This paper has been published: B. Ning et al., "Beamforming Technologies for Ultra-Massive MIMO in Terahertz Communications," in IEEE Open Journal of the Communications Society, vol. 4, pp. 614-658, 2023, doi: 10.1109/OJCOMS.2023.3245669. URL:https://ieeexplore.ieee.org/document/10045774
Terahertz (THz) communications with a frequency band $0.1-10$ THz are envisioned as a promising solution to future high-speed wireless communication. Although with tens of gigahertz available bandwidth, THz signals suffer from severe free-spreading loss and molecular-absorption loss, which limit the wireless transmission distance. To compensate for the propagation loss, the ultra-massive multiple-input-multiple-output (UM-MIMO) can be applied to generate a high-gain directional beam by beamforming technologies. In this paper, a review of beamforming technologies for THz UM-MIMO systems is provided. Specifically, we first present the system model of THz UM-MIMO and identify its channel parameters and architecture types. Then, we illustrate the basic principles of beamforming via UM-MIMO and discuss the far-field and near-field assumptions in THz UM-MIMO. Moreover, an important beamforming strategy in THz band, i.e., beam training, is introduced wherein the beam training protocol and codebook design approaches are summarized. The intelligent-reflecting-surface (IRS)-assisted joint beamforming and multi-user beamforming in THz UM-MIMO systems are studied, respectively. The spatial-wideband effect and frequency-wideband effect in the THz beamforming are analyzed and the corresponding solutions are provided. Further, we present the corresponding fabrication techniques and illuminate the emerging applications benefiting from THz beamforming. Open challenges and future research directions on THz UM-MIMO systems are finally highlighted.
Future wireless services, such as the metaverse require high information rate, reliability, and low latency. Multi-user wireless systems can meet such requirements by utilizing the abundant terahertz bandwidth with a massive number of antennas, creating narrow beamforming solutions. However, existing solutions lack proper modeling of channel dynamics, resulting in inaccurate beamforming solutions in high-mobility scenarios. Herein, a dynamic, semantically aware beamforming solution is proposed for the first time, utilizing novel artificial intelligence algorithms in variational causal inferenc…
To meet the demand of supreme data rates in terabits-per-second, the next-generation mobile system needs to exploit the abundant spectrum in the millimeter-wave and terahertz bands. However, high-frequency transmission heavily relies on large-scale antenna arrays to reap high beamforming gain, used to compensate for severe propagation loss. It raises a problem of omni-directional beamforming during the phase of initial access, where a base station is required to broadcast synchronization signals and system information to all users within its coverage. This paper proposes a novel initial beamfo…
In order to achieve terabits-per-second (Tbps) data rates in the sixth-generation (6G) mobile system, wireless communications are required to exploit the abundant spectrum in the millimeter-wave (mmWave) and terahertz (THz) bands. However, high-frequency transmission heavily relies on high beamforming gain to compensate for severe propagation loss. A beam-based system faces a barrier in the process of initial access, where a base station must broadcast synchronization signals and system information to all users within its coverage. Hence, this paper proposes a novel omnidirectional broadcastin…
We derive a fast and optimal algorithm for solving practical weighted max-min SINR problems in cell-free massive MIMO networks. For the first time, the optimization problem jointly covers long-term power control and distributed beamforming design under imperfect cooperation. In particular, we consider user-centric clusters of access points cooperating on the basis of possibly limited channel state information sharing. Our optimal algorithm merges powerful power control tools based on interference calculus with the recently developed team theoretic framework for distributed beamforming design. …
Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical stability and robustness to the channel uncertainty. However, in massive MIMO systems, the matrix inversion operation in RZF beamforming becomes computationally expensive. To address this computational issue, we shall propose a novel randomized sketching based RZF beamforming approach with low computational complexity. This is achieved by solv…
Full Duplex (FD) communication can revolutionize wireless communications as it avoids using independent channels for bi-directional communications. This work generalizes the point-to-point FD communication in millimeter wave (mmWave) band consisting of K-pairs of massive MIMO FD nodes operating simultaneously. We present a novel joint hybrid beamforming (HYBF) and combining scheme for weighted sum-rate (WSR) maximization to enable the coexistence of massive MIMO FD links cost-efficiently. The proposed algorithm relies on alternative optimization based on the minorization-maximization method. M…
This paper investigates terahertz ultra-massive (UM)-MIMO-based angle estimation for space-to-air communications, which can solve the performance degradation problem caused by the dual delay-beam squint effects of terahertz UM-MIMO channels. Specifically, we first design a grouping true-time delay unit module that can significantly mitigate the impact of delay-beam squint effects to establish the space-to-air THz link. Based on the subarray selection scheme, the UM hybrid array can be equivalently considered as a low-dimensional fully-digital array, and then the fine estimates of azimuth/eleva…
This paper investigates Cell-Free massive MIMO networks, where each access point (AP) is equipped with a hybrid transceiver, reducing the complexity and cost compared to a fully digital transceiver. Asymptotic approximations for the spectral efficiency are derived for uplink and downlink. Capitalizing on these expressions, a max-min problem is formulated to optimize the (i) analog beamformer at the APs and (ii) pilot assignment. Simulations show that the optimization of these variables substantially increases the network performance.
