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A Tutorial on Terahertz-Band Localization for 6G Communication Systems

Hui Chen, Hadi Sarieddeen, Tarig Ballal, Henk Wymeersch, Mohamed-Slim Alouini, Tareq Y. Al-Naffouri

arXiv:2110.08581v6eess.SP

TL;DR

This tutorial investigates THz localization for future communication systems by developing THz-specific models, formulations, algorithms, and optimization approaches. Preliminary comparisons indicate that THz localization can achieve better positioning performance than mmWave systems with the same power and footprint, or comparable performance with fewer resources.

  • Problem

    The tutorial addresses how to realize THz localization by examining its potential, challenges, requirements, and practical system-design issues for future communication systems.

  • Method

    The paper reviews localization methods, develops THz-specific channel and system models, formulates 3D position/orientation estimation, and studies algorithm design and system optimization.

  • Results

    THz localization is expected to provide approximately 5 times better positioning without prior information and approximately 20 times better positioning with prior information than mmWave systems at the same power and footprint.

  • Takeaways & Limitations

    The same localization performance as mmWave systems can be achieved at THz-band with less power or a smaller footprint, although multiple transmissions and prior knowledge are needed to address deafness.

Abstract

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Terahertz (THz) communications are celebrated as key enablers for converged localization and sensing in future sixth-generation (6G) wireless communication systems and beyond. Instead of being a byproduct of the communication system, localization in 6G is indispensable for location-aware communications. Towards this end, we aim to identify the prospects, challenges, and requirements of THz localization techniques. We first review the history and trends of localization methods and discuss their objectives, constraints, and applications in contemporary communication systems. We then detail the latest advances in THz communications and introduce the THz-specific channel and system models. Afterward, we formulate THz-band localization as a 3D position/orientation estimation problem, detailing geometry-based localization techniques and describing potential THz localization and sensing extensions. We further formulate the offline design and online optimization of THz localization systems, provide numerical simulation results, and conclude by providing lessons learned and future research directions. Preliminary results illustrate that under the same transmission power and array footprint, THz-based localization outperforms millimeter wave-based localization. In other words, the same level of localization performance can be achieved at THz-band with less transmission power or a smaller footprint.

I. INTRODUCTION

Localization is evolving from a communication by-product into an integrated capability for location-aware 5G and 6G systems. This tutorial examines THz localization’s prospects, requirements, models, optimization, applications, and open challenges.

  • Localization estimates a target’s position and orientation for applications including location-aware communications, autonomous driving, industrial IoT, and tactile internet.
  • 5G and future 6G systems increasingly integrate localization with communication to support ubiquitous connectivity, high data rates, and low latency.
  • THz systems offer higher frequencies, wider bandwidths, smaller footprints, and larger arrays, but also incur increased propagation and molecular absorption losses.
  • UM-MIMO provides angular resolution, wide bandwidth supports accurate delay estimation, and RISs can provide received-signal gains and geometrical diversity.
  • The tutorial develops THz-specific localization models, performance analysis, algorithms, and system-optimization formulations while identifying unresolved research questions.

B. Localization Techniques

Localization techniques estimate UE position and orientation from geometry measurements or learned models. Geometry-based methods use timing and angle information, while learning-based methods address scenarios where multipath geometry cannot be explicitly modeled.

  • Geometry-based and Learning-based Localization: TOA, TDOA, AOA, and ADOD provide basic geometry measurements for estimating UE position and orientation.
  • Geometry-based and Learning-based Localization: For many non-resolvable NLOS paths, geometry cannot be explicitly modeled, so learning-based methods are preferred.
  • Geometry-based and Learning-based Localization: Combinations of geometry measurements can reduce uncertainty and additional constraints can reduce the number of required BSs.
  • Orientation Estimation: UE orientation is classified as 1D, 2D, or 3D according to the number of Euler-angle components estimated from antenna-array AOD information.
  • Localization Objectives: Localization systems are evaluated using objectives including accuracy, coverage, latency, update rate, stability, scalability, mobility, and complexity.

1) Conventional Radio Frequency Systems (below 30 GHz):

The tutorial contrasts conventional RF, mmWave, visible-light, and THz systems, emphasizing how higher-frequency THz operation changes propagation, array, channel, and localization characteristics. THz offers localization potential but introduces hardware, coverage, synchronization, and complexity challenges.

