Near-Field Secure Beamfocusing With Receiver-Centered Protected Zone

TL;DR

This paper addresses secure near-field communications by leveraging a Receiver-Centered Protected Zone (RCPZ) and, when a physical zone is unavailable, a virtual protected zone via a full-duplex receiver (RCVPZ). It formulates a nonconvex max-min secrecy problem with and without artificial noise and develops a synchronous gradient descent-ascent (SGDA) framework to approximate the global maximin solution, complemented by a low-complexity Equal-SINRs/Equal-SNRs design. The work demonstrates that intentional beamfocusing, in conjunction with receiver-centered protection, substantially improves worst-case secrecy performance across various geometries, while the RCVPZ setup highlights the importance of self-interference cancellation. The proposed methods offer practical, scalable strategies for securing near-field wireless links in large antenna-array systems, with clear guidance on complexity-resolution tradeoffs and robustness considerations.

Abstract

This work studies near-field secure communications through transmit beamfocusing. We examine the benefit of having a protected eavesdropper-free zone around the legitimate receiver, and we determine the worst-case secrecy performance against a potential eavesdropper located anywhere outside the protected zone. A max-min optimization problem is formulated for the beamfocusing design with and without artificial noise transmission. Despite the NP-hardness of the problem, we develop a synchronous gradient descent-ascent framework that approximates the global maximin solution. A low-complexity solution is also derived that delivers excellent performance over a wide range of operating conditions. We further extend this study to a scenario where it is not possible to physically enforce a protected zone. To this end, we consider secure communications through the creation of a virtual protected zone using a full-duplex legitimate receiver. Numerical results demonstrate that exploiting either the physical or virtual receiver-centered protected zone with appropriately designed beamfocusing is an effective strategy for achieving secure near-field communications.

Figures (7)

• Figure 1: The considered near-field communication system where Alice is equipped with a UPA, Bob is surrounded by an RCPZ, and Eve is located anywhere outside the RCPZ.
• Figure 2: The impact of beamfocusing and beam nulling on information signal and AN signal transmissions, respectively.
• Figure 3: Worst-case secrecy capacity versus the security radius: a) Bob is located at $\mathbf{p}_{\rm B} = \left(0,0,10\right)$; b) Bob is located at $\mathbf{p}_{\rm B} = (5\sqrt{2}/2,5\sqrt{6}/2,5\sqrt{2})$ with the spherical coordinate $\left(\rho_{\rm B},\theta_{\rm B},\phi_{\rm B}\right) = \left(10,60^\circ,45^\circ\right)$.
• Figure 4: Worst-case secrecy capacity versus the distance between Alice and Bob when $R_{\rm S} = 3\,{\rm m}$: a) Bob is located at $\mathbf{p}_{\rm B} = \left(0,0,d_{\rm AB}\right)$; b) Bob is located at the spherical coordinate $\left(\rho_{\rm B},\theta_{\rm B},\phi_{\rm B}\right) = \left(d_{\rm AB},60^\circ,45^\circ\right)$.
• Figure 5: Minimum secrecy capacity with multiple non-colluding eavesdroppers: a) Bob is located at $\mathbf{p}_{\rm B} = (5\sqrt{2}/2,5\sqrt{6}/2,5\sqrt{2})$ with the spherical coordinate $\left(\rho_{\rm B},\theta_{\rm B},\phi_{\rm B}\right) = \left(10,60^\circ,45^\circ\right)$; b) Bob is located at the spherical coordinate $\left(\rho_{\rm B},\theta_{\rm B},\phi_{\rm B}\right) = \left(d_{\rm AB},60^\circ,45^\circ\right)$ with $R_{\rm S} = 3\,{\rm m}$.

Theorems & Definitions (9)

• Proposition 1
• proof
• Proposition 2
• proof
• Remark 1
• Proposition 3
• proof
• Remark 2
• Remark 3