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A Tutorial on Six-Dimensional Movable Antenna for 6G Networks: Synergizing Positionable and Rotatable Antennas

Xiaodan Shao, Weidong Mei, Changsheng You, Qingqing Wu, Beixiong Zheng, Cheng-Xiang Wang, Junling Li, Rui Zhang, Robert Schober, Lipeng Zhu, Weihua Zhuang, Xuemin Shen

arXiv:2503.18240v3cs.ITeess.SP

TL;DR

Future wireless networks need more spatial flexibility without the cost and power burden of larger fixed antenna arrays, motivating six-dimensional movable antennas. This tutorial develops 6DMA channel models, architectures, optimization and estimation methods, applications, special cases, and prototypes. It concludes that 6DMA offers a promising agile architecture for communication and sensing, while the field remains at an early research stage.

  • Problem

    6DMA must address new architecture, position-and-rotation optimization, channel-estimation, and communication-and-sensing design challenges while exploiting wireless-channel spatial variations.

  • Method

    The paper provides a tutorial covering 6DMA channel and hardware models, practical constraints, applications, special cases, optimization, channel estimation, path planning, and prototype development.

  • Results

    The tutorial demonstrates 6DMA-enhanced communication through prototype development and experimental results, while surveying its applications and design advances.

  • Takeaways & Limitations

    6DMA provides an agile wireless architecture that can exploit spatial channel variations for future 6G communication and sensing.

Abstract

from arXiv · show

Six-dimensional movable antenna (6DMA) is a new and revolutionary technique that fully exploits the wireless channel spatial variations at the transmitter/receiver by flexibly adjusting the three-dimensional (3D) positions and/or 3D rotations of antennas/antenna surfaces (sub-arrays), thereby improving the performance of wireless networks cost-effectively without the need to deploy additional antennas. It is thus expected that the integration of new 6DMAs into future sixth-generation (6G) wireless networks will fundamentally enhance antenna agility and adaptability, and introduce new degrees of freedom (DoFs) for system design. Despite its great potential, 6DMA faces new challenges to be efficiently implemented in wireless networks, including corresponding architectures, antenna position and rotation optimization, channel estimation, and system design from both communication and sensing perspectives. In this paper, we provide a tutorial on 6DMA-enhanced wireless networks to address the above issues by unveiling associated new channel models, hardware implementations and practical position/rotation constraints, as well as various appealing applications in wireless networks. Moreover, we discuss two special cases of 6DMA, namely, rotatable 6DMA with fixed antenna position and positionable 6DMA with fixed antenna rotation, and highlight their respective design challenges and applications. We further present prototypes developed for 6DMA-enhanced communication along with experimental results obtained with these prototypes. Finally, we outline promising directions for further investigation.

I. INTRODUCTION

6DMA addresses the cost, power, and spatial-flexibility limits of fixed-position antennas by enabling adaptive 3D antenna positioning and rotation. The tutorial introduces its architectures, implementation, channel-reconfiguration effects, and applications in future wireless networks.

  • Motivation: Fixed-position antennas cannot fully exploit spatial channel variations, while larger bandwidths and arrays increase hardware complexity, cost, and power consumption.These limitations motivate more spatially flexible antenna architectures for sustainable 6G networks.
  • Motivation: 6DMA flexibly adjusts antenna or antenna-surface 3D positions and rotations to exploit wireless-channel spatial variations without adding antennas.These adjustments provide additional spatial degrees of freedom for channel adaptation and performance enhancement.
  • Channel reconfiguration: 6DMA can allocate spatial degrees of freedom to user distributions, suppress interference, create line-of-sight links around obstacles, and compensate path loss through position and rotation adjustment.These effects reconfigure wireless channels without requiring additional antennas or arrays.
  • Architecture and implementation: A 6DMA surface connects to a transceiver CPU through an extendable, rotatable rod and moves as a whole surface to reduce implementation and control complexity.Positions and rotations change mainly with large-scale user-distribution variations, so movement can be slow and infrequent.
  • Applications: Applications include mMTC activity detection, hotspot-oriented cellular coverage, low-altitude connectivity, space-air-ground networks, sensing, and localization.Its benefits are especially relevant to non-uniform or dynamic user distributions.

C. What’s New?

6DMA extends distributed MIMO with collaborative control of antenna positions and rotations, creating a general six-dimensional design space. This flexibility introduces new optimization challenges involving cooperative focusing, interference cancellation, geometry, and practical constraints.