  • Millimeter-Wave Systems: mmWave systems provide higher-rate communications, lower latency, improved localization, orientation estimation, and single-BS operation using NLOS paths or RISs.
  • THz Systems: THz operation enables wide bandwidths and large wavelength-normalized arrays, while high path loss, beam split, near-field effects, and hardware imperfections complicate system design.
  • RIS-Assisted Localization: RISs support localization as passive anchors providing geometrical diversity and by creating near-field conditions that expose curvature-of-arrival information.
  • Open Challenges: THz localization research remains in its infancy, with unresolved questions about how THz signals improve localization performance.

3) Plasmonic Solutions (much smaller footprints, very high reconfigurability):

Plasmonic THz devices use compact surface-plasmon-based designs to support highly reconfigurable and flexible antenna arrays. The section also establishes the 3D geometric framework for modeling BS, RIS, UE, and propagation paths.

  • 3) Plasmonic Solutions (much smaller footprints, very high reconfigurability):: Graphene-based plasmonic transceivers support highly reconfigurable THz devices and more compact antenna-array designs than free-space-wavelength implementations.Surface plasmon polariton wavelengths are much smaller than free-space wavelengths, enabling compact and flexible arrays.
  • 3) Plasmonic Solutions (much smaller footprints, very high reconfigurability):: THz-operating metasurfaces support wide-angle beam steering, orbital-angular-momentum generation, and polarization conversion.HyperSurfaces, vanadium dioxide, and liquid crystals are also identified as tunable THz-device technologies.
  • 3) Plasmonic Solutions (much smaller footprints, very high reconfigurability):: The proposed geometry contains a BS, RIS, and UE, with NLOS paths represented by scatterers, reflectors, or diffractors at unknown locations.The array center and element positions define each device, while NLOS paths capture environmental propagation.
  • 3) Plasmonic Solutions (much smaller footprints, very high reconfigurability):: Each array is assigned a 3D global position and Euler-angle orientation, using a Z-Y-X rotation sequence for coordinate transformations.The rotation matrix maps local array coordinates to global coordinates.
  • 3) Plasmonic Solutions (much smaller footprints, very high reconfigurability):: Local AOA/AOD measurements are defined by azimuth and elevation angles, then converted between direction vectors and global or local coordinate systems.The paper emphasizes that angles are measured locally at the array, even when both local and global representations are defined.

C. Far-field MIMO Channel Model

The far-field model represents a multi-carrier MIMO channel through LOS, RIS, and NLOS components, with frequency-dependent propagation, antenna gains, steering vectors, and synchronization assumptions.

  • C. Far-field MIMO Channel Model: The far-field multi-carrier MIMO channel decomposes into LOS, RIS, and NLOS channel matrices.The model uses a planar-wave assumption for far-field propagation.
  • C. Far-field MIMO Channel Model: LOS channel gains use antenna gains and steering vectors determined by local AOA/AOD pairs.The steering-vector formulation applies to arrays with arbitrary layouts.
  • C. Far-field MIMO Channel Model: Path attenuation depends on frequency and distance, with THz molecular absorption modeled through an absorption coefficient derived from the HITRAN database.Water vapor and other gases increase THz path loss relative to mmWave atmospheric attenuation.
  • C. Far-field MIMO Channel Model: The ideal sector antenna model defines gain over azimuth and elevation beamwidths, while omnidirectional antennas have unit gain.Highly directional antenna directivity can be approximated from the E-plane and H-plane beamwidths.
  • C. Far-field MIMO Channel Model: The frequency-flat fading model assumes identical attenuation coefficients across subcarriers and ignores the Doppler effect.The subcarrier frequency and frequency ratio determine the modeled channel response.
  • C. Far-field MIMO Channel Model: The channel model treats synchronization as zero for a well-synchronized link, while multiple asynchronous BSs may have separate clock offsets.The synchronization offset is identical across channels within one BS–UE communication link.

2) RIS Channel:

The RIS channel models a two-hop UE–RIS–BS propagation path whose elements independently control phase and reflection amplitude, while the broader system model includes NLOS paths and practical MIMO architectures.

