Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks, as it offers orders of magnitude greater spectrum than current cellular bands. In contrast to conventional multiple-input–multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.

Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems

Millimeter wave (mmWave) communications have recently attracted large research interest, since the huge available bandwidth can potentially lead to the rates of multiple gigabit per second per user Though mmWave can be readily used in stationary scenarios, such as indoor hotspots or backhaul, it is challenging to use mmWave in mobile networks, where the transmitting/receiving nodes may be moving, channels may have a complicated structure, and the coordination among multiple nodes is difficult To fully exploit the high potential rates of mmWave in mobile networks, lots of technical problems must be addressed This paper presents a comprehensive survey of mmWave communications for future mobile networks (5G and beyond) We first summarize the recent channel measurement campaigns and modeling results Then, we discuss in detail recent progresses in multiple input multiple output transceiver design for mmWave communications After that, we provide an overview of the solution for multiple access and backhauling, followed by the analysis of coverage and connectivity Finally, the progresses in the standardization and deployment of mmWave for mobile networks are discussed

Millimeter Wave Communications for Future Mobile Networks

We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional sub-6-GHz cellular systems are: 1) vulnerability to blocking and 2) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: 1) mmWave systems are significantly more noise-limited than at sub-6 GHz for most parameter configurations; 2) initial access is much more difficult in mmWave; 3) self-backhauling is more viable than in sub-6-GHz systems, which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and 4) in sharp contrast to sub-6-GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research.

Modeling and Analyzing Millimeter Wave Cellular Systems

After about a decade of intense research, spurred by both economic and operational considerations, and by environmental concerns, energy efficiency has now become a key pillar in the design of communication networks. With the advent of the fifth generation of wireless networks, with millions more base stations and billions of connected devices, the need for energy-efficient system design and operation will be even more compelling. This survey provides an overview of energy-efficient wireless communications, reviews seminal and recent contribution to the state-of-the-art, including the papers published in this special issue, and discusses the most relevant research challenges to be addressed in the future.

A Survey of Energy-Efficient Techniques for 5G Networks and Challenges Ahead

6G and beyond will fulfill the requirements of a fully connected world and provide ubiquitous wireless connectivity for all. Transformative solutions are expected to drive the surge for accommodating a rapidly growing number of intelligent devices and services. Major technological breakthroughs to achieve connectivity goals within 6G include: (i) a network operating at the THz band with much wider spectrum resources, (ii) intelligent communication environments that enable a wireless propagation environment with active signal transmission and reception, (iii) pervasive artificial intelligence, (iv) large-scale network automation, (v) an all-spectrum reconfigurable front-end for dynamic spectrum access, (vi) ambient backscatter communications for energy savings, (vii) the Internet of Space Things enabled by CubeSats and UAVs, and (viii) cell-free massive MIMO communication networks. In this roadmap paper, use cases for these enabling techniques as well as recent advancements on related topics are highlighted, and open problems with possible solutions are discussed, followed by a development timeline outlining the worldwide efforts in the realization of 6G. Going beyond 6G, promising early-stage technologies such as the Internet of NanoThings, the Internet of BioNanoThings, and quantum communications, which are expected to have a far-reaching impact on wireless communications, have also been discussed at length in this paper.

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6G and Beyond: The Future of Wireless Communications Systems

Millimeter wave (mmWave) MIMO will likely use hybrid analog and digital precoding, which uses a small number of RF chains to reduce the energy consumption associated with mixed signal components like analog-to-digital components not to mention baseband processing complexity. However, most hybrid precoding techniques consider a fully connected architecture requiring a large number of phase shifters, which is also energy-intensive. In this paper, we focus on the more energy-efficient hybrid precoding with subconnected architecture, and propose a successive interference cancelation (SIC)-based hybrid precoding with near-optimal performance and low complexity. Inspired by the idea of SIC for multiuser signal detection, we first propose to decompose the total achievable rate optimization problem with nonconvex constraints into a series of simple subrate optimization problems, each of which only considers one subantenna array. Then, we prove that maximizing the achievable subrate of each subantenna array is equivalent to simply seeking a precoding vector sufficiently close (in terms of Euclidean distance) to the unconstrained optimal solution. Finally, we propose a low-complexity algorithm to realize SIC-based hybrid precoding, which can avoid the need for the singular value decomposition (SVD) and matrix inversion. Complexity evaluation shows that the complexity of SIC-based hybrid precoding is only about 10% as complex as that of the recently proposed spatially sparse precoding in typical mmWave MIMO systems. Simulation results verify that SIC-based hybrid precoding is near-optimal and enjoys higher energy efficiency than the spatially sparse precoding and the fully digital precoding.

