Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Near-Field Beam Tracking with Extremely Large Dynamic Metasurface Antennas

Panagiotis Gavriilidis, George C. Alexandropoulos

TL;DR

The paper addresses near-field tracking for DMA-based base stations in high-frequency wireless systems by deriving analytical expressions for beamforming gain under position mismatches, depth-of-focus limits, and an effective beam coherence time. It introduces a near-field beam-tracking framework with a dynamic non-uniform coordinate grid and hybrid analog–digital scanning, triggering beam sweeping when the gain drops below a threshold. The approach is validated through extensive simulations, showing superior performance over benchmarks and establishing its ability to adapt sampling density to the UE's location and motion. This work enables scalable, energy-efficient beam tracking for extremely large MIMO deployments in future 6G networks, where near-field effects are prominent.

Abstract

The interplay between large antenna apertures and high frequencies in future generations of wireless networks will give rise to near-field communications. In this paper, we focus on the hybrid analog and digital beamforming architecture of dynamic metasurface antennas, which constitutes a recent prominent enabler of extremely massive antenna architectures, and devise a near-field beam tracking framework that initiates near-field beam sweeping only when the base station estimates that its provided beamforming gain drops below a threshold from its theoretically optimum value. Novel analytical expressions for the correlation function between any two beam focusing vectors, the beamforming gain with respect to user coordinate mismatch, the direction of the user movement yielding the fastest beamforming gain deterioration, and the minimum user displacement for a certain performance loss are presented. We also design a non-uniform coordinate grid for effectively sampling the user area of interest at each position estimation slot. Our extensive simulation results validate our theoretical analysis and showcase the superiority of the proposed near-field beam tracking over benchmarks.

Near-Field Beam Tracking with Extremely Large Dynamic Metasurface Antennas

TL;DR

The paper addresses near-field tracking for DMA-based base stations in high-frequency wireless systems by deriving analytical expressions for beamforming gain under position mismatches, depth-of-focus limits, and an effective beam coherence time. It introduces a near-field beam-tracking framework with a dynamic non-uniform coordinate grid and hybrid analog–digital scanning, triggering beam sweeping when the gain drops below a threshold. The approach is validated through extensive simulations, showing superior performance over benchmarks and establishing its ability to adapt sampling density to the UE's location and motion. This work enables scalable, energy-efficient beam tracking for extremely large MIMO deployments in future 6G networks, where near-field effects are prominent.

Abstract

The interplay between large antenna apertures and high frequencies in future generations of wireless networks will give rise to near-field communications. In this paper, we focus on the hybrid analog and digital beamforming architecture of dynamic metasurface antennas, which constitutes a recent prominent enabler of extremely massive antenna architectures, and devise a near-field beam tracking framework that initiates near-field beam sweeping only when the base station estimates that its provided beamforming gain drops below a threshold from its theoretically optimum value. Novel analytical expressions for the correlation function between any two beam focusing vectors, the beamforming gain with respect to user coordinate mismatch, the direction of the user movement yielding the fastest beamforming gain deterioration, and the minimum user displacement for a certain performance loss are presented. We also design a non-uniform coordinate grid for effectively sampling the user area of interest at each position estimation slot. Our extensive simulation results validate our theoretical analysis and showcase the superiority of the proposed near-field beam tracking over benchmarks.
Paper Structure (24 sections, 5 theorems, 27 equations, 9 figures, 2 algorithms)

This paper contains 24 sections, 5 theorems, 27 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System and Channel Models
  3. DMA Modeling
  4. Channel Model and Received Signals
  5. Near-Field Beamforming Analysis
  6. Beamforming Optimization for a Given UE Position
  7. Beamforming Gain under UE Coordinate Mismatches
  8. Effective Beam Coherence Time
  9. Direction of the Fastest Beamforming Gain Deterioration
  10. Minimum Distance Covered for $(1-\kappa\%)$ Beamforming Gain Loss
  11. Proposed Near-Field Beam Tracking
  12. Design Objective
  13. Beam Focusing Grid and Sweeping
  14. Dynamic Non-Uniform Coordinate Grid
  15. Hybrid Analog and Digital Beam Scanning
  16. ...and 9 more sections

Key Result

Proposition 1

By setting the DMA analog beamforming weights as $q_{i,n}=0.5\left(\jmath + e^{\jmath(\angle{[\mathbf{a}(r,\phi)}]_{(i-1)N_e+n}+\beta \rho_{i,n})}\right)$$\forall$$i,n$ (consequently, the analog beamformer $\mathbf{Q}$ via eq:Q_matrix) and optimizing $G$ with respect to the DMA digital beamformer $\

Figures (9)

  • Figure 1: The considered system model comprising a static BS equipped with a DMA of an extremely large number of metamaterials, lying in the $yz$ plane and a mobile single-antenna UE moving inside the $xy$-plane.
  • Figure 2: The relative beamforming gain for only range mismatch derived in Lemma \ref{['prop_Dr']} (left vertical axis) and the range mismatch limits $\Delta^{\pm}_{\kappa}(r)$ in \ref{['eq:Dr']} for $\kappa=50$ (right vertical axis) as functions of the BS-UE distance $r_0$ in meters, considering a DMA at the BS with $N_e=200$ and $N_m = 10$ (i.e., $N=2000$ elements), $d_e=d_m=\lambda/2$ with $\lambda = 1$ cm, and $z_0 = 1$ m.
  • Figure 3: The relative beamforming gains for only azimuth angle mismatch (Lemma \ref{['prop_Dphi']}) and for both range and angle mismatches (Lemma \ref{['prop_dr_dphi']}) versus the BS-UE distance $r_0$ in meters for $\phi=\pi/4$ and the DMA parameters at the BS in Fig. \ref{['fig:Dr_limits']}.
  • Figure 4: The proposed non-uniform coordinate grid on the $xy$ plane where the UE moves, as implemented via Alg. \ref{['alg:sampling_proc']}, for a central point at the polar coordinates $\hat{r}=70$${\rm m}$ and $\hat{\phi} =\pi/4$, resolution $\delta\%=80\%$, and radius $\hat{c}=30$${\rm m}$. It is noted that, since $\sin(\phi_j) \to 0$ when $\phi_j \to 0$, the angular distances become wider in that regime, following the derived angular limits in \ref{['eq:Dphi']}, while for the presented radial distances in \ref{['eq:Dr']}, $\Delta^{\pm}_{\delta}(r_i)$ increases with increasing $r$.
  • Figure 5: UL and DL in TDD: (a) Conventional communication protocol where channel estimation is performed per TTI; and (b) Proposed communication protocol where channel estimation takes places according to the effective beam coherence time, which changes dynamically depending on the beamforming loss parameter $\kappa$. In this example, $T_{{\rm c},\kappa\%}(t-1)$ represents the time elapsing between the $(t-1)$-th and $t$-th consecutive estimation slots with the proposed near-field beam tracking protocol, the former taking place during the $({\rm t}-1)$-th TTI and the latter during the $({\rm t}+\lfloor T_{{\rm c},\kappa\%}(t-1)/{\rm TTI}\rfloor)$-th TTI.
  • ...and 4 more figures

Theorems & Definitions (10)

  • Proposition 1
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof