A Tutorial on Extremely Large-Scale MIMO for 6G: Fundamentals, Signal Processing, and Applications

• XL-MIMO uses much larger antenna arrays and apertures than mMIMO to support higher spectral efficiency, spatial resolution, and spatial degrees of freedom.Source: A. Motivation · pp. 2–3
• Its key challenges arise from the extremely large antenna count and near-field characteristics, which increase processing complexity and require electromagnetic effects beyond conventional mMIMO.Source: A. Motivation · p. 3
• XL-MIMO encompasses ULA, UPA with patch or point antennas, and CAP-based designs, whose characteristics and relationships guide implementation choices.Source: B. Comparisons and Key Contributions · p. 5
• The survey reviews XL-MIMO channel modeling, including LoS, NLoS, and hybrid propagation, together with electromagnetic characteristics, distance boundaries, and EM regions.Source: B. Comparisons and Key Contributions · p. 5
• It surveys channel estimation, beamforming, and machine-learning-enabled processing, emphasizing low-complexity methods to support practical XL-MIMO implementation.Source: B. Comparisons and Key Contributions · p. 5
• The paper also discusses applications including physical-layer security, integrated sensing and communications, and the Internet of Things, alongside future directions such as AI-aided resource allocation and green communication.Source: B. Comparisons and Key Contributions · p. 6

Hardware designs

• Section II introduces ULA-based, UPA-based, and CAP-based XL-MIMO hardware designs.Source: C. Organization of the Survey · p. 6

Channel modeling

• Section III reviews electromagnetic characteristics, distance boundaries, EM regions, and LoS, NLoS, and hybrid channel models.Source: C. Organization of the Survey · p. 6

Signal processing

• Section IV focuses on low-complexity signal processing for XL-MIMO, covering channel estimation, beamforming, and deep-learning-empowered processing.Source: C. Organization of the Survey · p. 6

Hardware designs

• Four general designs are introduced: ULA-based XL-MIMO, UPA-based XL-MIMO with patch or point antennas, and CAP-based XL-MIMO.The ULA and both UPA variants use discrete apertures, whereas CAP-based XL-MIMO uses a continuous array aperture.Source: §II · pp. 6–7

Comparative overview

• The survey compares the four designs through hardware diagrams and characteristic tables, emphasizing their implementation features and interrelationships.The ULA, UPA, and CAP architectures are treated as related XL-MIMO realization schemes.Source: §II · p. 7, Table IV · p. 8

ULA-based XL-MIMO

• ULA-based XL-MIMO extends conventional array sizes to 512, 1024, 2048, or thousands of antennas, increasing hardware and processing complexity.Most studies assume half-wavelength spacing; sub-arrays can reduce processing complexity and support distributed processing and spatial non-stationarity.Source: A. Uniform Linear Array (ULA)–Based… · pp. 7–8

UPA-based XL-MIMO

• UPA-based XL-MIMO uses rectangular or square planes with M = MV MH antennas, vertical and horizontal spacings ΔV and ΔH, and side lengths LV and LH.Its elements may be practical finite-size patches or analytically convenient sizeless point antennas.Source: A. Uniform Linear Array (ULA)–Based… · pp. 8–9
• For fixed-size UPA-based XL-MIMO, reducing antenna spacing may not improve performance while significantly increasing design complexity.Antenna spacing therefore remains an important vertical and horizontal design parameter.Source: A. Uniform Linear Array (ULA)–Based… · p. 9

CAP architecture

• CAP-based XL-MIMO uses meta-materials to embed extremely dense antennas in compact spaces, approximating a continuous aperture.An ideal CAP comprises infinitely many infinitesimal antennas forming a spatially continuous electromagnetic volume; related names include holographic MIMO and LISs.Source: C. Continuous Aperture (CAP)-Based… · p. 10

Aperture architecture

• CAP apertures are studied as one-dimensional line segments or two-dimensional planes, commonly rectangular or square but also allowing arbitrary shapes.The reviewed literature includes both 1D continuous lines and 2D continuous planes.Source: C. Continuous Aperture (CAP)-Based… · pp. 10–11

Aperture size

• CAP aperture size is determined by line length for 1D designs and area or side length for 2D designs, rather than antenna count and spacing.Examples include 5 m line segments and circular planes with a 10 m radius.Source: C. Continuous Aperture (CAP)-Based… · p. 11

