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Beamforming Technologies for Ultra-Massive MIMO in Terahertz Communications

Boyu Ning, Zhongbao Tian, Weidong Mei, Zhi Chen, Chong Han, Shaoqian Li, Jinhong Yuan, Rui Zhang

arXiv:2107.03032v6cs.ITeess.SP

TL;DR

THz communications offer tens of gigahertz of bandwidth but suffer spreading and molecular-absorption losses that limit transmission distance. The paper reviews beamforming technologies for THz UM-MIMO, covering system models, beam training, near- and far-field operation, IRS and multi-user beamforming, wideband effects, fabrication, applications, and open challenges. It reports that far-field beamforming remains effective for most scenarios at 0.3 THz, while near-field beamforming supplements it in some cases.

  • Problem

    THz signals provide broad bandwidth but experience severe spreading and molecular-absorption losses, creating a transmission-distance challenge; detailed beamforming guidance for THz UM-MIMO is lacking.

  • Method

    The paper reviews THz UM-MIMO beamforming, including system modeling, beam training, near- and far-field assumptions, IRS-assisted and multi-user beamforming, wideband effects, fabrication, and applications.

  • Results

    At 0.3 THz, far-field beamforming remains effective with less than 5% performance loss beyond 1.8 m even with 10,000 antenna elements.

  • Takeaways & Limitations

    Far-field beamforming is suitable for most THz UM-MIMO scenarios, with near-field beamforming serving as a supplement for a few scenarios.

Abstract

from arXiv · show

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.

I. INTRODUCTION

The THz band is proposed for future high-speed wireless communication because it offers new spectrum beyond mmWave, but propagation loss limits transmission distance. This review focuses on UM-MIMO beamforming as a means to compensate for that loss and surveys the field’s prior work and technical context.

  • THz motivation: The THz band spans 0.1-10 THz and is considered for high-speed transmission beyond extensively explored radio, microwave/mmWave, and FSO bands.Its position between electronic and photonic generation regions creates electromagnetic-generation difficulty.
  • THz motivation: THz wireless links face high spreading loss and severe molecular-absorption loss, which limit transmission distance.
  • UM-MIMO beamforming: UM-MIMO uses hundreds to thousands of THz antenna elements to generate high-gain directional beams through beamforming.The term includes conventional half-wavelength metallic-antenna arrays and is not restricted to nano-antenna arrays.
  • Review scope: The review establishes THz UM-MIMO concepts, classifies MIMO arrays, explains beamforming principles, and discusses emerging applications and open challenges.
  • Related work: Earlier THz literature covered applications, devices, propagation, architectures, channels, standards, and broader opportunities, while detailed beamforming guidance remained lacking.The paper identifies a gap in a holistic tutorial covering theory, technology, fabrication, and deployment considerations.

B. Contributions of this Paper

The paper surveys THz UM-MIMO beamforming from system fundamentals through beam training, IRS-assisted and multi-user methods, wideband effects, fabrication, applications, and open challenges.

  • The paper presents a basic THz UM-MIMO system model, determines channel parameters, and discusses how antenna geometry and transceiver architecture affect the system.
  • It explains beamforming principles through electromagnetic-field visualization, characterizes large-array beam patterns, and addresses near-field and far-field assumptions.
  • It introduces CSI-free beam training and discusses its training protocol, codebook design, and lens-antenna-array implementation.
  • It studies IRS-assisted THz UM-MIMO, including joint active and passive beamforming for enhanced signal coverage and spectral efficiency with low energy consumption.
  • It develops multi-user beamforming coverage and revisits linear algorithms for eliminating inter-user interference in THz UM-MIMO systems.
  • It analyzes spatial-wideband and frequency-wideband effects, reviews dynamically steerable THz arrays by fabrication technique, and identifies applications and open challenges.

C. Organization and Notations

This section outlines the paper’s organization and notation, then introduces the THz UM-MIMO system model, channel characteristics, attenuation, and LoS-oriented beamforming context.