  • What’s New?: 6DMA combines distributed MIMO with collaborative, adaptive adjustment of antenna positions and rotations according to user spatial distributions.Compared with traditional large-scale MIMO and antenna selection, it offers more spatial degrees of freedom with potentially fewer antennas.
  • What’s New?: The general 6DMA model supports arbitrary position and rotation-adjustable antennas by allowing both 3D positions and 3D rotations to vary.This flexibility makes 6DMA compatible with restricted-dimensional special cases.
  • What’s New?: Designing 6DMA systems requires jointly optimizing positions and rotations for cooperative signal focusing and interference cancellation under geometric and practical constraints.The high-dimensional design space makes this optimization distinct from conventional antenna architectures.

1) New challenges:

6DMA introduces difficult implementation and channel-estimation problems because positions and rotations create high-dimensional, uneven channel variations. Mechanical movement also imposes cost, energy, and latency constraints.

  • New challenges: Continuous 3D position and rotation flexibility increases channel-estimation complexity because candidate antennas can have substantially different channel-power distributions.Opposing surface orientations can produce markedly different user-channel distributions.
  • New challenges: Mechanical movement of 6DMA surfaces requires accounting for hardware cost, power consumption, and movement or rotation delay, especially across larger movement regions.These constraints must be included when designing and deploying practical systems.

2) New Advances Compared to State-of-the-Art Technologies:

Compared with fluid antennas, antenna selection, and XL-MIMO, 6DMA combines position and rotation flexibility with distributed antenna resources and fewer physically deployed radiating elements. Its adjustments can follow slowly changing channel distributions rather than requiring frequent movement.

  • Fluid Antenna System: Unlike fluid antenna systems, 6DMA adjusts distributed antenna surfaces in both position and orientation, typically over longer intervals as channel distributions change gradually.The cited comparison describes adjustment intervals such as hours, days, or longer.
  • Antenna Selection: Unlike antenna selection, 6DMA optimizes the positions and rotations of surfaces rather than selecting from a fixed set of antennas at predetermined locations.It also requires fewer physically deployed radiating elements than traditional antenna-selection systems.
  • Extremely Large-Scale MIMO: Compared with XL-MIMO, 6DMA uses distributed 3D position and rotation control to adapt spatial degrees of freedom while reducing radiating elements, RF chains, implementation cost, and energy consumption.The paper gives an example in which two active 6DMA surfaces can match an XL-MIMO setup requiring many more antennas.

I. Introduction

The introduction covers the motivation for 6DMA, its role in wireless networks, and associated channel-estimation and optimization topics.

  • I. Introduction: The introduction frames motivation and explains what 6DMA is before discussing what is new.
  • I. Introduction: It includes 6DMA optimization and channel estimation among the related technical topics.

A. Antenna Position and Rotation

This section organizes related material around antenna rotation, wireless sensing, UAV applications, and future directions.

  • Antenna Position and Rotation: The section also includes 6DMA for UAV networks and other related works and future directions.
  • Antenna Position and Rotation: It covers 6DMA for wireless sensing, including positionable 6DMA-aided ISAC and path planning.
  • Antenna Position and Rotation: The tutorial distinguishes element-wise and array-wise rotatable 6DMA.

VI. Positionable 6DMA

The listed material for positionable 6DMA includes path planning and is situated within the tutorial’s overall organization.

  • VI. Positionable 6DMA: Positionable 6DMA is associated with path planning in the tutorial organization.
  • VI. Positionable 6DMA: The tutorial’s organization is presented in Fig. 4.

D. Objectives, Contributions, and Organization

The paper presents an in-depth tutorial on 6DMA and organizes its coverage around system models, implementations, design issues, applications, and future research.

  • D. Objectives, Contributions, and Organization: The paper positions itself as the first in-depth tutorial focused on 6DMA with flexible antenna position and rotation.
  • D. Objectives, Contributions, and Organization: Its coverage includes system models, implementation architectures, advantages, design issues, positionable and rotatable 6DMA, and wireless-system applications.
  • D. Objectives, Contributions, and Organization: The paper is organized to introduce 6DMA fundamentals, including its channel model and architecture.
  • D. Objectives, Contributions, and Organization: Table I lists main industry activities, prototypes, and projects related to 6DMA.

II. 6DMA FUNDAMENTALS

This section introduces 6DMA fundamentals and situates them among related movable-antenna and fluid-antenna overviews. It frames channel models, architectures, hardware, constraints, and open issues as core foundations for 6DMA-enhanced networks.