System architecture

• CAP systems may place line segments or planes at both transmitter and receiver, using centralized or distributed architectures.Distributed CAP architectures can employ multiple randomly deployed CAP planes and therefore multiple CAP-equipped base stations.Source: C. Continuous Aperture (CAP)-Based… · p. 11

Carrier frequencies

• CAP-based XL-MIMO studies span carrier frequencies from 2 GHz to 300 GHz, including Sub-6GHz, mmWave, and THz operation.Reported examples include 2.4 GHz, 2 GHz, 28 GHz, 30 GHz, and 300 GHz.Source: C. Continuous Aperture (CAP)-Based… · pp. 11–12

Design Interconversion

• UPA-based XL-MIMO with patch antennas is a general design, while ULA, point-antenna UPA, and CAP designs are special cases.Point antennas arise as patch size approaches zero; ULA uses one row or column, and 1D CAP uses infinitesimal spacing.Source: D. Design Interconversion and Analysis… · p. 12

Analysis Comparison

• Existing comparison frameworks derive ULA EDoF from a channel matrix and 1D CAP EDoF through a source auto-correlation kernel and asymptotic analysis.These methods provide guidelines for comparing different XL-MIMO hardware designs.Source: D. Design Interconversion and Analysis… · p. 12
• EDoF for discrete ULA converged to 1D CAP EDoF as antenna count increased under equivalent array-aperture conditions.The comparison analytically computed EDoF and then derived capacity for both designs.Source: D. Design Interconversion and Analysis… · p. 12

Open Issues

• Performance behavior and comparison-metric effectiveness require further study, especially for UPA-based versus 2D CAP-based XL-MIMO.The 2D CAP case requires a new source auto-correlation kernel, extending the 1D framework.Source: D. Design Interconversion and Analysis… · p. 12

Analysis Comparison

• Performance comparisons should equalize array aperture, antenna number, or other geometric settings to preserve fairness.ULA and 1D CAP comparisons use the same array length, while discrete-array comparisons can use the same antenna count or aperture.Source: D. Design Interconversion and Analysis… · p. 12

Comparison Criteria

• The survey organizes antenna number, spacing, aperture size, and analysis framework as design-comparison dimensions for future analysis and optimization.XL-MIMO may use thousands or tens of thousands of antennas, with aperture determined by array geometry and spacing.Source: D. Design Interconversion and Analysis… · pp. 12–13

Electromagnetic Characteristics

• XL-MIMO’s increased antenna count and aperture make receivers likely to lie in the near field, where plane-wave channel models become less applicable.Vectorial spherical-wave characteristics should instead be considered for XL-MIMO channel modeling.Source: §III · p. 13, A. Electromagnetic Characteristics for… · p. 14

Spatial Non-Stationarity

• XL-MIMO arrays exhibit spatial non-stationarity because different array regions observe propagation paths with different powers or different visible paths.A terminal’s visible region is called its visibility region, and terminal power is concentrated mainly within that region.Source: A. Electromagnetic Characteristics for… · p. 14

Mutual Coupling

• Closely packed antennas make mutual coupling significant; the resulting channel deterioration can degrade SINR and processing-algorithm convergence.The voltage at one element depends on both its incident field and voltages on other elements.Source: A. Electromagnetic Characteristics for… · p. 15

Electromagnetic Characteristics

• Four representative XL-MIMO electromagnetic characteristics are spherical waves, spatial non-stationarity, EM polarization, and mutual coupling.These effects are often omitted in conventional mMIMO but are vital for accurate XL-MIMO modeling and analysis.Source: A. Electromagnetic Characteristics for… · p. 15

Distance Boundaries

• The Rayleigh distance divides near- and far-field regions according to phase discrepancy caused by wave curvature.Near-field waves are spherical, whereas far-field waves can use a first-order phase approximation and planar-wave characteristics.Source: Figure 3 · p. 14, B. Distance Boundaries and EM Regions · p. 15
• 96% of maximum antenna array gain was achieved at the Björnson distance for N = 10^4 and A = (λ/4)^2, while Rayleigh distance was about 35 times larger.The reported normalized antenna array gain was almost 1 when propagation distance reached the Rayleigh distance.Source: B. Distance Boundaries and EM Regions · p. 16
• Multiple distance boundaries offer distinct perspectives for choosing electromagnetic models and analyzing XL-MIMO systems.The survey presents these boundaries as tools for design and analysis rather than a single universal criterion.Source: B. Distance Boundaries and EM Regions · p. 18