  • Organization: The paper proceeds from THz UM-MIMO system modeling to beamforming principles, beam training, IRS-assisted joint beamforming, multiuser and wideband beamforming, fabrication, applications, and future directions.The organization also identifies sections devoted to existing THz MIMO arrays and concludes with a final summary.
  • Notations: Scalars, vectors, and matrices use distinct typefaces, while transpose, conjugate, Hermitian transpose, modulus, Frobenius norm, and diagonal-matrix operators follow defined notation.The notation also identifies R and C as the real- and complex-number sets.
  • System model: A point-to-point THz UM-MIMO system uses transmit and receive antenna elements, a channel matrix, a transmitted signal vector, and a noise vector in its received-signal model.The model assumes quasi-static block fading.
  • Channel model: THz channel modeling considers path loss exponent, shadow fading, K factor, delay spread, azimuth spread of arrival, and elevation spread of arrival.The paper presents the Saleh–Valenzuela model and distinguishes deterministic, statistical, and hybrid channel models.
  • Beamforming context: THz beamforming emphasizes the line-of-sight path and can use beam training without channel-state information, while propagation includes severe free-spreading loss.The paper also introduces attenuation models and channel-gain components involving antenna gains and array responses.

2) Path Gain:

THz path gain is shaped by frequency-squared spreading loss, molecular absorption, and antenna gains. MIMO array gain can compensate for spreading loss, leaving molecular absorption as the remaining loss, whose frequency dependence is nonmonotonic.

  • Path-loss components: Spreading loss increases with the square of carrier frequency, while molecular absorption adds severe THz attenuation.The path gain includes both spreading loss and molecular absorption, with absorption mainly arising from water vapor.
  • Molecular absorption: The total absorption coefficient k(f) is a weighted sum of molecular absorption coefficients and is relatively large above 1 THz.HITRAN provides k_i(f) under specified temperature and pressure conditions; two absorption drops occur around 7–8 THz.
  • Path-loss validation: Path-loss calculations from the molecular-absorption coefficient and the ITU-R model show nearly the same trend across transmit distances, with jump points at the same frequencies.The two methods differ in the magnitude of the calculated loss.
  • Antenna gain: Antenna gain combines element gain and array gain, with coherent addition from N elements producing an array gain of N.The element radiation pattern generally concentrates energy perpendicular to the antenna element.
  • Frequency dependence: In MISO systems, increased antenna gain cannot compensate for spreading loss, so received power decreases as frequency increases.This statement excludes small-scale frequency fluctuations.
  • Frequency dependence: In MIMO systems, antenna gain can compensate for spreading loss, leaving molecular absorption as the remaining loss; consequently, received power may increase with frequency.The paper gives the example that received power at 7.2 THz can exceed that at 3 THz because absorption is nonmonotonic.

B. Array Response Vector

Array response vectors describe propagation paths for different antenna geometries and can serve as beamforming codewords. Increasing the element count raises gain but narrows beams, increasing beam-management complexity.

  • Array response vectors: Each array response vector represents a propagation path associated with a specific angle of departure or arrival.The path angles may be one- or two-dimensional depending on antenna geometry.
  • Array geometries: The paper presents four typical geometries: ULA, URPA, UHPA, and UCPA.These include linear, rectangular planar, hexagonal planar, and circular planar arrays.
  • URPA: For URPA, the array has Ny × Nz elements on the yz-plane, with Na = NyNz and angles ϕ and θ denoting azimuth and elevation arrival angles.The inter-element spacings along the y- and z-axes are dy and dz.
  • UCPA: A UCPA consists of C concentric circles on the xy-plane, with elements uniformly distributed around each circle.The c-th circle has radius rc, and each element is specified by its angle ϕ_nc to the x-axis.
  • Beam patterns: An array response vector can be used as a beamforming codeword covering a designated spatial zone.Increasing the number of elements improves beam gain but produces narrower beams requiring more spatial beams.
  • Beam patterns: For URPA, increasing the array from 16 elements in MIMO to 1600 in UM-MIMO raises maximum beam gain from 16 to 1600 and required beams from 64 to 6400.The comparison uses 4×4 versus 40×40 arrays at θ = 0.

