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Non-Stationarities in Extra-Large Scale Massive MIMO
Elisabeth De Carvalho, Anum Ali, Abolfazl Amiri, Marko Angjelichinoski, Robert W. Heath
TL;DR
The paper asks how massive MIMO changes when apertures become extremely large and spatial non-stationarity emerges. It models visibility regions and incorporates them into performance analysis and transceiver design, finding benefits when non-stationarity is embraced but losses when it is neglected. The study also identifies scarce measurements and simplified electromagnetic modeling as important boundaries.
Problem
Massive MIMO theory assumes moderately sized, compact apertures, leaving the behavior and non-stationary features of extra-large arrays insufficiently characterized.
Method
The paper uses visibility-region-based channel modeling and non-stationarity-aware linear and hybrid analog-digital transceiver designs for discrete extra-large arrays.
Results
Non-stationarity can improve performance in favorable cases, worsen it in unfavorable cases, and reduce computational load when used in transceiver design.
Takeaways & Limitations
Visibility regions provide an additional antenna-assignment degree of freedom for balancing computational cost, data requirements, and fairness.
Takeaways & Limitations
The hybrid-beamforming results are preliminary and rely on genie-aided channel state information, while practical dynamic architectures remain challenging.
Abstract
from arXiv · showhide
Massive MIMO, a key technology for increasing area spectral efficiency in cellular systems, was developed assuming moderately sized apertures. In this paper, we argue that massive MIMO systems behave differently in large-scale regimes due to spatial non-stationarity. In the large-scale regime, with arrays of around fifty wavelengths, the terminals see the whole array but non-stationarities occur because different regions of the array see different propagation paths. At even larger dimensions, which we call the extra-large scale regime, terminals see a portion of the array and inside the first type of non-stationarities might occur. We show that the non-stationarity properties of the massive MIMO channel changes several important MIMO design aspects. In simulations, we demonstrate how non-stationarity is a curse when neglected but a blessing when embraced in terms of computational load and multi-user transceiver design.
I. INTRODUCTION
XL-MIMO extends massive MIMO to arrays spanning large structures, where spatial non-stationarity and visibility regions create distinct propagation and transceiver-design challenges.
- I. INTRODUCTION: XL-MIMO uses discrete antenna arrays with dimensions reaching several tens of meters, integrated into structures such as building walls, airports, malls, or stadiums.The paper treats XL-MIMO as a distinct operating regime of massive MIMO.
- I. INTRODUCTION: Different array regions can observe propagation paths with different powers or different paths, producing spatial non-stationarity.At extreme dimensions, terminals may illuminate only a portion of the array called a visibility region.
- I. INTRODUCTION: The paper focuses on discrete arrays, visibility regions, and their effects on performance and transceiver design rather than continuous electromagnetic surfaces.The scope explicitly excludes continuous surfaces.
- I. INTRODUCTION: Larger-aperture deployments also include large intelligent surfaces and distributed antenna systems as alternative ways to create extended spatial dimensions.Figure 1 presents these deployment concepts alongside large and extra-large antenna arrays.
- I. INTRODUCTION: Non-stationarity is incorporated into linear multi-terminal transceiver assessment and hybrid analog-digital beamforming to reduce transceiver computational complexity.This makes the channel's spatial structure part of the system-design strategy.
II. TYPES OF SPATIAL NON-STATIONARY REGIMES
The paper organizes larger-aperture systems around spatial non-stationarity and extends visibility regions from terminal locations to portions of the antenna array.
- II. TYPES OF SPATIAL NON-STATIONARY REGIMES: The deployment overview includes large or extra-large antenna arrays, large intelligent surfaces, and distributed antenna systems.These are presented as different ways to create larger apertures.
- II. TYPES OF SPATIAL NON-STATIONARY REGIMES: A cluster-based channel model distinguishes stationary channels from two spatial non-stationary regimes using visibility regions along an antenna array.The visibility-region concept originates in the COST 2100 channel model.
- II. TYPES OF SPATIAL NON-STATIONARY REGIMES: Visibility regions are extended from geographical areas where terminals see cluster sets to array portions from which particular cluster sets are visible.The paper distinguishes terminal-domain VR-T and array-domain VR-A.