Terahertz (THz) communications are regarded as a pillar technology for the 6G systems, by offering multi-ten-GHz bandwidth. To overcome the huge propagation loss while reducing the hardware complexity, THz ultra-massive (UM) MIMO systems with hybrid beamforming are proposed to offer high array gain. Notably, the adjustable-phase-shifters considered in most existing hybrid beamforming studies are power-hungry and difficult to realize in the THz band. Moreover, due to the ultra-massive antennas, full channel-state-information (CSI) is challenging to obtain. To address these practical concerns, i…
Massive multiple-input multiple-out (MIMO) technology is vital in millimeter-wave (mmWave) bands to obtain large array gains. However, there are practical challenges, such as high hardware cost and power consumption in such systems. A promising solution to these problems is to adopt a hybrid beamforming architecture. This architecture has a much lower number of transceiver (TRx) chains than the total antenna number, resulting in cost- and energy-efficient systems. In this paper, we present a real-time mmWave (28 GHz) massive MIMO testbed with hybrid beamforming. This testbed has a 64-antenna/1…
In this paper, a novel optimization model for joint beamforming and power control in the downlink (DL) of a cell-free massive MIMO (CFmMIMO) system is presented. The objective of the proposed optimization model is to minimize the maximum user interference while satisfying quality of service (QoS) constraints and power consumption limits. The proposed min-max optimization model is formulated as a mixed-integer nonlinear program, that is directly tractable. Numerical results show that the proposed joint beamforming and power control scheme is effective and outperforms competing schemes in terms …
We consider a multiple-input multiple-output (MIMO) relaying boardcast channel in downlink cellular networks, where the base station and the relay stations are both equipped with multiple antennas, and each user terminal has only a single antenna. In practical scenarios, channel estimation is imperfect at the receivers. Aiming at maximizing the SINR at each user, we develop two robust linear beamforming schemes respectively for the single relay case and the multi-relay case. The two proposed schemes are based on sigular value decomposition (SVD), minimum mean square error (MMSE) and regularize…
Beamforming is indispensable in the operation of 60-GHz millimeter-wave directional multi-gigabit Wi-Fi. Simple power method and its extensions enable the transmitting and receiving antenna arrays to form a beam for single spatial stream. To further improve the spectral efficiency in future 60-GHz directional Wi-Fi, alternating least square (ALS) algorithm can form multiple beams between the transmitter and receiver for multi-input-multi-output (MIMO) operations. For both shared and split MIMO architecture, the ALS beamforming algorithm can be operated in both frequency-flat and frequency-sele…
In this article we compare the performance of two typical hyrbid beamforming structures for multiuser massive MIMO systems, i.e., the full- and partial-connection structures. Under the assumption of small angular spread for mmWave channels, given the analog precoder formed towards users and the zero-forcing digital precoder, we develop an explicit upper bound for the analog-and-digital-precoded channel gain of users, based on which the relationship between the two structures is investigated. The analysis results show that the full-connection structure is not always better than the partial-conn…
Full-dimensional (FD) multi-user massive multiple input multiple output (m-MIMO) systems employ large two-dimensional (2D) rectangular antenna arrays to control both the azimuth and elevation angles of signal transmission. We introduce the sum of two outer products of the azimuth and elevation beamforming vectors having moderate dimensions as a new class of FD beamforming. We show that this low-complexity class is capable of outperforming 2D beamforming relying on the single outer product of the azimuth and elevation beamforming vectors. It is also capable of performing close to its FD counter…
Terahertz (THz) communications open a new frontier for the wireless network thanks to their dramatically wider available bandwidth compared to the current micro-wave and forthcoming millimeter-wave communications. However, due to the short length of THz waves, they also suffer from severe path attenuation and poor diffraction. To compensate the THz-induced propagation loss, this paper proposes to combine two promising techniques, viz., massive multiple input multiple output (MIMO) and intelligent reflecting surface (IRS), in THz multi-user communications, considering their significant beamform…
Hybrid beamforming for Terahertz (THz) ultra-massive multiple-input multiple-output (UM-MIMO) systems is a promising technology for 6G space-air-ground integrated networks, which can overcome huge propagation loss and offer unprecedented data rates. With ultra-wide bandwidth and ultra-large-scale antennas array in THz band, the beam squint becomes one of the critical problems which could reduce the array gain and degrade the data rate substantially. However, the traditional phase-shifters-based hybrid beamforming architectures cannot tackle this issue due to the frequency-flat property of the …