C. Transceiver Architectures

THz UM-MIMO transceivers use analog, digital, or hybrid beamforming architectures, with hybrid designs trading hardware cost and power for beamforming flexibility and performance.

  • C. Transceiver Architectures: Analog beamforming applies phase shifts to a common symbol across antennas but cannot independently control signal magnitudes.This constant-modulus constraint limits control flexibility and beamforming performance.
  • C. Transceiver Architectures: Digital beamforming realizes arbitrary linear transformations across signal streams and antenna elements, providing greater degrees of freedom at high cost and power consumption.The architecture is considered unaffordable for UM-MIMO systems because of its hardware and energy demands.
  • C. Transceiver Architectures: Hybrid beamforming combines analog beamforming with digital precoding to approach digital-beamforming performance in some cases with lower hardware cost and power consumption.Its operation spans both baseband and analog domains.
  • C. Transceiver Architectures: Fully-connected hybrid architectures connect every antenna element to every RF chain, so each antenna receives overlapped signals from all RF chains.The architecture uses NRF RF chains and Nt antenna elements with phase shifters implementing the analog beamformer.
  • C. Transceiver Architectures: Partially-connected architectures assign each RF chain to a unique antenna subarray, reducing the hardware connection count but limiting adaptive control.Their analog beamformer has a block-diagonal structure, and the architecture further reduces hardware cost to Nt links.

3) Dynamically-Connected Architecture:

Dynamic connection adds a switch network to partially-connected hybrid beamforming, improving processing flexibility while retaining lower-cost characteristics. The section also explains array-response beamforming and the conditions under which far-field models remain effective in THz UM-MIMO.

  • 3) Dynamically-Connected Architecture:: Dynamic hybrid beamforming uses a Boolean switching network between RF chains and antenna elements, with each antenna connected to one RF signal at a time.The switching constraint is expressed as the sum of connection indicators for each antenna equaling one.
  • 3) Dynamically-Connected Architecture:: Dynamic connection preserves the low-cost advantage of partial connection while increasing processing freedom, but more sophisticated dynamic arrays may be infeasible for UM-MIMO.The DAoSA architecture was reported to save power relative to fully-connected hybrid beamforming, while requiring more complex hardware.
  • Beamforming Principles: Beamforming maps data streams to transmit signals, while combining maps received signals back to data streams; beam steering is analog beamforming with one data stream.Digital beamforming is commonly treated as precoding, with combining correspondingly called decoding.
  • Beamforming Principles: A phased array electronically steers radiation by phase-shifting each antenna signal so waves add in desired directions and are suppressed elsewhere.For transmit steering, array-response phases align wavefronts toward the departure angle; half-wavelength spacing is commonly used.
  • C. Far-field and Near-field: The far-field array-response model assumes a planar wavefront with common arrival and departure angles, whereas nearby sources produce near-field spherical-wave effects.The Rayleigh distance defines the general boundary, with D = (Na−1)da representing the array side length.
  • C. Far-field and Near-field: At 0.3 THz, far-field beamforming remains effective beyond 1.8 m even with 10,000 antennas, when performance loss is below 5%.Near-field beamforming is therefore presented as a supplement for only a few scenarios.

IV. BEAM TRAINING

Beam training enables THz UM-MIMO beamforming without channel-state information by searching codebooks of directional array-response beams. Its reliability and worst-case performance depend on the training protocol and codebook design.

