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Asymptotic Analysis of Near-Field Coupling in Massive MISO and Massive SIMO Systems

Aniol Martí, Jaume Riba, Meritxell Lamarca, Xavier Gràcia

TL;DR

This work develops a multiport circuit-based framework to analyze near-field receiver-to-transmitter coupling in massive MISO and SIMO systems. It derives a general noiseless input-output relation and a quantitative unilateral-coupling condition, then analyzes two asymptotic regimes (fixed inter-element spacing and fixed array size) to show that inter-array coupling can be neglected in both downlink and uplink under radiative near-field and far-field conditions. The main contributions are the explicit unilateral condition $\|\mathbf{z}_{\mathrm{TR}}\mathbf{z}_{\mathrm{TR}}^{\mathrm{T}} / Z_{\mathrm{RL}}\|_{\mathrm{F}} \ll \|\mathbf{Z}_{\mathrm{GT}}\|_{\mathrm{F}}$ and its validation for MISO and SIMO, along with tight Frobenius-norm bounds and asymptotic scaling results for fixed spacing and fixed aperture. Practically, the results justify omitting matching networks and inter-array coupling considerations in large mmWave/THz MIMO deployments, simplifying design without sacrificing accuracy in near-field operation.

Abstract

This paper studies the receiver to transmitter antenna coupling in near-field communications with massive arrays. Although most works in the literature consider that it is negligible and approximate it by zero, there is no rigorous analysis on its relevance for practical systems. In this work, we leverage multiport communication theory to obtain conditions for the aforementioned approximation to be valid in MISO and SIMO systems. These conditions are then particularized for arrays with fixed inter-element spacing and arrays with fixed size.

Asymptotic Analysis of Near-Field Coupling in Massive MISO and Massive SIMO Systems

TL;DR

This work develops a multiport circuit-based framework to analyze near-field receiver-to-transmitter coupling in massive MISO and SIMO systems. It derives a general noiseless input-output relation and a quantitative unilateral-coupling condition, then analyzes two asymptotic regimes (fixed inter-element spacing and fixed array size) to show that inter-array coupling can be neglected in both downlink and uplink under radiative near-field and far-field conditions. The main contributions are the explicit unilateral condition and its validation for MISO and SIMO, along with tight Frobenius-norm bounds and asymptotic scaling results for fixed spacing and fixed aperture. Practically, the results justify omitting matching networks and inter-array coupling considerations in large mmWave/THz MIMO deployments, simplifying design without sacrificing accuracy in near-field operation.

Abstract

This paper studies the receiver to transmitter antenna coupling in near-field communications with massive arrays. Although most works in the literature consider that it is negligible and approximate it by zero, there is no rigorous analysis on its relevance for practical systems. In this work, we leverage multiport communication theory to obtain conditions for the aforementioned approximation to be valid in MISO and SIMO systems. These conditions are then particularized for arrays with fixed inter-element spacing and arrays with fixed size.
Paper Structure (13 sections, 30 equations, 3 figures, 1 table)

This paper contains 13 sections, 30 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Multiport Communication
  3. Impedance matching
  4. Antenna mutual coupling
  5. End-to-end (noiseless) system
  6. System Model
  7. Study of Coupling Effects
  8. Massive MISO
  9. Fixed inter-element spacing
  10. Fixed array size
  11. Massive SIMO
  12. Numerical Results
  13. Conclusions

Figures (3)

  • Figure 1: Multiport communication model of a $N_{\mathrm{T}} \times N_{\mathrm{R}}$mimo system. In the figure, $Z_{\mathrm{G}}$ and $Z_{\mathrm{L}}$ represent the generator and load impedances, respectively, and $v_{\mathrm{G},i}$ represents the generator source. Besides, $v_{\mathrm{EN},i}$, $v_{\mathrm{LNA},i}$ and $i_{\mathrm{LNA},i}$ stand for the noise sources (see ivrlac_toward_2010 for details).
  • Figure 2: Fixed inter-element spacing $d=\lambda/2$ coupling condition as a function of $N$ with $r=55\m$. $\mathopen{}\mathclose{\left\|\mathbf{Z}_{\mathrm{GT}}\right\|_{\mathrm{F}}}$ is displayed up to $N=10^4$ due to computational limitations.
  • Figure 3: Fixed array size $D=1\m$ coupling condition as a function of $N$ with $r\approx20\m$ (i.e. the Fresnel distance). $\mathopen{}\mathclose{\left\|\mathbf{Z}_{\mathrm{GT}}\right\|_{\mathrm{F}}}$ is displayed up to $N=10^4$ due to computational limitations.