Power Scaling Laws and Near-Field Behaviors of Massive MIMO and Intelligent Reflecting Surfaces (2002.04960v5)

Abstract: 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 $N$ 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 $N^2$, which seems like a major benefit. In this paper, 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 $N\to\infty$. 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.

• The paper derives a closed-form channel gain expression for mMIMO and IRS that incorporates polarization mismatches and near-field effects.
• The study shows that while mMIMO SNR grows linearly up to practical limits, IRS performance is inherently limited due to power losses.
• The research reveals that optimal IRS configurations function like a concave mirror, focusing signals optimally based on user location and array geometry.

Overview of the Paper on Power Scaling Laws and Near-Field Behaviors of Massive MIMO and Intelligent Reflecting Surfaces

The paper by Emil Björnson and Luca Sanguinetti, published in the IEEE Open Journal of the Communications Society, explores the exploration of power scaling laws and near-field behavior applicable to Massive Multiple-Input Multiple-Output (mMIMO) systems and Intelligent Reflecting Surfaces (IRSs). It distinctly addresses the limitations identified in existing research, where asymptotic analyses typically rely on assumptions valid only in the far-field. The paper derives insights into how these systems behave in the near-field, presenting new avenues for evaluating power scaling laws accurately.

Key Contributions and Findings

1. Channel Gain Expression: The paper presents a closed-form expression for channel gain pertinent to both mMIMO and IRS configurations by incorporating polarization mismatches, varied distances, and effective areas in the near-field. This expression resolves previous inconsistencies seen with far-field approximations when applied to very large arrays.
2. Near-Field Behavior and Asymptotic Limits:
   • The paper elucidates the conditions under which SNR grows proportionally to the number of antennas (N) in mMIMO systems, emphasizing that conventional power scaling laws only apply where the far-field approximation is valid. This holds true up to practical limits where array sizes exceed typical operational scales, beyond which the SNR growth tapers and the channel gain approaches a finite limit of 1/3 as N tends to infinity.
   • For IRS-aided communications, while SNR growth with N is initially rapid (suggestive of a quadratic increase), the paper demonstrates that IRS setups cannot exceed the SNR of equivalent-sized mMIMO arrays due to inherent power losses in reflecting surfaces.
3. IRS versus mMIMO and Relay Systems: The IRS, often theorized as providing significant physical layer advantages due to flexible reflection properties, is mathematically demonstrated not to surpass the performance of equally sized mMIMO or regenerative relay systems. The paper quantifies the effective preconditions where IRS can achieve parity in terms of SNR, noting it requires a significantly larger physical area.
4. Geometric and Operational Insights: The authors challenge the characterization of IRSs as "anomalous mirrors". They show that optimal IRS configuration does not reflect signals as a plane mirror but rather synthesizes a concave mirror's operation, focusing incident waves optimally, contingent on user location and array geometry.

Theoretical Implications and Practical Considerations

The findings stipulate a formal basis for reviewing assumptions underlying the design of future wireless systems employing mMIMO and IRS technologies. By offering an accurate depiction of how these systems behave as N scales to infinity, the research dismisses the practical viability of certain extrapolated scaling laws, particularly emphasizing scenarios requiring near-field analysis due to shorter operational distances or larger arrays.

These results hold significant implications for the deployment of beyond-5G and 6G technologies that will increasingly rely on mMIMO and IRS setups to achieve enhanced spectral efficiency and spatial accuracy. Future research trajectories could explore stochastic channel modeling under these newly defined paradigms, paving the way for designs that factor both traditional theoretical findings and the nuanced understandings unveiled here.

In summary, the paper is a crucial step toward refining the power scaling laws applicable to modern wireless systems and underscores the need to incorporate physically accurate models in assessing the asymptotic behavior and near-field performance of both mMIMO and IRS technologies.