Motivation

• XL-MIMO’s large aperture shortens transmission range, making line-of-sight links common and predominant in electromagnetic transmission.Near-field receiver locations further motivate dedicated LoS channel models.Source: C. LoS Propagation Channel Modeling · p. 18

Modeling Schemes

• The two major LoS modeling schemes are Green’s-function-based channel modeling and complex-valued channel-response representation.Both approaches provide channel models for XL-MIMO analysis.Source: C. LoS Propagation Channel Modeling · pp. 18–19

Green’s-Function Modeling

• Green’s-function modeling numerically solves Maxwell’s equations to describe the electric field between arbitrary transmitting and receiving points.The associated formulation relates current distribution density at transmit points to electric fields at receive points.Source: C. LoS Propagation Channel Modeling · p. 18

Modeling Schemes

• Table IX organizes Green’s-function-based LoS channel modeling for single-base-station multi-user and single-user scenarios.SB-MU and SB-SU denote these two deployment settings.Source: Table IX · p. 19

Green’s-function modeling

• The dyadic Green’s function links transmit current density to received electric fields and reduces to a far-field approximation when distance greatly exceeds wavelength.It can be interpreted as the system impulse response.Source: 1) Green’s Function Based Channel… · p. 19
• Dyadic Green’s-function channels capture near-field evanescent waves and provide about one-fold EDoF improvement over scalar Green’s-function channels.Scalar models remain easier to analyze, so the choice depends on the research objective.Source: 1) Green’s Function Based Channel… · p. 19

Complex-valued channel-response modeling

• Complex-valued channel-response modeling separates propagation into amplitude and phase components whose behavior changes across electromagnetic regions.Amplitude models can vary in precision, while phase modeling uses propagation characteristics specific to the region.Source: 2) Complex-Valued Channel Response… · p. 20
• In the NUSW region, both amplitude and phase vary across the aperture, requiring exact propagation distances between transmitting and receiving points.This region is defined by d < d_UPD.Source: 2) Complex-Valued Channel Response… · p. 20
• In the USW region, amplitude is treated as uniform across the aperture while phase retains exact spherical-wave variation; beyond the Rayleigh distance, planar-wave modeling neglects both variations.The regions are d_UPD < d < d_ra for USW and d > d_ra for UPW.Source: 2) Complex-Valued Channel Response… · p. 20

Amplitude modeling

• Generalized gain modeling captures distance variation, effective element areas, and polarization-mismatch losses across the array aperture.Free-space-pathloss and reference-power models provide simpler amplitude representations based on propagation distance or a reference gain.Source: 2) Complex-Valued Channel Response… · pp. 20–21

NLoS modeling requirements

• NLoS channel models must account for scattered propagation environments, near-field characteristics, and spatial non-stationarity across the array.These requirements distinguish XL-MIMO NLoS modeling from simpler propagation representations.Source: D. NLoS Propagation Channel Modeling · p. 21

Fourier plane-wave representation

• Fourier plane-wave representation models arbitrary scattering by decomposing spherical waves into plane waves and representing source, received, and angular responses.The angular response captures scattering propagation and random channel characteristics through a 4D power spectral density.Source: 1) Fourier Plane-Wave Representation… · pp. 21–22
• Discrete Fourier plane-wave series expansion samples the finite wavenumber-support region to produce a tractable and easily analyzed channel model.The discretized plane waves are defined within lattice ellipses.Source: 1) Fourier Plane-Wave Representation… · p. 22

Extensions and limitations

• Fourier plane-wave models have been extended from CAP transmitter–receiver pairs to UPA-based systems, multiple BSs and UEs, and more practical antenna effects.These extensions jointly consider factors including angular power spectra, antenna-pattern distortion, and antenna-efficiency decrease.Source: 1) Fourier Plane-Wave Representation… · p. 22
• Existing Fourier plane-wave studies focus on small-scale fading and neglect large-scale fading gain, leaving its integration as a future research direction.Full electromagnetic-characteristic capture also requires the number of antennas per plane to exceed the number of sampling lattice ellipses.Source: 1) Fourier Plane-Wave Representation… · p. 22

