Near-Field Beampointing with Low Exposure Regions: a Dominant Subspace Projection Approach

TL;DR

This work tackles near-field beampointing under a two-dimensional low exposure region constraint by discretizing the region into many sample points, which is computationally prohibitive under standard optimization. It introduces Dominant Subspace Projection (DoSP), a low-rank approach that uses the SVD of the constraint matrix $oldsymbol{A}$ to form a dominant subspace and solve a reduced-dimension beamformer by projecting the user steering vector off this subspace. The method achieves near-optimal user power $P_ ext{us}$ while strictly limiting power within the continuous LER, with markedly lower computational complexity than a full IP/SOCP solution and better continuous-LER behavior than prior low-complexity baselines. Numerical results on XL-MIMO NF scenarios show DoSP provides strong performance-complexity trade-offs and enables real-time NF beampointing with high-frequency arrays. The approach offers practical benefits for protecting sensitive regions and enabling dynamic, 2D NF beam control in dense urban or indoor environments.

Abstract

The spherical nature of the wavefronts exhibited in the near-field of antenna arrays enables advanced beamforming capabilities, such as beampointing and beamnulling. In this paper, we exploit these properties to design a near-field beam pattern under a low exposure region constraint. We address the continuous region constraint through spatial discretization, which results in a large number of constraints that lead to prohibitive computational complexity. We propose a novel low-complexity algorithm that enables a computationally tractable beam pattern design. It uses a low-dimensional subspace representation of the low exposure region based on a singular value decomposition. Our approach achieves low complexity while providing a power received at a target user close to the optimal achievable power, yet with uniform power mitigation over the low exposure region.

Figures (6)

• Figure 1: Scenario
• Figure 2: Singular values of $\mathbf{A}$ in a decreasing order, for a rank $r=N=1000$.
• Figure 3: The power $\underset{q}{\max} \: |\widehat{\mathbf{w}}_k^H\mathbf{a}_q|^2$ is the maximum power (compared to MRT) received across all sampled positions of the LER, with a precoding vector $\widehat{\mathbf{w}}$ computed with $k$ basis vectors. In this example, $t=-80$ dB compared to MRT, and the start value is $k_\textrm{init}=156$.
• Figure 4: Beam pattern compared to MRT (in dB). The user location and the LER delimitation are indicated as the black dot and black rectangle, respectively.
• Figure 5: Achievable $P_\textrm{us}$ compared to MRT (in dB), with respect to the user position. The LER is indicated in black and is located in $[2000\lambda; 2200\lambda] \times [0; 500\lambda]$ (left) and $[900\lambda; 1100\lambda] \times [-100\lambda; 100\lambda]$ (right).