  • IV. BEAM TRAINING: Beam training avoids explicit CSI by searching transmitter and receiver beam pairs, exploiting the dominant line-of-sight path in THz channels.The feasible beam-selection space is reduced from vectors to angle-of-arrival and angle-of-departure coordinates.
  • A. Basic Concept: The codebook contains array-response vectors representing narrow beams over candidate AoAs and AoDs, with ULA angles restricted using beam-pattern symmetry.Narrow beams at equivalent symmetric directions produce equivalent patterns for a ULA.
  • A. Basic Concept: Non-uniform angular beam placement can improve worst-case performance, with the optimal AoA/AoD distribution uniform in sine space.The beam pattern is narrower near broadside and wider near ±π/2, motivating non-uniform angle spacing.
  • A. Basic Concept: Larger codebooks bring beam-training performance closer to optimal beamforming, while the required beam count generally scales with the number of antennas.The compared coverage cases use N = Na and N = 2Na beams distributed uniformly in sine space.
  • A. Basic Concept: Exhaustive beam training tests all narrow-beam pairs, using array-response codewords whose AoAs or AoDs are uniformly distributed in sine space.This protocol is straightforward but requires testing every transmitter–receiver pair.

B. Training Protocol

Training protocols trade reliability, feedback, and search complexity, while codebook design shapes how effectively hierarchical beams cover their assigned regions. M-tree search narrows the search stage by stage, but practical wide-beam design remains challenging.

  • B. Training Protocol: Exhaustive beam search offers high reliability but incurs training complexity N^2, making it time-consuming for UM-MIMO systems.Alternative protocols reduce complexity through one-sided, parallel, adaptive, two-stage, or hierarchical searches.
  • B. Training Protocol: M-tree search uses S = log_M N stages, with each stage testing M^s beams of decreasing width before selecting a narrower beam region.The ternary-tree case divides each wide-beam region into three narrower regions, beginning with an omnidirectional root.
  • B. Training Protocol: One-side M-tree search has lower complexity than both-side search when M ≠ 2, while both-side search requires S feedbacks and ternary search has the lowest M-tree complexity.The two approaches have equal complexity when M = 2.
  • Codebook Design: Codebook design optimizes codeword weights so each beam pattern covers the region assigned by the protocol, but wide-beam design remains an open problem.Bottom-stage narrow beams can use array-response vectors, whereas practical wide beams cannot realize the ideal uniform-inside and zero-outside pattern exactly.
  • Codebook Design: Wide-beam approaches include ROP, COP, SNB, SNB-GP, and SCA-based methods, which are compared against an ideal beam pattern.The paper’s scope mainly considers designs using all antenna elements in fully digital beamforming.

2) COP:

COP extends ROP with a phase degree of freedom and formulates wide-beam design using a beam-pattern objective. An iterative coordinate-descent method solves the resulting problem, while related approaches address main-lobe fluctuation and pattern error.

  • 2) COP:: COP extends ROP by adding a phase degree of freedom to the objective vector.
  • 2) COP:: The SNB method constructs a wide beam by adding orthogonal narrow beams whose angles lie within the target coverage range.
  • 2) COP:: PSA introduces variables to minimize main-lobe gain variation, but its formulation is NP-hard.
  • 2) COP:: SCA-ATP uses the beam-pattern error metric to characterize the gap between practical and ideal beam patterns.
  • 2) COP:: The symmetrical array response vector assumes zero signal phase at the ULA center and supports wide-beam construction by adding responses at selected angles.

6) S-SARV:

S-SARV constructs wide beams using symmetrical array response vectors, while lens-array beamspace processing reduces beam-training dimensionality. The section also covers IRS-assisted architectures and joint beamforming challenges.

  • 6) S-SARV:: S-SARV directly adds symmetrical array response vectors associated with selected angles to construct a wide beam.
  • 6) S-SARV:: SCA-ATP is reported closest to the ideal beam pattern, while S-SARV best balances performance and computational complexity.
  • 6) S-SARV:: Beamspace MIMO uses an optical-lens-like spatial Fourier transformation to reduce beam-training dimensionality.
  • 6) S-SARV:: Lens antenna arrays combine an electromagnetic lens with antenna elements in its focal region, with fabrication based on transmission lines, dielectric materials, or periodic structures.
  • 6) S-SARV:: The lens-array virtual channel is sparse because THz UM-MIMO has limited spatial paths, enabling antenna or beam selection using fewer RF-chain ports.
  • 6) S-SARV:: IRS-assisted UM-MIMO jointly optimizes transmitter precoding and IRS phase shifts, but the resulting problem remains non-convex and computationally demanding.