  • 6DMA fundamentals: The fundamentals section covers channel models, architectures, hardware implementations, movement constraints, channel dependence on position and rotation, performance-gain sources, and open issues.These topics are presented as foundations for developing 6DMA system models and future research.
  • Related work: Prior overview work addresses movable-antenna hardware, channel characteristics, performance benefits over fixed-position arrays, and design challenges.
  • Related work: Related surveys cover flexible-position MIMO hardware, structural design, and applications, alongside fluid-antenna foundations, implementations, and challenges.
  • Related work: Other cited work proposes positionable 6DMA architectures using antenna-design and mechanical-control ideas for implementation.
  • Related work: Fluid-antenna research also examines 6G potential, six research topics, artificial-intelligence solutions, and relationships with intelligent reflecting surfaces.

A. 6DMA Channel Model

The 6DMA channel-model section develops models for position- and rotation-adjustable surfaces, including fundamental, polarized, rotatable, and positionable cases. It connects global and local geometry, steering, antenna gain, polarization, and hardware realization.

  • Channel-model framework: The channel analysis considers downlink multiuser transmission and models channels from each user to antennas on all 6DMA-BS surfaces.It introduces fundamental, polarized, rotatable, and positionable channel models.
  • Geometry: Each 6DMA surface center is described by three-dimensional position q_b and three-dimensional rotation u_b, providing up to six movement dimensions.The position and rotation are represented by six parameters within a finite convex deployment space.
  • Fundamental model: The general multipath channel combines path coefficients, six-dimensional steering vectors, and rotation-dependent effective antenna gains for each surface.The steering vector captures geometry and wavelength-dependent phase, while the gain follows the surface radiation pattern.
  • Fundamental model: Surface rotations transform global pointing vectors into local coordinates, where local azimuth and elevation determine the effective antenna gain.The gain is obtained from the adopted antenna radiation pattern and converted from dBi to linear scale.
  • Polarized model: The polarized model represents electromagnetic polarization with orthogonal electric-field components and uses transmit/receive projections to form a dual-polarized response matrix.For sufficiently large transmission distances, the LoS phase shift is shared by both polarization ports.
  • Rotatable model: With fixed position, directive rotatable 6DMA reshapes angular radiation coverage, whereas omnidirectional rotation changes channel phase to exploit small-scale variations and mitigate deep fading.The omnidirectional special case is simplified using a one-dimensional rotation angle.
  • Implementations: The tutorial surveys mechanical, liquid, electrical, dielectric-particle, and parasitic controls for implementing positionable and rotatable 6DMA.

2) 6DMA Position and Rotation Constraints:

This section states geometric constraints for safe 6DMA movement and explains how position and rotation create distinct channel and performance effects. It also identifies practical modeling and measurement limitations.

  • Position and rotation constraints: A minimum center-to-center distance prevents surface overlap and mutual coupling.The constraint requires ||q_b-q_j||_2 ≥ d_min for distinct surfaces.
  • Position and rotation constraints: Rotation constraints prevent mutual signal reflections by requiring each surface not to form an acute angle with another surface.They are expressed using the outward normal and the displacement between surface centers.
  • Position and rotation constraints: Surfaces must also avoid rotating toward the BS CPU, preventing signal blockage through a normal-vector constraint.
  • Performance mechanisms: Wavelength-scale translation primarily changes channel phase, while larger movements can alter average link strength and line-of-sight availability.Position changes can exploit small-scale variations and support flexible beamforming without changing amplitude or polarization alignment at wavelength scale.
  • Performance mechanisms: Rotation changes channel-gain amplitude by modifying both the antenna radiation pattern and polarization.Position and rotation therefore affect different channel characteristics.
  • Performance advantages: Flexible antenna geometry can improve sensing accuracy by optimizing the relative geometry between transmitting antennas and targets.
  • Open problems: 6DMA channel modeling remains limited by neglected mutual coupling and by the early stage of prototype development needed for empirical measurements.Increasing movement precision can reduce element spacing and make coupling more pronounced, while reliable empirical models require measurements across diverse environments.

2) Discrete Antenna Position and Rotation Optimization:

Discrete position and rotation optimization increases 6DMA spatial degrees of freedom but creates a difficult non-convex integer problem and requires extensive channel information. Directional sparsity and staged estimation can reduce the resulting training burden.