  • 2) RIS Channel:: The RIS channel is formed by cascading the BS–RIS channel, a diagonal RIS coefficient matrix, and the RIS–UE channel.The transmitted signal reaches the RIS from the UE, is modified by RIS elements, and then propagates to the BS.
  • 2) RIS Channel:: Each RIS element applies a phase shift and reflection coefficient, with phase in [0, 2π) and reflection amplitude in [0, 1].The model assumes unit power-radiation pattern and RIS-element gain, with each element area set to λ^2/(4π).
  • 2) RIS Channel:: THz NLOS paths are increasingly sparse and lossy compared with mmWave paths, requiring reflection coefficients in addition to channel gains.The model considers resolvable reflectors, one ray per reflector, and ignores second-order reflections exceeding 15 dB attenuation.
  • 2) RIS Channel:: The section places the RIS and NLOS components within a broader far-field MIMO model before extending the signal model to conventional and AOSA-based receivers.Large conventional arrays are favored for beamforming gain but are impractical in hardware realization and power consumption.
  • 2) RIS Channel:: The benchmark conventional MIMO signal model combines a noise-free received signal with AWGN and normalized transmitted signals across subcarriers and transmissions.The model is used as a benchmark for mmWave localization systems.

3) Fully-connected Hybrid MIMO Model:

The paper contrasts fully connected and AOSA-based MIMO architectures, emphasizing hardware constraints at THz frequencies and modeling subarray-level steering and beamforming gains.

  • 3) Fully-connected Hybrid MIMO Model:: Connecting every antenna to an RFC is impractical because of hardware cost and complexity, motivating hybrid architectures with fewer RFCs.The hybrid received signal uses RF combiner and precoder matrices before localization processing.
  • 3) Fully-connected Hybrid MIMO Model:: The fully connected hybrid model connects each RFC to all antennas through phase shifters, offering a performance–cost tradeoff but remaining inefficient for THz systems.Its practical limitation is tied to transmit-power and circuit-feeding constraints.
  • 3) Fully-connected Hybrid MIMO Model:: In AOSA-based MIMO, each RFC drives a subarray, reducing RFC count and connecting each RFC only to its antenna subset.Each subarray acts as the minimum communication element and performs analog beamforming.
  • 3) Fully-connected Hybrid MIMO Model:: An SA array factor represents beamforming gain for a channel angle and beamforming angle, reaching maximum gain when those angles match.The steering and beamforming vectors can be expressed using local or global angles and positions.
  • 3) Fully-connected Hybrid MIMO Model:: The effective AOSA channel combines an array-factor matrix with an SA-level channel matrix through a Hadamard product.SA-level channel parameters replace antenna-element parameters, including subarray count, centers, and spacing.
  • 3) Fully-connected Hybrid MIMO Model:: The signal-model framework extends conventional and AOSA-based far-field models to near-field scenarios using a spherical wave model.The extension is intended to accommodate additional channel features and signal types.

E. Additional Model Features

THz localization models must account for near-field propagation, beam split, and hardware imperfections that become prominent with large, wideband arrays and high carrier frequencies.

  • Near-field model: Higher carrier frequencies can make even small-footprint arrays operate over a larger near-field range, invalidating far-field channel models.The near-field region extends between the Fresnel boundary 0.62D^3/λ and Fraunhofer distance 2D^2/λ.
  • Near-field model: The near-field model assumes equal received signal strength across antennas while retaining antenna-dependent phase changes.For LOS channels, this phase behavior differentiates the near-field model from the far-field model under SWM and PWM assumptions.
  • Near-field AOSA model: For near-field AOSA-based MIMO, each subarray follows a PWM, while SWM is represented through phase differences between subarrays.This approximation is motivated by subarrays being relatively small compared with the whole array.
  • Near-field AOSA model: Near-field array factors calculate angles for each subarray pair rather than using AOA/AOD pairs referenced to the array center.
  • Beam split: Beam split arises when frequency-independent analog phase shifts produce frequency-dependent steering vectors across wideband subcarriers.Array size in wavelengths, bandwidth, and beamforming angle affect beam split; only the central frequency achieves the highest beamforming gain under the stated condition.
  • Beam split: True-time delays and delay-phase precoding can mitigate beam split, but the model retains it for systems using pure phase shifters.Beam split can also make RIS coefficients frequency-dependent.
  • Hardware imperfections: Hardware imperfections may arise in RFCs, phase shifters, and RIS elements, including distortion noise, phase noise, and quantization error.Quantized RIS phases can reduce accuracy while lowering power cost and system complexity.
  • Hardware imperfections: Using an ideal mismatched model on impaired observations causes performance loss, for which the misspecified CRB can provide a lower bound.