B. Cooperative Beam Training

Cooperative IRS beam training identifies direct and reflected path angles through staged measurements. A practical protocol combines wide-beam alignment, ternary-tree search, and partial IRS search to reduce testing complexity.

  • B. Cooperative Beam Training: The cooperative procedure assumes the IRS, BS, and user share a horizontal level and seeks six direct and reflected path angles.
  • B. Cooperative Beam Training: The primary protocol sequentially estimates direct paths, IRS return-mode paths, and reflected paths using three measurement phases.
  • B. Cooperative Beam Training: The primary strategy is limited by ineffective THz omni-beam detection, interference from simultaneous transmission and reception, and costly narrow-beam sweeping.
  • B. Cooperative Beam Training: The practical protocol first searches IRS codewords using 3×3 wide beams, then estimates direct-link angles with ternary-tree searches.
  • B. Cooperative Beam Training: With the IRS codeword fixed, the final phase estimates reflected-path angles while accounting for the direct BS-user path.

VI. MULTI-USER THZ UM-MIMO BEAMFORMING

THz UM-MIMO multi-user beamforming faces high-dimensional channel estimation and precoding complexity. The section combines analog beam training with digital precoding, evaluates linear algorithms, and discusses wideband impairments.

  • VI. MULTI-USER THZ UM-MIMO BEAMFORMING: THz UM-MIMO’s extremely large antenna arrays create high-dimensional channels, making accurate estimation and multi-user precoding costly.
  • VI. MULTI-USER THZ UM-MIMO BEAMFORMING: The proposed AoSA strategy combines analog-domain beam training with digital-domain precoding to reduce multi-user processing overhead.
  • VI. MULTI-USER THZ UM-MIMO BEAMFORMING: Beam training compresses the antenna channel Hant into a smaller digital-port channel Hdig, where channel estimation and precoding are performed.
  • VI. MULTI-USER THZ UM-MIMO BEAMFORMING: Sequential multi-user precoding can require evaluating K! user orderings to find the best ordering.
  • VI. MULTI-USER THZ UM-MIMO BEAMFORMING: QR-RBD and T-MMSE achieve comparable performance and the largest sum-rate among the five evaluated digital beamforming algorithms.
  • VI. MULTI-USER THZ UM-MIMO BEAMFORMING: Spatial-wideband effects arise when signals reach a large array with different symbol timing, so phase shifters alone cannot coherently combine wideband signals.

B. Frequency-Wideband Effect

The frequency-wideband effect makes phased-array beam patterns vary across frequency because flat phase shifts cannot match the wideband array response. Beam squint can reduce edge-frequency gain, while max-min beamforming and true-time-delay architectures provide mitigation options.

  • Frequency-wideband effect: Flat phase shifts cannot match the frequency-dependent array response, so phased arrays cannot simultaneously maximize beam gains across the signal band.This frequency-wideband effect causes the beam pattern to change with signal frequency.
  • Beam squint: At the carrier frequency, beam squint is absent; it increases with both arrival angle ψ and the ratio B/fc.The beam squint angle is defined as |ϕ−ψ|.
  • Beam squint: When the highest- and lowest-frequency beam patterns split, the minimum beam gain becomes zero, producing beam squint loss.A representative case uses ψ = π/4, fc = 0.14 THz, B = 10 GHz, and Na = 80, with frequency-dependent angle shifts.
  • Mitigation: The time-delay spread over antenna arrays causes both spatial-wideband and frequency-wideband effects, which phased arrays cannot eliminate.True-time-delay components can completely offset the time-delay spread.
  • TTD architectures: Full-connected, partially-connected, delay-phase, and dynamic-subarray fixed-TTD architectures are feasible wideband TTD designs.Dynamic-subarray fixed TTD lowers hardware complexity because its delays need not be adjusted.
  • Mitigation: A max-min beamformer optimizes the minimum performance metric U(f) over f ∈ [fc−B/2, fc+B/2] to reduce frequency-wideband degradation.For fc = 100 GHz and B = 10 GHz, the conventional beamformer's wideband beam gain is zero, whereas the max-min beamformer forms a wider beam that avoids beam misalignment under beam squint.