Array response vector representation

• Array-response-vector NLoS modeling expresses the channel as a superposition of response vectors or matrices associated with scattering paths.For ULA-based XL-MIMO, each matrix depends on path gain and transmitter and receiver response vectors.Source: 2) Array Response Vector… · p. 22, Array Response Vector Representation… · p. 23
• Near-field array-response vectors depend on both AoA/AoD and distance to represent spherical waves, whereas far-field vectors depend only on AoA/AoD.This distinction enables near-field channel structure to be retained in the representation.Source: Array Response Vector Representation… · p. 23

Model-selection tutorial

• The channel-modeling tutorial first selects LoS or NLoS propagation, then chooses a method suited to the propagation type and aperture.Green’s-function models derive from Maxwell’s equations, while Fourier plane-wave models contain source, received, and angular responses.Source: Array Response Vector Representation… · pp. 23–24

Hybrid propagation-path modeling

• Hybrid propagation-path modeling combines LoS and NLoS links using either complex-valued channel responses or Fourier plane-wave representations.The paper provides tutorials for generating the resulting hybrid channel from the two components.Source: 1) Hybrid Propagation Path Channel… · pp. 24–25
• The complex-valued hybrid model generates LoS responses and NLoS array-response components separately before combining them into the hybrid channel.The described procedure uses geometric characteristics, position coordinates, and electromagnetic parameters as inputs.Source: 1) Hybrid Propagation Path Channel… · p. 24
• The Fourier plane-wave hybrid model similarly generates 2D Fourier LoS and 4D Fourier NLoS components before combining them.This formulation relies on the Fourier plane-wave representation for both propagation types.Source: 1) Hybrid Propagation Path Channel… · p. 25

Hybrid-field channel modeling

• Hybrid-field channels combine near-field and far-field path components because practical scatters can occupy both regions.An adjustable parameter controls the proportion of the two path types.Source: 2) Hybrid-Field Channel Modeling · p. 25

Channel estimation motivation

• XL-MIMO channel estimation requires accurate CSI while accounting for spherical waves, spatial non-stationarity, electromagnetic polarization, and high computational complexity.The paper identifies high accuracy and acceptable complexity as joint design goals.Source: §IV · p. 25, A. Channel Estimation · p. 25

Polar-domain estimation

• Angular-domain compressive-sensing methods developed for conventional mMIMO cannot be directly applied because XL-MIMO channels do not exhibit the same angular-domain sparsity.Near-field methods instead exploit sparsity in a polar domain.Source: 1) Polar Domain Based Channel… · p. 26
• Polar-domain representations encode both angular and distance information, enabling P-SOMP to estimate LoS and NLoS channels and P-SIGW to estimate near-field parameters.These methods are designed around near-field spherical-wave characteristics.Source: 1) Polar Domain Based Channel… · p. 26
• P-SOMP and P-SIGW outperformed angular-domain SOMP and SIGW algorithms that rely on angular-domain channel sparsity.The comparison supports using polar-domain structure for XL-MIMO near-field estimation.Source: 1) Polar Domain Based Channel… · p. 27

Hybrid-field estimation

• Hybrid-field OMP estimates far-field and near-field path components by exploiting hybrid-field structure and polar-domain sparsity.Simulation results showed better NMSE performance than the compared far-field approach.Source: 1) Polar Domain Based Channel… · p. 27

Complexity considerations

• Polar-domain transform dictionaries capture near-field sparsity but impose high storage requirements and computational complexity.A distance-parameterized angular-domain representation was proposed as an alternative direction.Source: 1) Polar Domain Based Channel… · p. 27