F. Summary

The paper summarizes an AOSA-based THz model and uses it to formulate localization around UE position, orientation, and channel parameters across increasingly rich propagation settings.

  • F. Summary: The proposed AOSA-based THz system model represents geometry through position, direction, Euler-angle, rotation-matrix, and local/global AOA/AOD relationships.
  • F. Summary: A near-field effective AOSA channel model reduces the complexity of UM-MIMO systems considered as potential THz structures.
  • F. Summary: The THz signal model includes LOS, RIS, and NLOS channels.
  • F. Summary: The model incorporates beam split and hardware imperfections before being used to formulate THz-band localization problems.
  • F. Summary: The localization formulation targets UE position and orientation while allowing channel quantities and scatterer positions to appear as nuisance parameters.The paper considers CRB analysis, geometry-based methods, learning-based localization, cooperation, tracking, and SLAM.
  • F. Summary: The paper compares multi-BS, far-field mmWave, and near-field THz scenarios, using fully digital MIMO for mmWave and hybrid AOSA for THz.
  • F. Summary: Near-field THz systems with RIS replace local angle vectors with global angles and UE orientation, while near-field CRLBs cannot be derived directly from local angles.

4) Parameters in Direct Localization:

Direct localization estimates state parameters from received signals, while CRB, PEB, and OEB provide performance measures whose applicability depends on the propagation model and parameterization.

  • Parameters in Direct Localization: Direct localization estimates the state vector directly by optimizing an objective function, with the measurement and state parameter vectors treated as identical.
  • Parameters in Direct Localization: The parameter list may include BS/RIS position and orientation errors or synchronization offsets, but selected parameters depend on the signal, geometry, and estimation models.
  • Performance bounds: Positioning accuracy is commonly measured by MSE or RMSE, while PEB and OEB derived from the CRB are used to evaluate geometry-based systems.
  • Performance bounds: The CRB for direct and multi-stage approaches is the same when all available measurement variables are included in the state analysis.
  • Performance bounds: The FIM is transferred from measurement parameters to state parameters through the chain rule and Jacobian, with the number of transmissions entering the measurement information.
  • Performance bounds: An EFIM isolates UE-state information from nuisance parameters, enabling corresponding PEB and OEB calculations.
  • Orientation estimation: Far-field 3D orientation requires a constrained CRB because UE orientation cannot be individually mapped from far-field angles.
  • Orientation estimation: The rotation-matrix and Euler-angle OEB definitions differ, but both can indicate orientation-estimation performance.

5) CRB for an LOS Channel:

The paper relates LOS-channel bounds and localization algorithms to signal information, propagation geometry, optimization complexity, and the trade-offs of learning-based extensions.

  • CRB for an LOS Channel: For a single LOS path, PEB and OEB components are determined by delay, AOA, and AOD, while a common SNR term depends on noise, path loss, antennas, transmissions, and power.
  • Direct localization: Direct localization maximizes a likelihood objective from received signals without estimating intermediate parameters.
  • Direct localization: Direct localization supports quasi-synchronous and asynchronous systems, but its non-convex optimization and large search space create high computational complexity.Prior information can limit the search area.
  • Multi-stage localization: Multi-stage localization first estimates geometry-related measurements and then extracts position and orientation, reducing the complexity of estimating all unknowns jointly.
  • Multi-stage localization: Multi-stage methods are inherently sub-optimal and usually inferior to direct localization, though incorporating all multipath components can reduce the gap.
  • Multi-stage localization: Multi-stage measurement estimation can use least squares for channel gains and MUSIC, compressed sensing, deep learning, or Bayesian inference for angles.
  • Optimization methods: Gradient, Hessian, projection, and expectation-maximization methods can reduce computational burden but may reach local solutions depending on formulation and iteration parameters.
  • Optimization methods: Heuristic methods handle non-differentiable nonlinear objectives and can reach near-optimal solutions faster; sparse high-frequency channels may favor multi-stage localization.

3) Practical ML algorithms:

The paper surveys practical learning-based localization extensions alongside tracking and SLAM formulations for THz systems. It emphasizes the tradeoffs among data requirements, model complexity, state estimation, and map construction.

  • Learning-based localization: Supervised learning covers classification and regression, but requires sufficient labeled data and careful model-parameter selection.Real data are difficult to collect, synthesized data may be inaccurate, and deep-learning architectures can be difficult to choose.
  • Learning-based localization: Unsupervised learning avoids well-labeled datasets and supports clustering or feature extraction, but cannot directly obtain location information.Channel charting maps high-dimensional channel features into a lower-dimensional representation without supervision.
  • Learning-based localization: Semi-supervised, reinforcement, and transfer learning address partially labeled data, unclear objectives, or reuse of existing models.These approaches are presented as alternatives to the limitations of supervised and unsupervised learning.
  • Tracking: Tracking estimates a time-varying user state from sequential measurements of angles and delays under a stochastic mobility model.The posterior state is inferred from all measurements collected up to the current time, with a prior on the initial state.
  • Tracking: Kalman-family filters offer low-complexity approximations, whereas particle filters handle highly nonlinear and non-Gaussian models at high computational cost.Particle-filter complexity grows with the number of particles and state dimensionality.
  • SLAM: THz tracking and SLAM face narrow-beam challenges, while narrow beams, dense deployments, and wide bandwidths can improve angular resolution and SLAM performance.THz SLAM additionally requires channel models tied to scatterer locations, data-association likelihoods, and joint state-map posterior estimation.

1) Motivation:

THz localization system design must balance accuracy, coverage, latency, energy, and communication objectives under practical constraints. The paper organizes this design into offline planning and online adaptation across network, hardware, signal, and resource variables.

  • Motivation: Localization objectives such as accuracy and coverage are coupled with tradeoffs involving latency, update rate, and other practical constraints.For example, increased coverage may increase latency, while a higher update rate may affect accuracy.
  • Problem formulation: THz localization optimization uses an objective function and constraints over variables including device counts, positions, antenna layouts, beam angles, RIS coefficients, and transmissions.Multiple-objective formulations can combine several objectives and constraints.
  • Offline design: Offline design operates without UE position or orientation knowledge and includes layout, array, and codebook optimization.The surrounding environment may nevertheless be available to the offline designer.
  • Network design: Network choices include heterogeneous, RIS-assisted, and cell-free structures that address deafness, coverage, deployment flexibility, or geometric diversity.Cell-free distributed MIMO can improve coverage probability and localization through distributed base-station geometry.
  • Cooperation: Cooperative localization improves accuracy and coverage but introduces communication overhead and energy consumption.The paper also identifies UAV assistance and fusion with IMU or camera data as cooperation options.
  • Hardware and signals: Hardware, modulation, and signal parameters must balance performance with cost, complexity, power efficiency, sampling limits, and data size.Bandwidth improves delay-domain path separation, while molecular absorption and multipath affect modulation choices.

3) Codebook Optimization:

THz codebook and online optimization must address narrow-beam initial access, resource allocation, beamforming, and RIS control. The paper highlights coverage–delay tradeoffs and the difficulty of non-convex multi-variable optimization.

  • Initial access: Narrow THz beams make initial access vulnerable to deafness and blockage, requiring effective procedures and dedicated codebooks.Initial access establishes a physical link between a new UE and BS without UE prior information.
  • Codebook strategies: Codebook search can be exhaustive, iterative, or scene-aware, depending on available coverage, delay, prior information, and environmental knowledge.Iterative search starts with wide sectors and narrows the beams progressively; scene-aware search learns beams for partitioned areas.
  • Codebook strategies: Exhaustive search provides the best coverage and hardware feasibility, but discovery delay grows linearly with beamforming gain.Iterative search reduces discovery delay at the expense of limited coverage, while scene-aware search is expected for THz SLAM.
  • RIS optimization: RIS placement can be optimized by minimizing the area where position error exceeds a threshold, using FIM-derived PEB values over candidate placements and UE locations.The resulting coverage-area problem is generally non-convex, so grid search may be used.
  • Offline optimization: Offline optimization must jointly handle precoders, combiners, RIS coefficients, and layouts, while multiple-BS/RIS problems are highly non-convex.Heuristic algorithms can provide time-saving, satisfactory sub-optimal solutions when globally optimal solutions are difficult to obtain.
  • Online optimization: Online optimization uses prior UE information to allocate resources and optimize active beamforming and RIS coefficients for localization performance.The considered resources include time, frequency, power, and spatial assignments across multiple users and tasks.