  • Problem formulation: Binary indicators assign each 6DMA surface one position and one rotation while preventing multiple surfaces from selecting the same position.The formulation uses separate position and rotation indicator vectors with feasibility constraints.
  • Problem formulation: Discrete position and rotation design is a non-convex integer program whose exhaustive solution becomes impractical as candidate positions, rotations, and antennas increase.The objective also requires statistical multiple-access channel information that may not be readily available.
  • Performance evaluation: Increasing the numbers of discrete positions or rotations improves sum rate by providing more spatial degrees of freedom for adapting to user distributions and gaining array and spatial multiplexing benefits.The result is reported for the offline optimization algorithm evaluated against users’ transmit power.
  • Performance evaluation: Discrete position and rotation optimization performs worse than continuous alternating optimization because discretization limits the available spatial degrees of freedom.The comparison concerns discrete adjustments versus continuous positions and rotations.
  • Channel estimation: The large number of movable channels and uneven channel-power distribution increase pilot overhead, while sparsity-based methods can reduce training by sampling only limited positions and rotations.The sparsity assumption is not universal, so both statistical and instantaneous channel-estimation approaches remain relevant.
  • Channel estimation: Directional sparsity occurs when each user has significant channel gains for only a subset of candidate position-rotation pairs.Candidate pairs oriented away from a user can have approximately zero channel gain, producing sparse channel support.
  • Channel estimation: A three-stage protocol exploits directional sparsity, continuing data transmission throughout and achieving enhanced data rates after surfaces are optimally positioned and rotated.The protocol uses channel information to support later-stage configuration while maintaining transmission across the frame.

4) Instantaneous Channel Estimation:

Instantaneous channel estimation is costly because movable antennas create many rapidly varying channels, motivating distributed processing and sparsity-aware recovery. The tutorial also connects these estimation issues to broader optimization, application, and hardware trade-offs.

  • Related works and future directions: Table III surveys representative position and rotation optimization studies by system setup, optimization technique, and key findings.The surveyed works mainly use centralized processing, while distributed or parallel optimization remains an identified need.
  • Instantaneous channel estimation: Rapidly varying instantaneous channels make centralized estimation costly and latent, motivating distributed processing in which local processing units estimate channels in parallel.The distributed architecture is considered specifically to reduce the processing burden associated with frequent instantaneous estimation.
  • Instantaneous channel estimation: Support-restricted least-squares recovery uses the estimated directional-sparsity support to retain only indexed non-zero channel elements.The support is constructed from the estimated sparsity matrix before forming the reduced LS problem.
  • Instantaneous channel estimation: The proposed sparsity-aware estimation algorithm achieves lower NMSE than AMP and BOMP while sampling 32 position-rotation pairs instead of 350 for covariance-based exhaustive measurement.Its statistical reconstruction has slightly higher NMSE than covariance-based exhaustive measurement, whereas its directional-sparsity-aided LS method substantially improves instantaneous estimation over traditional LS.
  • Related works and future directions: Future optimization research needs more computationally efficient algorithms for large arrays and should account for spatial correlation, mutual coupling, polarization changes, and tractable performance analysis.Circular 6DMA is suggested as one simplification for making analysis more manageable.
  • Related works and future directions: The minimum number of observable sampling positions and rotations needed for reliable CSI recovery across surface configurations remains open, with sampling theory and electromagnetic functional degrees of freedom proposed as possible tools.The issue depends on movement-region size and position/rotation dimensions.
  • Passive 6DMA applications: Passive 6DMA can use distributed or centralized reflecting surfaces, and both outperform fixed IRS in the reported setting; distributed surfaces perform better but cost more and are harder to control.The distributed advantage is attributed to greater position and rotation flexibility and improved inter-user-interference mitigation.

B. 6DMA Cell-Free Network

6DMA cell-free networks adapt multiple AP-mounted surfaces to spatially heterogeneous users through rotation and position/orientation optimization. Related sensing designs use 6DMA spatial DoFs to reduce CRB and allocate antenna resources toward denser target regions.

