Pearcey-Inspired Quartic Wavefront Shaping for Obstructed Near-Field Multi-User Communications

Abstract

Radiative near-field (RNF) beamforming is vulnerable to blockages that disrupt Fresnel zones. This letter proposes an obstruction-unaware wavefront shaping strategy inspired by catastrophe optics. By superimposing a calibrated quartic phase, we generate a Pearcey-like wave packet that exhibits structural stability against perturbations. We establish a fair comparison protocol where the quartic beam is calibrated in free space to avoid exploiting obstruction knowledge. Numerical results demonstrate up to 8.5~dB SINR gain over conventional focusing for multi-user scenarios near the depth-of-focus limit. Crucially, this gain stems from improved channel conditioning under partial blockage, which mitigates the severe noise amplification inherent to zero-forcing precoding.

Figures (4)

• Figure 1: System geometry illustrating the ULA with aperture $D = N_{\text{elem}} d$, the two co-angular users $\text{UE}_1$ and $\text{UE}_2$ separated by $\Delta z$, and the finite obstruction of width $2W_{\text{obs}}$ located at $z_{\text{obs}}$.
• Figure 2: Free-space axial intensity profiles ($|E(0,z)|^2$) of the calibrated Pearcey-inspired quartic beam under varying quartic phase strengths $\Delta\phi_{4,\text{edge}} \in \{0.5\pi, \pi, 1.5\pi, 2\pi\}$, normalized to the diffraction-limited baseline peak (blue solid). The blind calibration successfully aligns the focus to $z_1=150\lambda$ for all cases. As the edge phase swing increases to $2\pi$, the peak intensity exhibits a progressive penalty ($\approx 1.0$ dB), reflecting the energy redistribution into the caustic wings that confers self-healing capability.
• Figure 3: Performance comparison versus normalized obstruction width $W_{\text{obs}}/r_F$ for $\mu \in \{0.5, 1.0, 2.0\}$. (a) Common SINR gain $\Delta\mathrm{SINR}_\mathrm{dB}$ of the Pearcey-inspired quartic beam over baseline, with star markers ($\bigstar$) indicating the exact 0 dB crossover thresholds extracted by linear interpolation. (b) Channel condition number ratio $\kappa_A/\kappa_P$, illustrating how the Pearcey wavefront mitigates ill-conditioning caused by Fresnel-zone blockage.
• Figure 4: Heatmap of the SINR advantage ($\Delta\mathrm{SINR}_{\mathrm{dB}}$) of the proposed Pearcey-inspired quartic beam over baseline, over the $(\mu,\, W_{\text{obs}}/r_F)$ plane. The bold black contour is the 0 dB break-even boundary; green dashed contours mark the 2, 5, and 8 dB levels. A mild Gaussian smoothing ($\sigma=1.5$ grid units) is applied to the displayed heatmap to reveal the underlying trend; residual oscillation of the 0 dB contour along the $\mu$ axis reflects the axial Fresnel periodicity discussed in Sec. \ref{['sec:results']}.A.