A. Large-scale massive MIMO
Large-scale and extra-large-scale regimes differ in which terminals and propagation clusters are visible across array portions, with measurements illustrating XL-MIMO propagation complexity.
- A. Large-scale massive MIMO: In the L-MIMO regime, different array portions see different cluster sets while the whole array remains visible to every terminal.This generally corresponds to terminals at a significant distance from the array.
- B. Extra-large scale massive MIMO: In the XL-MIMO regime, different array portions see different cluster sets and different terminal sets because terminals are closer or the array is larger.A terminal's visibility region can include multiple array-domain regions.
- B. Extra-large scale massive MIMO: A six-meter, 64-antenna indoor array measurement campaign used eight terminals positioned about 2 and 6 meters from the array.The campaign was designed specifically to study XL-MIMO.
- B. Extra-large scale massive MIMO: The three MIMO scales are presented as distinct regimes in the paper's spatial non-stationarity framework.Figure 2 summarizes the conventional, large-scale, and extra-large-scale cases.
C. Distributed massive MIMO
XL-MIMO relates to distributed massive MIMO while requiring channel models that capture spatially varying gains, near-field effects, and subarray-level processing.
- C. Distributed massive MIMO: XL-MIMO is a special case of distributed massive MIMO in which the complete set of arrays is collocated.Dense distributed deployments can likewise make clusters and terminals visible only from subsets of arrays.
- D. Impact on key channel assumptions: Very large arrays depart from conventional correlated channel models because average channel gain varies along the array.The Gaussian assumption may remain valid, but stationary correlation properties do not capture this variation.
- D. Impact on key channel assumptions: The measurement figure reports average received power in dBm across a 64-antenna array, averaged over small terminal movements.The setup and results are from the XL-MIMO measurement campaign.
- D. Impact on key channel assumptions: Near-field modeling requires spherical-wave phase behavior and amplitude variations that depend on terminal position, panel size, and magnetic properties.The paper uses simplified models to highlight energy variations along array panels.
- D. Impact on key channel assumptions: Decomposing the array into approximately stationary subarrays supports performance analysis and processing adapted to non-stationarity patterns.A transition zone can be added between subarrays.
III. EXPLOITING SPATIAL NON-STATIONARITY
The paper evaluates how visibility-region non-stationarity affects ZF performance and argues that it should guide performance assessment and transceiver design.
- Scope: VR-based non-stationarity is incorporated into performance analysis and transceiver design for extra-large MIMO systems.The paper provides ZF performance bounds, considers hybrid analog-digital precoding and combining, and exploits low-power array regions for lower-complexity receivers.
- ZF performance bounds: The ZF SINRs all scale as M/K, while non-stationary configurations differ in lower-order terms.The comparison includes best-case and worst-case VR arrangements against the stationary case.
- ZF performance bounds: The best-case non-stationary scenario outperforms the stationary case, especially with small or non-overlapping VRs.Its largest value occurs when M/D is large, corresponding to small VRs or non-overlapping VRs.
- ZF performance bounds: The worst-case non-stationary scenario underperforms the stationary case, with greater SINR loss as terminal VRs become smaller.In the worst case, terminals have completely overlapping VRs and receive signals from the same D antennas.
- ZF performance bounds: For M = 256 antennas and K = 64 users, simulated SINR varies significantly with active antennas per terminal and VR configuration.The differences from stationary channels are larger for smaller D.
- Implications: The analysis finds that non-stationarity has a significant impact on massive MIMO performance and should be exploited in system design.The conclusion applies the VR-based analysis to massive MIMO design rather than treating non-stationarity as irrelevant.
B. Hybrid beamforming
The paper examines hybrid analog-digital architectures that connect selected antennas according to terminal visibility regions, reducing hardware demands while retaining multi-terminal processing.
- Motivation: Hybrid analog-digital architectures control cost and complexity by using fewer RF-chains than antennas.They enable multi-terminal multi-stream precoding that analog-only architectures cannot provide.
