Sensing-Aided Near-Field Beam Tracking

TL;DR

This work investigates sensing-aided near-field beam tracking for XL MIMO systems employing Dynamic Metasurface Antennas. It develops a closed-form correlation framework and depth-of-focus analysis to quantify beamforming gain loss under UE coordinate mismatches, introduces a dynamic non-uniform polar grid for efficient localization, and defines the beam coherence time to guide proactive beam tracking. An algorithmic framework combines localization, adaptive sampling, and hybrid analog-digital beamforming to maintain high beamforming gains with reduced overhead, even in the presence of microstrip losses. Simulations with randomized trajectories validate the theory and demonstrate substantial gains over baseline fixed-interval tracking, highlighting the practical impact for robust near-field communications and sensing.

Abstract

The interplay between large antenna apertures and high carrier frequencies in future wireless systems gives rise to near-field communications, where the curvature of spherical wavefronts renders traditional far-field beamforming models inadequate. This chapter addresses the following fundamental questions on near-field operation: (i) What is the maximum distance where far-field approximations remain effective for path gain prediction and beam design? (ii) What level of position resolution is needed for accurate near-field beam focusing? (iii) How frequently must channel state information be updated to maintain highly directive bweamforming in dynamic scenarios? We develop an analytical framework for assessing near-field beamforming gain degradation due to mismatches between the focusing point and the coordinates of a user. Closed-form expressions for beam correlation, beam sensitivity to user movement, and the direction of fastest beamforming gain degradation are derived. A dynamic polar coordinate grid is also proposed for low complexity and adaptive near-field beam search. Furthermore, we introduce the novel concept of beam coherence time, quantifying the temporal robustness of focused beams and enabling proactive sensing-aided beam tracking strategies. The effect of microstrip losses on the preceding derivations is also analyzed. Finally, extensive simulation results validate the presented theoretical analysis and beam tracking method over randomly generated user trajectories.

Figures (8)

• Figure 1: The considered system model comprising a static BS equipped with a DMA lying in the $xz$-plane and a mobile single-antenna UE moving inside the $xy$-plane.
• Figure 2: The range mismatch limits $\Delta^{\pm}_{\kappa}(r)$ for $\kappa=50$ are illustrated for three microstrip attenuation cases: i) lossless $\alpha=0$ (solid lines), ii) Duroid 5880 with $\alpha = 0.7381\,\text{m}^{-1}$ (dashed lines with triangle markers), and iii) RO 3003 with $\alpha = 0.8629\,\text{m}^{-1}$ (dashed lines with circle markers). The comparison is conducted for increasing number of antenna elements per microstrip, $N_e \in [200, 10^4]$, which effectively extends the DMA length, leading to more elements being significantly attenuated. The setup includes a DMA at the BS with $N_m = 10$, $d_e = d_m = \lambda/2$, where $\lambda = 1\,\text{cm}$, and fixed values $r = 28\,\text{m}$, $\phi = \pi/4$ (rad), and $z_0 = -0.5(N_e - 1)d_e = -0.5\,\text{m}$. The left vertical axis shows the values of $\Delta^{-}_{\kappa}(r)$, while the right vertical axis shows $\Delta^{+}_{\kappa}(r)$. For all considered cases, when $N_e \geq 800$, the plus and minus range mismatch limits converge, that is, $\Delta^{+}_{\kappa}(r) = \Delta^{-}_{\kappa}(r)$. This convergence is not clearly visible in the main plot due to the different scaling of the right and left vertical axes, but it becomes evident in the inset, where both limits are plotted against a common vertical axis.
• Figure 3: The relative beamforming gain for only range mismatch (left vertical axis) and the range mismatch limits $\Delta^{\pm}_{\kappa}(r)$ in \ref{['eq: prop_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 $\lambda = 1\,\text{cm}$, and $z_0 = -0.5N_ed_e=-0.5\,\text{m}$. The blue and red error bars (i.e., shadowed areas) depict the range of values that the expressions $\frac{1}{N^2} |\mathbf{a}^{\rm H}(r,\phi)\mathbf{a}(r \pm \Delta^{\pm}_{50}(r),\phi) |^{2}$ take $\forall \phi \in [0,\pi]$, while the blue and red dashed lines depict the average values of these expressions with respect to $\phi$.
• Figure 4: The relative beamforming gains for only azimuth angle mismatch (Statement \ref{['box: Dphi beamfocusing']}) and for both range and angle mismatches (Statement \ref{['box: Dr and Dphi beamfocusing']}) versus the BS-UE distance $r_0$ (m) for $\phi=\pi/4$ (rad) and using the same DMA parameters as in Fig. \ref{['fig: Dr limits']}.
• Figure 5: The proposed non-uniform coordinate grid on the $xy$ plane where the UE moves, as implemented via Algorithm \ref{['alg:sampling_proc']}, for a central point at the polar coordinates $\hat{r}=70$${\rm m}$ and $\hat{\phi} =\pi/2$, resolution $\delta\%=80\%$, and radius $\hat{c}=30$${\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 $r$. The parameters of the DMA-based BS considered are the same as in Figs. \ref{['fig: Dr limits']}-\ref{['fig: Dr and Dphi limits']}.