  • 6DMA Cell-Free Network: Circular 6DMA cell-free networks deploy multiple APs with independently rotatable surfaces to jointly serve users across heterogeneous spatial distributions.Each AP contains B surfaces, and each surface contains N = Nh × Nv antennas.
  • 6DMA Cell-Free Network: Circular 6DMA with B = 1 cannot freely allocate antenna resources according to user distribution, motivating architectures with B > 1 surfaces that move along fixed circular tracks.
  • 6DMA Cell-Free Network: The cell-free design maximizes average achievable sum-rate by jointly optimizing all AP surface rotation angles under minimum-angle constraints that prevent overlap and coupling.Bayesian optimization iteratively refines a Gaussian-process surrogate to select observation points.
  • 6DMA Cell-Free Network: With user-density ratio µA/µB = 5, CMMSE rotates surfaces toward the high-density region, whereas LMMSE rotates them toward the low-density region because it lacks global CSI.The resulting configurations are non-uniform and reflect heterogeneous user distributions.
  • 6DMA Cell-Free Network: The proposed 6DMA cell-free scheme with directional or half-space isotropic antennas outperforms centralized 6DMA using a single circular AP with the same antenna count.The cited discussion attributes this to the cell-free scheme’s adaptability to broader angular coverage, reducing channel correlation and improving local-CSI interference suppression.
  • 6DMA for Wireless Sensing: 6DMA sensing jointly optimizes surface positions and orientations to minimize CRB across target subregions, with PSO solving the resulting non-convex problem.The optimized configuration depends on typical DOAs assigned to sufficiently small subregions.
  • 6DMA for Wireless Sensing: 6DMA achieves superior sensing performance against FPA, antenna selection, and fluid antenna schemes by allocating more antennas to regions with higher target or subregion density.The comparison uses a directive antenna pattern with N = 2 and B = 24.
  • 6DMA for UAV: For cellular-connected UAVs, jointly designing 6DMA surface orientation and antenna positions can significantly mitigate aerial-ground interference.A BCD-based design alternates position and rotation optimization after deriving the optimal receive beamformer for fixed geometry and association.

E. Other Related Works and Future Directions

The tutorial relates 6DMA to emerging communication and sensing applications while distinguishing rotatable 6DMA as a lower-complexity option when antenna translation is impractical. It presents element-wise and array-wise architectures, their benefits, and optimization challenges.

  • Other Related Works and Future Directions: 6DMA-related directions include secure communication and sensing, NGMA resource allocation across multiple domains, and THz communication’s integration with spatially agile antennas.
  • Rotatable 6DMA: Rotatable 6DMA is more viable than full position-and-orientation adjustment when only modest performance enhancement is required or hardware prevents antenna translation.It retains angular radiation-pattern control while keeping antenna positions fixed.
  • Element-wise Rotatable 6DMA: Element-wise rotatable 6DMA changes each antenna’s orientation without moving its position, adjusting radiation characteristics without increasing array costs or reducing aperture efficiency.It can also support wide angular beam scanning without dedicated phase-control beamforming.
  • Array-wise Rotatable 6DMA: Array-wise rotatable 6DMA rotates the entire array about its center to control radiation and coverage, suppress interference from undesired directions, and support spectrum sharing.
  • Array-wise Rotatable 6DMA: Array-wise rotation provides 3D rotational DoFs for mitigating inter-user interference, enhancing coverage, and increasing multiplexing gain.
  • Array-wise Rotatable 6DMA: For 3D array rotation, exhaustive search becomes prohibitive when jointly optimizing rotation with beamforming or resource allocation, motivating AO and SCA methods.
  • Element-wise Rotatable 6DMA: Element rotation controls spatial radiation and polarization, while also enabling ambiguity-free 2D DOA estimation through polarization sensitivity.
  • Element-wise Rotatable 6DMA: Optimized element-wise orientations significantly outperform conventional FPA arrays with directional or isotropic antennas in theoretical and numerical evaluations.

C. Other Related Works and Future Directions

Positionable 6DMA fixes antenna rotations while permitting movement, creating a special-case platform for joint position optimization, resource allocation, channel estimation, and related communication and sensing applications. The section also surveys rotatable-6DMA applications and representative rotation-optimization and channel-estimation studies.