- VR-aware design: Dynamic hybrid architectures can connect RF-chains only to antennas inside each terminal’s VR because outside antennas have insignificant channel power.This makes the architecture responsive to non-stationary channel energy patterns.
- Evaluation: The simulations evaluate ZF SINR for 256 antennas, D = M/2 VRs, and K = 8 terminals across different hardware architectures.The array is linear, antennas are half-wavelength spaced, and the dynamic architecture is compared with fully digital and hybrid alternatives.
- Scope and limitation: The reported dynamic-hybrid results are preliminary and rely on genie-aided channel-state information.Efficient channel-state-information acquisition remains a major practical challenge.
C. Low complexity transceivers
The paper uses visibility regions and distributed sub-array processing to reduce the complexity of transceivers for extra-large arrays while preserving multi-terminal processing options.
- Motivation: Extremely large arrays make even simple linear transceivers computationally demanding, especially with many terminals.Reducing transceiver complexity is therefore identified as a major implementation challenge.
- Distributed ZF: VRs make ZF matrices banded or potentially sparse, reducing the cost of matrix inversion.Distributed processing further improves flexibility and lowers complexity by assigning local processing to sub-arrays and fusing outputs centrally.
- Sparse processing: A graph connecting terminals to sub-arrays becomes sparse when terminals use only a small number of sub-arrays.Dynamic sub-array divisions can fit the multi-terminal VR patterns better than fixed divisions.
- Hierarchical fusion: Distributed processing can be organized hierarchically with multi-stage fusion across subsets of sub-arrays.This structure is suited to arrays deployed across very large physical structures.
- Nonlinear receivers: Nonlinear processing can exploit favorable sub-array interference conditions through successive interference cancellation.Detecting a terminal where interference is favorable and removing its contributions can improve the signal-to-interference ratio of other terminals.
- Evaluation: The Fig. 6 experiment compares centralized and distributed ZF as the number of contributing antennas in each terminal’s VR decreases.For a 1024-antenna array at 2.4 GHz, the text reports saturation in centralized-processing performance for this channel model.
A. Characterizing the channel
The paper identifies a lack of near-field measurements for extremely large arrays and motivates broader measurement campaigns to characterize their non-stationary propagation behavior.
- Measurement gap: Near-field measurements of extremely large arrays with visible non-stationary patterns are scarce.The paper presents this scarcity as a reason that real-world non-stationary features remain insufficiently understood.
- Open propagation questions: Large indoor venues raise unresolved questions about whether very large wall-mounted panels produce sparse or richly scattered channels.The paper emphasizes that channel energy variations arise from path loss and nearby building and reflecting structures.
- Measurement needs: Measurements are needed across indoor and outdoor deployment scenarios to establish statistically meaningful channel characteristics.The campaigns should extract non-stationary attributes alongside other channel-modeling features.
B. Embracing electromagnetics
Advanced electromagnetic features constrain channel modeling and increase algorithmic complexity, while visibility-region-based antenna assignment offers a way to reduce MIMO transceiver computation.
- Near-field spherical-wave propagation depends on terminal position, panel size, and magnetic properties, requiring more faithful electromagnetic modeling.
- Advanced electromagnetic features likely increase algorithmic complexity, including in sparse channel-estimation methods.
- Spherical waves require more parameters in the dictionary used by compressed-sensing channel estimation.
- Assigning each terminal a subset of antennas, often restricted to its visibility region, reduces processing cost and supports metric-driven area allocation.Within the assigned area, the terminal signal is treated as desired; outside it, the signal is treated as interference.
V. CONCLUSIONS
XL-MIMO extends massive MIMO to extremely large discrete arrays, where non-stationarity and visibility regions affect system performance and transceiver computation. Near-field operation further requires adjusted models and more complex beamforming.
- XL-MIMO is an extreme but practical massive-MIMO regime using larger-aperture discrete antenna arrays integrated into large structures.
- Visibility regions can reduce the computational load of centralized or distributed MIMO transceivers.
- Near-field communication changes propagation attributes from conventional far-field behavior, requiring adjusted channel models and new measurements.
- Directional beamforming becomes more complex in the near field because beams depend on more than direction alone.