A relentless trend in wireless communications is the hunger for bandwidth, and fresh bandwidth is only to be found at ever-higher frequencies. While 5G systems are seizing the mmWave band, the attention of researchers is shifting already to the terahertz range. In that distant land of tiny wavelengths, antenna arrays can serve for more than power-enhancing beamforming. Defying lower-frequency wisdom, spatial multiplexing becomes feasible even in line-of-sight conditions. This paper reviews the underpinnings of this phenomenon, and it surveys recent results on the ensuing information-theoretic …
As communication systems that employ millimeter wave (mmWave) frequency bands must use large antenna arrays to overcome the severe propagation loss of mmWave signals, hybrid beamforming has been considered as an integral component of mmWave communications. Recently, intelligent reflecting surface (IRS) has been proposed as an innovative technology that can significantly improve the performance of mmWave communication systems through the use of low-cost passive reflecting elements. In this paper, we study IRS-aided mmWave multiple-input multiple-output (MIMO) systems with hybrid beamforming arc…
Reconfigurable Intelligent Surfaces (RISs) are one of the key emerging 6th Generation (6G) technologies that are expected to improve the link budgets between transmitters and receivers by adding artificial propagation paths. In such re-configured propagation environment, Downlink (DL) Multi-User Multi-Input Multi-Output (MU-MIMO) brings capacity improvement to cellular networks. It benefits from the spatial dimension offered by MIMO systems to enable simultaneous transmission of independent data streams to multiple users on the same radio resources by applying appropriate Beamforming (BF) sche…
In limited feedback multi-user multiple-input multiple-output (MU-MIMO) cellular networks, users send quantized information about the channel conditions to the associated base station (BS) for downlink beamforming. However, channel quantization and beamforming have been treated as two separate tasks conventionally, which makes it difficult to achieve global system optimality. In this paper, we propose an augmented deep unfolding (ADU) approach that jointly optimizes the beamforming scheme at the BSs and the channel quantization scheme at the users. In particular, the classic WMMSE beamformer i…
Terahertz (THz) communications are regarded as a pillar technology for the sixth generation (6G) wireless systems, by offering multi-ten-GHz bandwidth. To overcome the short transmission distance and huge propagation loss, ultra-massive (UM) MIMO systems that employ sub-millimeter wavelength antennas array are proposed to enable an enticingly high array gain. In the UM-MIMO systems, hybrid beamforming stands out for its great potential in promisingly high data rate and reduced power consumption. In this paper, challenges and features of the THz hybrid beamforming design are investigated, in li…
Wireless communication in the TeraHertz band (0.1--10 THz) is envisioned as one of the key enabling technologies for the future six generation (6G) wireless communication systems. However, very high propagation attenuations and molecular absorptions of THz frequencies often limit the signal transmission distance and coverage range. Benefited from the recent breakthrough on the reconfigurable intelligent surfaces (RIS) for realizing smart radio propagation environment, we propose a novel hybrid beamforming scheme for the multi-hop RIS-assisted communication networks to improve the coverage rang…
This paper investigates the passive beamforming and information transfer (PBIT) technique for the multiuser multiple-input multiple-output (MIMO) systems with the aid of a reconfigurable intelligent surface (RIS), where the RIS enhances the primary communication via passive beamforming and at the same time delivers additional information by the spatial modulation (which adjusts the on-off states of the reflecting elements). For the passive beamforming design, we propose to maximize the sum channel capacity of the RIS-aided multiuser MIMO channel and formulate the problem as a two-step stochast…
Reconfigurable intelligent surface (RIS) is considered to be an energy-efficient approach to reshape the wireless environment for improved throughput. Its passive feature greatly reduces the energy consumption, which makes RIS a promising technique for enabling the future smart city. Existing beamforming designs for RIS mainly focus on optimizing the spectral efficiency for single carrier systems. To avoid the complicated bit allocation on different spatial domain subchannels in MIMO systems, in this paper, we propose a geometric mean decomposition-based beamforming for RIS-assisted millimeter…