• Parameter-based schemes first estimate angle and distance, then use them to reconstruct the XL-MIMO channel.Source: 2) Parameter Based Channel Estimation… · p. 27
• Near-field channel estimation exploits pathloss-based models, tiled apertures, subarray structure, or scatterer visibility regions.Source: 2) Parameter Based Channel Estimation… · p. 27
• Wideband beam training controls near-field beam split to focus different frequencies at desired locations while estimating distance, angle, and channel response.Source: 2) Parameter Based Channel Estimation… · p. 27
• Grant-free access produces doubly sparse, user-specific channels, motivating bilinear inference for joint activity and channel estimation.Source: 3) Joint Activity and Channel… · pp. 27–28
• XL-MIMO channel estimation must trade accuracy against complexity because conventional MMSE estimation is rarely adopted at very large antenna dimensions.Source: 4) Low-Complexity Channel Estimation… · p. 28
• Reduced-subspace LS exploits spatial-correlation eigenstructure to provide a lower-complexity alternative combining MMSE and LS ideas.Source: 4) Low-Complexity Channel Estimation… · p. 28
• Bayesian turbo-OAMP performs low-complexity inference for structured sparsity in the antenna-delay domain and non-stationary channels.Source: 4) Low-Complexity Channel Estimation… · p. 28
• Machine-learning estimators report high NMSE performance with low complexity, although further examination is needed before practical deployment.Source: 5) Machine Learning Based Channel… · pp. 28–29

Beamforming Schemes Design

• Near-field spherical-wave propagation changes XL-MIMO beamforming from far-field steering to beam focusing.Source: B. Beamforming Schemes Design · p. 29, 1) Conventional Linear Beamforming… · p. 30
• Linear beamforming remains attractive because increasing antennas can deliver near-optimal performance, but far-field beam-split methods perform poorly in the near field.Source: 1) Conventional Linear Beamforming… · pp. 29–30
• MMSE combining achieved optimal performance in the studied scenarios, whereas ZF, MR, and conventional matrix operations motivate lower-complexity alternatives.Source: 1) Conventional Linear Beamforming… · p. 30, 2) Low-Complexity Beamforming Schemes · p. 30
• Randomized Kaczmarz methods simplify linear processing, with SwoR-RK reducing computational complexity by about 51.3% versus traditional RZF.Source: 2) Low-Complexity Beamforming Schemes · p. 30
• A decentralized BP-VMP receiver decodes in parallel across local processing units and nearly matches a centralized benchmark.Source: 2) Low-Complexity Beamforming Schemes · pp. 30–31
• AMP-GNN unfolds AMP with a graph neural network to cancel multi-user interference while retaining low-complexity processing.Source: 2) Low-Complexity Beamforming Schemes · p. 31
• Polynomial-expansion EP detectors achieved much lower complexity than original EP detectors while approaching their performance.Source: 2) Low-Complexity Beamforming Schemes · pp. 31–32

Optimization Design for Beamforming Schemes

• Near-field resource allocation jointly optimizes beamforming precoding and power control using numerical, reinforcement-learning, or AI-generated optimization tools.Source: 3) Optimization Design for Beamforming… · p. 32
• Holographic and digital beamforming are jointly designed for UPA-based XL-MIMO satellite links to maximize sum rate.Source: 3) Optimization Design for Beamforming… · p. 32
• Distance-aware precoding jointly designs digital, analog, and selection components while formulating spectral-efficiency maximization.Source: 3) Optimization Design for Beamforming… · p. 32
• Alternating optimization jointly configures dynamic metasurface antennas and digital precoding for multi-user near-field beam focusing.Source: 3) Optimization Design for Beamforming… · pp. 32–33
• Pattern-division multiplexing optimizes electric-current-density patterns on continuous apertures for sum-capacity maximization.Source: 3) Optimization Design for Beamforming… · p. 33
• Energy-efficiency maximization is identified as important for sustainable XL-MIMO deployment, with transmit precoding and tuning optimized using channel-state information.Source: 3) Optimization Design for Beamforming… · p. 33
• The surveyed optimization designs motivate further work across different scenarios, objectives, and methods for exploiting XL-MIMO potential.Source: 3) Optimization Design for Beamforming… · pp. 33–34