Energy-Efficient Hybrid Analog and Digital Precoding for MmWave MIMO Systems With Large Antenna Arrays

Millimeter wave (mmWave) MIMO will likely use hybrid analog and digital precoding, which uses a small number of RF chains to avoid energy consumption associated with mixed signal components like analog-to-digital components not to mention baseband processing complexity. However, most hybrid precoding techniques consider a fully-connected architecture requiring a large number of phase shifters, which is also energyintensive. In this paper, we focus on the more energy-efficient hybrid precoding with sub-connected architecture, and propose a successive interference cancelation (SIC)-based hybrid precoding with near-optimal performance and low complexity. Inspired by the idea of SIC for multi-user signal detection, we first propose to decompose the total achievable rate optimization problem with non-convex constraints into a series of simple sub-rate optimization problems, each of which only considers one sub-antenna array. Then, we prove that maximizing the achievable sub-rate of each sub-antenna array is equivalent to simply seeking a precoding vector sufficiently close (in terms of Euclidean distance) to the unconstrained optimal solution. Finally, we propose a low-complexity algorithm to realize SICbased hybrid precoding, which can avoid the need for the singular value decomposition (SVD) and matrix inversion. Complexity evaluation shows that the complexity of SIC-based hybrid precoding is only about 10% as complex as that of the recently proposed spatially sparse precoding in typical mmWave MIMO systems. Simulation results verify the near-optimal performance of SIC-based hybrid precoding.

Energy-Efficient Hybrid Analog and Digital Precoding for mmWave MIMO Systems with Large Antenna Arrays

The recent concept of beamspace MIMO can utilize beam selection to reduce the number of required radio-frequency (RF) chains in mmWave massive MIMO systems without obvious performance loss. However, as the same beam in the beamspace is likely to be selected for different users, conventional beam selection schemes will suffer from serious multiuser interferences, and some RF chains may be wasted since they have no contribution to the sum-rate performance. To solve these problems, in this letter, we propose an interference-aware (IA) beam selection. Specifically, by considering the potential multiuser interferences, the proposed IA beam selection first classifies all users into two user groups, i.e., the interference-users (IUs) and noninterference-users (NIUs). For NIUs, the beams with large power are selected, while for IUs, the appropriate beams are selected by a low-complexity incremental algorithm based on the criterion of sum-rate maximization. Simulation results verify that IA beam selection can achieve the near-optimal sum-rate performance and higher energy efficiency than conventional schemes.

Near-Optimal Beam Selection for Beamspace MmWave Massive MIMO Systems

The recent concept of beamspace multiple input multiple output (MIMO) with discrete lens array can utilize beam selection to reduce the number of radio-frequency chains (RF) required in terahertz (THz) massive MIMO systems. However, to achieve the capacity-approaching performance, beam selection requires information on a beamspace channel of large size. This is difficult to obtain since the user mobility usually leads to the fast variation of THz beamspace channels, and the conventional real-time channel estimation schemes involve unaffordable pilot overhead. To solve this problem, in this paper, we propose the a priori aided (PA) channel tracking scheme. Specifically, by considering a practical user motion model, we first excavate a temporal variation law of the physical direction between the base station and each mobile user. Then, based on this law and the special sparse structure of THz beamspace channels, we propose to utilize the obtained beamspace channels in the previous time slots to predict the prior information of the beamspace channel in the following time slot without channel estimation. Finally, aided by the obtained prior information, the time-varying beamspace channels can be tracked with low pilot overhead. Simulation results verify that to achieve the same accuracy, the proposed PA channel tracking scheme requires much lower pilot overhead and signal-to-noise ratio (SNR) than the conventional schemes.

Fast Channel Tracking for Terahertz Beamspace Massive MIMO Systems

For uplink large-scale multiple-input–multiple-output (MIMO) systems, the minimum mean square error (MMSE) algorithm is near optimal but involves matrix inversion with high complexity. In this paper, we propose to exploit the Gauss–Seidel (GS) method to iteratively realize the MMSE algorithm without the complicated matrix inversion. To further accelerate the convergence rate and reduce the complexity, we propose a diagonal-approximate initial solution to the GS method, which is much closer to the final solution than the traditional zero-vector initial solution. We also propose an approximated method to compute log-likelihood ratios for soft channel decoding with a negligible performance loss. The analysis shows that the proposed GS-based algorithm can reduce the computational complexity from ${{\mathcal O}({K^3})}$ to ${{\mathcal O}({K^2})}$ , where ${K}$ is the number of users. Simulation results verify that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm and achieves the near-optimal performance of the classical MMSE algorithm with a small number of iterations.

Xinyu Gao

Papers

Energy-Efficient Hybrid Analog and Digital Precoding for MmWave MIMO Systems With Large Antenna Arrays

Energy-Efficient Hybrid Analog and Digital Precoding for mmWave MIMO Systems with Large Antenna Arrays

Near-Optimal Beam Selection for Beamspace MmWave Massive MIMO Systems

Fast Channel Tracking for Terahertz Beamspace Massive MIMO Systems

Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method for Uplink Multiuser Large-Scale MIMO Systems