A critical task of a radar receiver is data association, which assigns radar target detections to target filter tracks. Motivated by its importance, this paper introduces the problem of jointly designing multiple-input multiple-output (MIMO) radar transmit beam patterns and the corresponding data association schemes. We show that the coupling of the beamforming and the association subproblems can be conveniently parameterized by what we term an ambiguity graph, which prescribes if two targets are to be disambiguated by the beamforming design or by the data association scheme. The choice of amb…
Massive Multiple-input Multiple-output (MIMO) adaption is one of the primary evolving objectives for the next generation high speed train (HST) communication system. In this paper, we consider how to design an efficient low-complexity location-aware beamforming for the multi-user (MU) massive MIMO system in HST scenario. We first put forward a low-complexity beamforming based on location information, where multiple users are considered. Then, without considering inter-beam interference, a closed-form solution to maximize the total service competence of base station (BS) is proposed in this MU …
In this letter, we consider hybrid beamforming for millimeter wave (mmWave) MIMO integrated sensing and communications (ISAC). We design the transmit beam of a dual-functional radar-communication (DFRC) base station (BS), aiming at approaching the objective radar beam pattern, subject to the constraints of the signal to interference-plus-noise ratio (SINR) of communication users and total transmission power of the DFRC BS. To provide additional degree of freedom for the beam design problem, we introduce a phase vector to the objective beam pattern and propose an alternating minimization method…
In this paper, adaptive hybrid beamforming methods are proposed for millimeter-wave range massive multiple-input-multiple-output (MIMO) systems considering single carrier wideband transmission in uplink data mode. A statistical analog beamformer is adaptively constructed in slow-time, while the channel is time-varying and erroneously estimated. A recursive filtering approach is proposed, which aims robustness against estimation errors for generalized eigen-beamformer (GEB). Approximated expressions are obtained for channel covariance matrices that decouple angular spread and center angle of mu…
In this paper, we develop a framework to investigate the performances of different hybrid beamforming architectures for massive multiple input multiple output (MIMO) systems impaired by power amplifier (PA) nonlinearities. Indirect learning architecture based on feedback after anti-beamforming is adopted in design of digital pre-distortion (DPD) in order to compensate the nonlinear distortion caused by PA. In addition, we propose a novel analog beamformer design for partially connected architecture based on generalized eigen-beamformer (GEB) approach. In literature, the effects of nonlinear PA…
Massive multi-input multi-output (MIMO) uses a very large number of low-power transmit antennas to serve much smaller numbers of users. The most widely proposed type of massive MIMO transmit beamforming is zero-forcing, which is based on the right inverse of the overall MIMO channel matrix to force the inter-user interference to zero. The performance of massive MIMO is then analyzed based on the throughput of cell-edge users. This paper reassesses this beamforming philosophy, to instead consider the maximization of the energy efficiency of massive MIMO systems in assuring the quality-of- servi…
Terahertz (THz) communications with multi-GHz bandwidth are envisioned as a key technology for 6G systems. Ultra-massive (UM) MIMO with hybrid beamforming architectures are widely investigated to provide a high array gain to overcome the huge propagation loss. However, most of the existing hybrid beamforming architectures can only utilize the multiplexing offered by the multipath components, i.e., inter-path multiplexing, which is very limited due to the spatially sparse THz channel. In this paper, a widely-spaced multi-subarray (WSMS) hybrid beamforming architecture is proposed, which improve…
Sixth generation (6G) cellular systems are expected to extend the operational range to sub-Terahertz (THz) frequencies between 100 and 300 GHz due to the broad unexploited spectrum therein. A proper channel model is needed to accurately describe spatial and temporal channel characteristics and faithfully create channel impulse responses at sub-THz frequencies. This paper studies the channel spatial statistics such as the number of spatial clusters and cluster power distribution based on recent radio propagation measurements conducted at 142 GHz in an urban microcell (UMi) scenario. For the 28 …
The problem of radio resource allocation for global energy efficiency (GEE) maximization in mmWaves large-scale multiple-input multiple-output (MIMO) systems using hybrid-beamforming with spatial modulation is addressed. The theoretical properties of the optimization problem at hand are analyzed and two provably convergent optimization algorithms with affordable complexity are proposed. The former achieves the global optimum, while the latter trades off optimality with a lower computational complexity. Nevertheless, numerical results show that both algorithms attain global optimality in practi…