VI. SIMULATION AND EVALUATION

Simulations compare THz and mmWave localization under controlled resources and examine how transmissions, channel models, beam split, RIS, NLOS paths, and blind areas affect error bounds. THz systems can achieve lower bounds than mmWave systems with the same power and footprint, but their performance depends on beamforming, propagation assumptions, and environmental paths.

  • A. A Comparison between mmWave and THz Systems: Under fixed transmission power, time, and maximum footprint, the THz AOSA system achieves lower PEB and OEB than the benchmark mmWave system.The comparison uses a fully connected mmWave array and an AOSA THz structure, with CRB-based PEB/OEB evaluation.
  • A. A Comparison between mmWave and THz Systems: The same localization performance as mmWave can be achieved with less THz transmission power or a smaller array footprint.The reported comparison holds transmission power and array footprint constant when demonstrating the THz advantage.
  • B. The Effect of Transmission Numbers on CRB: Multiple transmissions are needed for AOSA error bounds to converge, and the required number increases with the SA dimension.More transmissions also address deafness and improve UE localization accuracy, whereas transmissions have only a minor effect in the small-array mmWave benchmark.
  • C. The Evaluation of PWM/SWM for Different Channel Models: Around 1 m separates near-field and far-field behavior: SWM is more accurate near the BS, while SWM and PWM PEBs converge with distance.SWM has higher computational complexity and can help synchronization by exploiting arrival curvature; synchronized and asynchronized PEBs converge in the near field.
  • D. Evaluation of the Beam Split Effect: Beam split can lower the CRB, especially with wide bandwidth, because different subcarriers provide additional directional geometry.The effect is evaluated with prior position information and beamforming pointed toward the UE.
  • E. The Effect of RIS on CRB: A large RIS with optimized coefficients improves PEB, while 2-bit coefficient quantization remains close to continuous-phase localization performance.With AOSA, performance also depends on SA beamforming angles, motivating joint active and passive beamforming optimization.
  • F. The Effect of NLOS Paths: Resolvable NLOS paths with large reflection coefficients improve localization, but fewer THz NLOS paths trade reduced complexity for lost geometrical diversity.The latter condition requires more transmission times to improve localization and map the environment; random beamforming can also create AOSA blind areas.

H. Summary

The paper highlights lessons for practical THz localization modeling and identifies future work spanning channel models, performance analysis, algorithms, and system optimization. It emphasizes THz localization’s potential while noting unresolved scalability, reliability, calibration, and model-mismatch challenges.

  • Lessons learned: PWM is computationally simpler than SWM but can lose accuracy in the near field, where its approximation should be avoided when possible.SWM also introduces amplitude variations and higher computational complexity across the array.
  • System requirements: THz localization systems must address scalability, position integrity, availability, and RIS-related synchronization and information-sharing requirements.These requirements become important as antenna, RIS-element, and data volumes grow.
  • Future research directions: THz localization is still at an early stage, with open directions covering channel modeling, performance analysis, algorithm design, and system optimization.The paper organizes its future directions into these four aspects.
  • Channel modeling: Deterministic channel models should be extended with stochastic scattered-signal behavior and more accurate THz-specific effects, because model mismatch can degrade localization performance.The current approach extrapolates mmWave models and may omit hardware impairments and other THz-specific aspects.
  • Simulation lessons: The paper compares THz and mmWave localization using PEB and OEB and recommends practical algorithm design for RIS-assisted AOSA-based MIMO systems.It also reports simulations illustrating THz systems’ potential for localization and sensing.
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