  • Rotatable 6DMA applications: Rotatable 6DMA supports high-speed-rail communication by adjusting transceiver-panel rotations to improve array gain and spatial multiplexing.A differential-evolution algorithm was used to optimize rotation angles and was validated experimentally.
  • Rotatable 6DMA applications: Rotatable radar can dynamically adjust scanning angles and beam directions to optimize sensing coverage and accuracy in wireless sensing networks.The passage also identifies spectral coexistence between rotating radar and power-controlled cellular networks as an application area.
  • Positionable 6DMA: Positionable 6DMA fixes antenna rotation while allowing translation along a line or plane, generally performing below fully adaptive 6DMA but presenting distinct design challenges and applications.This implementation is motivated in part by hardware limitations on antenna rotation.
  • Positionable 6DMA optimization: Positionable 6DMA-aided multicast jointly optimizes antenna positions and beamforming for max-min fairness or QoS objectives under movement and transmit-power constraints.The system includes a BS with Q transmit antennas and K single-antenna users partitioned into Z multicast groups.
  • Positionable 6DMA optimization: Alternating optimization updates transmit positions, receive positions, and beamforming successively, using methods such as SCA, gradient descent, PSO, SDR, or ADMM.Because the MMF and QoS problems are dual, MMF solutions can also be obtained by iteratively solving the QoS problem.
  • Positionable 6DMA optimization: The proposed antenna-position optimization consistently achieves higher max-min SINR than benchmark schemes and can mitigate inter-group interference even when classical beamforming conditions are not satisfied.The cited results attribute the gains to channel diversity and spatial-domain interference mitigation, with max-min SINR growing almost linearly with maximum transmit power.

2) Positionable 6DMA-Aided Interference Networks:

Positionable 6DMA improves interference management through antenna movement, while two-timescale transmission uses statistical CSI for slow position optimization and short-timescale beamforming. The section also covers rich-scattering channel estimation, where learning-based methods address the cost and difficulty of sampling many antenna ports.

  • Interference-network formulation: Positionable 6DMA interference networks minimize total transmit power under QoS, antenna-separation, movement-region, and beamforming constraints.The formulation considers networks with multiple BS-user pairs and jointly optimizes antenna positions and transmission variables.
  • Interference-network results: When the number of channel paths exceeds 5, additional power reduction slows because the finite set of elevation and azimuth angles limits further channel-correlation reduction.For K = 5 BS-user pairs, antenna movement yields lower total transmit power than FPA with K = 3 pairs.
  • Two-timescale transmission: The two-timescale framework optimizes antenna positions using relatively stable statistical CSI at the large timescale and updates beamforming at the short timescale.This avoids requiring accurate instantaneous CSI across the entire movement region for every antenna repositioning decision.
  • Two-timescale transmission: P-6DMA-ZF achieves the highest ergodic sum rate across the evaluated Rician factors, while P-6DMA-MRT approaches FPA-ZF and FPA-OPT near κ = 30 dB.P-6DMA-ZF uses equal power allocation and suboptimal beamforming, whereas P-6DMA-MRT remains below P-6DMA-ZF because interference suppression is more limited.
  • Channel estimation: Rich-scattering P-6DMA channel estimation uses learning-based tools and interpolation because conventional sparse-channel methods may be ineffective and exhaustive port sampling is costly.One approach reconstructs unsampled channels from selected ports with a lightweight ResNet containing 9 conventional layers and 22000 tunable parameters.

2) Sparse Channels:

Sparse channel estimation exploits multipath structure to recover angle information and channel coefficients from limited antenna-position measurements. Compressed sensing reduces measurement requirements, while quantization and sequential estimation introduce accuracy and error-accumulation challenges.

  • Channel structure: The end-to-end channel depends on multipath angles of departure, angles of arrival, and a channel coefficient matrix rather than every transmit–receive position pair.This structure motivates estimating path parameters instead of directly estimating h(q_t, q_r) across continuous movement regions.
  • Compressed-sensing estimation: A sequential compressed-sensing method estimates AoDs, AoAs, and channel coefficients from sampled antenna positions and limited pilot measurements.The method samples transmit positions while holding the receive position fixed, then applies the procedure to the receiver and estimates coefficients using least squares.
  • Compressed-sensing estimation: Compressed sensing reformulates AoD estimation as sparse signal recovery over a discretized angular grid and can solve it with algorithms such as OMP.The grid uses G points with G ≫ L_t, producing a sparse vector with L_t nonzero elements.
  • Compressed-sensing estimation: Joint compressed-sensing estimation reduces channel-measurement requirements relative to sequential parameter estimation, which can accumulate error and incur high overhead.The joint framework estimates AoDs, AoAs, and complex channel coefficients together from fewer measurements.
  • Estimation limitations: Discrete angle quantization limits estimation accuracy, motivating tensor-decomposition methods for more precise multipath-component estimation with reduced pilot-training overhead.The limitation applies to the described compressed-sensing approaches for both SISO and MIMO systems.
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