Reconfigurable Intelligent Surface (RIS) is one of the key technologies for the upcoming 6th Generation (6G) communications, which can improve the signal strength at the receivers by adding artificial propagation paths. In the context of Downlink (DL) Multi-User Multiple-Input Multiple-Output (MU-MIMO) communications, designing an appropriate Beamforming (BF) scheme to take full advantage of this reconfigured propagation environment and improve the network capacity is a major challenge. Due to the spatial dimension provided by MIMO systems, independent data streams can be transmitted to multip…
In this paper, we investigate a unified linear transceiver design with mean-square-error (MSE) as the objective function for a wide range of wireless systems. The unified design is based on an elegant mathematical programming technology namely quadratic matrix programming (QMP). It is revealed that for different wireless systems such as multi-cell coordination systems, multi-user MIMO systems, MIMO cognitive radio systems, amplify-and-forward MIMO relaying systems, the MSE minimization beamforming design problems can always be solved by solving a number of QMP problems. A comprehensive framewo…
To accommodate the explosive wireless traffics, massive multiple-input multiple-output (MIMO) is regarded as one of the key enabling technologies for next-generation communication systems. In massive MIMO cellular networks, coordinated beamforming (CBF), which jointly designs the beamformers of multiple base stations (BSs), is an efficient method to enhance the network performance. In this paper, we investigate the sum rate maximization problem in a massive MIMO mobile cellular network, where in each cell a multi-antenna BS serves multiple mobile users simultaneously via downlink beamforming. …
Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）
Hybrid beamforming is widely recognized as an important technique for millimeter wave (mmWave) multiple input multiple output (MIMO) systems. Generalized spatial modulation (GSM) is further introduced to improve the spectrum efficiency. However, most of the existing works on beamforming assume the perfect channel state information (CSI), which is unrealistic in practical systems. In this paper, joint optimization of downlink pilot training, channel estimation, CSI feedback, and hybrid beamforming is considered in GSM aided frequency division duplexing (FDD) mmWave MIMO systems. With the help o…
Opportunistic scheduling and beamforming schemes with reduced feedback are proposed for MIMO-OFDMA downlink systems. Unlike the conventional beamforming schemes in which beamforming is implemented solely by the base station (BS) in a per-subcarrier fashion, the proposed schemes take advantages of a novel channel decomposition technique to perform beamforming jointly by the BS and the mobile terminal (MT). The resulting beamforming schemes allow the BS to employ only {\em one} beamforming matrix (BFM) to form beams for {\em all} subcarriers while each MT completes the beamforming task for each …
Hybrid beamforming (HB) has been widely studied for reducing the number of costly radio frequency (RF) chains in massive multiple-input multiple-output (MIMO) systems. However, previous works on HB are limited to a single user equipment (UE) or a single group of UEs, employing the frequency-flat first-level analog beamforming (AB) that cannot be applied to multiple groups of UEs served in different frequency resources in an orthogonal frequency-division multiplexing (OFDM) system. In this paper, a novel HB algorithm with unified AB based on the spatial covariance matrix (SCM) knowledge of all …
Opportunistic scheduling and beamforming schemes have been proposed previously by the authors for reduced-feedback MIMO-OFDMA downlink systems where the MIMO channel of each subcarrier is decomposed into layered spatial subchannels. It has been demonstrated that significant feedback reduction can be achieved by returning information about only one beamforming matrix (BFM) for all subcarriers from each MT, compared to one BFM for each subcarrier in the conventional schemes. However, since the previously proposed channel decomposition was derived based on singular value decomposition, the result…
The application of precoding algorithms in multi-user massive multiple-input multiple-output (MU-Massive-MIMO) systems is restricted by the dimensionality constraint that the number of transmit antennas has to be greater than or equal to the total number of receive antennas. In this paper, a lattice reduction (LR)-aided flexible coordinated beamforming (LR-FlexCoBF) algorithm is proposed to overcome the dimensionality constraint in overloaded MU-Massive-MIMO systems. A random user selection scheme is integrated with the proposed LR-FlexCoBF to extend its application to MU-Massive-MIMO systems …