E. BSAM

Beam split aggregation and multiplexing address the limited effective bandwidth caused by beam splitting in multi-user THz arrays. BSAM combines their advantages to meet users' wideband demand while reducing the required number of subarrays.

  • BSAM: BSAM uses conventional beamformers on multiple phased arrays and jointly optimizes frequency allocation to serve multiple users in wideband communications.The scheme combines beam split aggregation and multiplexing within an AoSA architecture.
  • Beam split aggregation: Beam split aggregation uses multiple subarrays to transmit independent subband beams that a user combines to satisfy its wideband demand.Each subarray transmits a beam over an independent subband.
  • Beam split multiplexing: Beam split multiplexing allows each subarray to serve multiple users, but each user's effective bandwidth is limited by the beam split effect.A beam split coverage is defined for assigning users and frequency bands according to their angular positions.
  • BSAM: BSAM satisfies users' wideband demand while reducing the number of subarrays used compared with beam split aggregation alone.Aggregation incurs high cost because each subarray serves only one user; multiplexing improves sharing but limits each user's effective bandwidth.
  • Fabrication context: THz array fabrication includes electronic, photonic, and new-material approaches, but current work still targets greater beam flexibility and larger arrays.Open directions include more accurate and wider scanning, arrays with thousands of elements, and managing mutual coupling.
  • Fabrication context: Silicon-based arrays offer compact integration and potential low cost but are mostly limited to 0.5 THz and face a major power-drop bottleneck.Photonic and graphene-based approaches provide additional routes to dynamic beam scanning and reconfigurable beam control.

IX. EMERGING APPLICATIONS

THz beamforming is positioned for high-rate, directional links across satellite, transportation, indoor WLAN, data-center, secure-transmission, and chip-scale scenarios. Its deployment remains constrained by channel-modeling, hardware, wideband, and security challenges.

  • Application scope: The paper surveys six application scenarios for THz beamforming and their envisioned benefits.The scenarios are summarized in Fig. 38.
  • Satellite networks: THz links are considered for satellite networks because they offer high bandwidth and negligible molecular absorption in that scenario.Directional transmission also provides security-related benefits for satellite communications.
  • Intelligent transportation: Vehicle networks require high rates, low latency, and reliability; THz communication is anticipated to support high-mobility and high-reliability intelligent transportation.Dynamic beam tracking has been shown for high-speed mobile railway scenarios.
  • Indoor WLAN: Indoor THz WLAN can connect high-capacity wired networks with mobile devices and support bandwidth-intensive applications.THz access points can provide local high-rate transmissions in hotspot areas such as building entrances and shopping malls.
  • Data centers and networks-on-chip: THz communication is proposed for reconfigurable, fast wireless data-center connections and graphene-based on-chip links that replace conventional wiring.These applications target dense wireless interconnects and chip-to-chip communication.
  • Secure transmission: Directional THz beams reduce scattering components and space sparsity, which can prevent nodes outside the beam direction from eavesdropping.Aligned transmit and receive beams can considerably reduce interference from other angles, but security remains imperfect along the propagation path.
  • Open challenges: Accurate THz UM-MIMO channel modeling remains difficult because large arrays create near-field, correlation, and mutual-coupling effects while spherical models require many parameters.High-precision THz channel measurements also require diverse scenarios, costly equipment, and long iteration cycles.
  • Open challenges: THz transceiver generation remains challenging because the band is too low for optical devices and exceeds conventional electronic oscillators' upper limit.SiGe, GaN, InP, QCL, and graphene each retain technology-specific limitations.
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