most comprehensive case in RSM-MIMO scenarios. Simulation results demonstrate that the proposed schemes outperform the imperfect-CSIT based and two-stage zero-forcing procedures and offer similar or significant performance compared to conventional MIMO counterparts at low to mid signal-to-noise ratio regimes, depending on the configurations.

Optimal ZF Precoder for MU massive MIMO Systems over Ricean Channel with per Antenna Power Allocation

Multiuser massive multiple-input multiple-output systems have the potential to increase the data rate. However, with a large base station (BS) antenna, the non-square channel matrix restricts the zero-forcing (ZF) precoder rotations to obtain the best optimal solution with the per-antenna power allocation. In this paper, we propose the beamforming and lattice reduction (LR) approach to restrain the channel matrix and transform the lattice of the channel vectors to be near orthogonal. Numerical results show that the LR-based ZF precoder outperforms other ZF precoder schemes, such as, the norm approximation of the beamforming matrix. In particular, the sum rate of the proposed optimal ZF precoder requires a small number of BS antenna. Subsequently, with the strong line of sight (LoS) channel, the optimal power allocations in the subchannels depend on the dominance of the users in order to achieve substantial multiplexing and diversity gains. Specifically, the Ricean channel gain with the water-filling allocation at high SNR is non-negligible.

Secure Transmission in Multi-Cell Multi-User Massive MIMO Systems With an Active Eavesdropper

In this letter, we investigate secure transmission for multi-cell multi-user massive multiple-input multiple-output systems with an active eavesdropper. During the uplink (UL) training, the eavesdropper can attack the training phase to cause pilot contamination. To resist such pilot contamination attack (PCA), we propose a secure transmission that does not require statistical information of the channels. In the proposed transmission strategy, we first detect PCA by a simple method. If the PCA is not detected, we then estimate the UL data of the users by a semi-blind method based on an asynchronous protocol. After that, we perform the data-aided channel estimation and design the corresponding precoder. Simulation results demonstrate that the proposed transmission can effectively resist the PCA even when the PCA detection method fails.