Power Scaling Laws and Near-Field Behaviors of Massive MIMO and Intelligent Reflecting Surfaces

By Emil Björnson, Luca Sanguinetti. IEEE Open Journal of the Communications Society, 2020

427 citations recorded by the source corpus.

The use of large arrays might be the solution to the capacity problems in wireless communications. The signal-to-noise ratio (SNR) grows linearly with the number of array elements <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> when using Massive MIMO receivers and half-duplex relays. Moreover, intelligent reflecting surfaces (IRSs) have recently attracted attention since these can relay signals to achieve an SNR that grows as <inline-formula> <tex-math notation="LaTeX">$N^{2}$ </tex-math></inline-formula>, which seems like a major benefit. In this article, we use a deterministic propagation model for a planar array of arbitrary size, to demonstrate that the mentioned SNR behaviors, and associated power scaling laws, only apply in the far-field. They cannot be used to study the regime where <inline-formula> <tex-math notation="LaTeX">$N\to \infty $ </tex-math></inline-formula>. We derive an exact channel gain expression that captures three essential near-field behaviors and use it to revisit the power scaling laws. We derive new finite asymptotic SNR limits but also conclude that these are unlikely to be approached in practice. We further prove that an IRS-aided setup cannot achieve a higher SNR than an equal-sized Massive MIMO setup, despite its faster SNR growth. We quantify analytically how much larger the IRS must be to achieve the same SNR. Finally, we show that an optimized IRS does not behave as an “anomalous” mirror but can vastly outperform that benchmark.

Subfields: Aerospace Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/4dc601082629b58c439fdabae53ca34cef60d124

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Citations in the corpus

A Tutorial on Near-Field XL-MIMO Communications Toward 6G (2023, neutral): “Besides, BS-side VR w.r.t. scatterer, denoted as Φ NLoS , is the portion of array that is visible to the scatterer.”
Rayleigh Fading Modeling and Channel Hardening for Reconfigurable Intelligent Surfaces (2020, background): “The type of convergence is irrelevant in this context since it is the behavior for large but finite N that matters; the channel models break down if we physically let N → ∞ [17].”
RIS-Aided Wireless Communications: Prototyping, Adaptive Beamforming, and Indoor/Outdoor Field Trials (2021, background): “We recall from [34] that the main near-ﬁeld effects only occurs when the propagation distance is proportional to the RIS size (in 80 cm in our prototype).”
White Paper on Broadband Connectivity in 6G (2020, background): “Since the surface needs to be physically large to beat a classical half-duplex relay and is subject to beam-squinting [31, 33], the most promising use case for IRS is to increase the propagation conditions in short-range communications, particularly in sub-THz and THz bands where relaying…”
Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How It Works, State of Research, and The Road Ahead (2020, background): “The authors of [258] move from the findings in [23], and analyze the scaling laws of RISs and massive MIMO as a function of the number of reflecting elements.”
Near-Field Communications: A Tutorial Review (2023, background): “It is worth noting that the influence of polarization loss was also considered in [40], [41].”
An Overview of Signal Processing Techniques for Terahertz Communications (2020, background): “The near-field behavior of IRSs is studied in [165], [394], where a physically accurate near-field channel gain expression is derived for planar arrays, also considering the mismatch”
Physics-Based Modeling and Scalable Optimization of Large Intelligent Reflecting Surfaces (2020, background): “In [17], the authors studied the power scaling laws for asymptotically large IRSs; however, similar to [16], general incident and reﬂection directions were not considered.”
A Tutorial on Extremely Large-Scale MIMO for 6G: Fundamentals, Signal Processing, and Applications (2023, methodology): “The authors in [119] investigated the XL-MIMO system operated in the THz band with 300 GHz carrier frequency.”
Prospective Multiple Antenna Technologies for Beyond 5G (2019, background): “Even if it tempting to view an IRS as a mirror, it actually behaves as a reconﬁgurable lens that can focus signals at points in the near-ﬁeld or beamform signals towards points in the far-ﬁeld [165].”
Reconfigurable Intelligent Surfaces: Three Myths and Two Critical Questions (2020, background): “The pathloss from the transmitter to each RIS element is huge in the far-field, thus it is more accurate to say that the power loss between the transmitter and RIS reduces as 1/N [11].”
Reconfigurable Intelligent Surfaces: A signal processing perspective with wireless applications (2021, positive): “The general SNR expressions presented in this tutorial remain valid, and if propagation loss models that capture the radiative near-field properties are utilized, one can derive how the SNR converges to a finite upper limit [23].”
An Overview of Signal Processing Techniques for RIS/IRS-Aided Wireless Systems (2021, neutral): “Depending on the size of the RIS, the operating frequency, and its distance from the transmitter and the receiver, it may be necessary to utilize a near-ﬁeld communication model [22], [249]–[251].”
Holographic MIMO Communications: Theoretical Foundations, Enabling Technologies, and Future Directions (2022, background): “However, [222] proved that this power scaling holds only in far-field regime and tapers off in nearfield region.”
A Tutorial on Fluid Antenna System for 6G Networks: Encompassing Communication Theory, Optimization Methods and Hardware Designs (2024, background): “The Rayleigh distance is proportional to the product of the square of the array aperture and the operating frequency [271], [272].”
Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How it Works, State of Research, and Road Ahead (2020, background): “The authors of [257] move from the findings in [258], and analyze the scaling laws of RISs and massive MIMO as a function of the number of reflecting elements.”