Machine Learning Empowered Signal Processing

• Machine-learning methods are proposed because spherical-wave propagation makes traditional signal-processing methods less accurate for XL-MIMO near-field analysis.Source: C. Machine Learning Empowered Signal… · p. 34
• Distributed learning addresses XL-MIMO’s antenna-dependent data-processing burden by moving computation toward network edges.Source: 2) Distributed Learning · p. 34
• MARL treats base stations, users, and antennas as agents for resource allocation, with antenna selection achieving a 26% EE improvement.Source: 2) Distributed Learning · p. 34
• Fuzzy logic combined with MARL reduces computational complexity in centralized-training and centralized- or decentralized-execution architectures.Source: 2) Distributed Learning · p. 34
• A decoupled architecture prioritizing high-loss experiences achieved faster convergence and comparable performance with conventional methods.Source: 2) Distributed Learning · p. 34
• Spherical-wavefront propagation supports physical-layer security against eavesdroppers in similar angular orientations.Source: A. Physical Layer Security Enhancement · pp. 34–35
• Leakage subspace precoding increased spectral secrecy efficiency by more than 40 percent over traditional zero-forcing under varied eavesdropper collusion strategies.Source: A. Physical Layer Security Enhancement · p. 35
• Security analyses report higher secrecy rates for spherical-wavefront than plane-wave models across colluding and non-colluding eavesdropper settings.Source: A. Physical Layer Security Enhancement · p. 35

UAV Communications

• UAV–XL-MIMO integration can improve communication performance, energy efficiency, and coverage, while UAV channel models address dynamic propagation environments.Reviewed models include geometric 3D non-stationary mmWave wideband channels with stationary and moving clusters.Source: B. UAV Communications · p. 35
• RIS-assisted UAV optimization jointly considers trajectory and RIS phase decisions to reduce energy consumption while maintaining users’ QoS, with extensions proposed for XL-MIMO.The framework can incorporate immense antenna arrays and XL-MIMO features to further reduce UAV and BS energy consumption.Source: B. UAV Communications · pp. 35–36

Integrated Sensing and Communications (ISAC)

• XL-MIMO supports ISAC by combining communication with radar and near-field radio sensing, using models that capture spherical wavefronts and spatial non-stationarities.Its large spatial extent enhances communication performance and provides finer spatial resolution.Source: C. Integrated Sensing and… · p. 36

IoT Communications

• High-density IoT deployments require QoS-aware scheduling and distance-aware precoding to manage massive connections across heterogeneous devices.A DAP framework exploits near-field effects by optimizing activated RF chains and precoding matrices according to increased DoFs.Source: D. Internet-of-Things · p. 36

Edge Computing

• XL-MIMO combined with edge computing provides reliable access links, spatial diversity, and resource coordination for ultra-low-latency services.Related work formulates joint communication and computing resource allocation under delay constraints and uses distributed cooperative learning.Source: E. Edge Computing · p. 37

Massive Connectivity

• XL-MIMO enables massive connectivity through large apertures but introduces near-field access channels, high costs, and spatially varying visibility regions.Users may perceive different array parts, requiring connectivity mechanisms linked to physical location and visible regions.Source: F. Massive Connectivity · p. 37
• NOVR-XL improves the average sum rate from 160 to 520 bits/channel use when the average number of contending UEs per pilot is 2.The scheme combines NOMA with XL-MIMO and allows overlapping users to share the same XL subarray.Source: F. Massive Connectivity · p. 37

A. AI-Aided Resource Allocation Scheme

• Future AI methods can adapt channel estimation, beamforming, scheduling, and resource allocation to changing environments and dense XL-MIMO user distributions.AI-based beamforming can exploit near-field effects to improve SINR and SE, while generative diffusion models are proposed for resource allocation.Source: A. AI-Aided Resource Allocation Scheme · pp. 37–38

Future Research Directions

• Sustainable XL-MIMO requires energy-efficient processing, power allocation, antenna selection, and distributed computation strategies.Distributed processing can offload complex computations to cloud-based BBUs.Source: B. Energy Efficiency and Green… · p. 38
• Semantic communications can reduce wireless data-transmission burden by extracting task-related information and using semantic importance in resource allocation and beamforming.Under constrained resources, beamforming can prioritize more critical semantic information.Source: C. Semantic Communications · p. 38
• Future work must address XL-MIMO security, privacy, and practical validation through secure processing, authentication, encryption, testbeds, and prototypes.The paper also identifies jamming and eavesdropping as threats requiring attention.Source: D. XL-MIMO-Aided Wireless Network… · p. 38, E. Testbeds and Experimental Evaluation · p. 38, §VII · p. 39