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IEEE Transactions on Vehicular Technology

STAR-RIS-Assisted Physical-Layer Key Generation

Zheng Wan, Zheng Chu, De Mi, Hui‐Ming Wang, Liang Jin, Kaizhi Huang

Published Feb 5, 2024• 6 citations
Publisher

Abstract

This paper investigates the application of simultaneously transmitting and reflecting reconfigurable surface (STARRIS) in physical layer key generation (PKG), and proposes a novel STAR-RIS-assisted multiuser PKG framework. We formulate a sum secret key rate maximization problem for the proposed framework, by optimizing phase shift and amplitude coefficients for both independent and coupled phase-shift models. To tackle this non-convex problem, we derive the optimal phase shift in the closed form and demonstrate that the coupled phase shifts do not compromise key generation performance. The original problem is thus simplified into an optimization of amplitude coefficients, for which we use the alternating optimization scheme. Simulation results validate the effectiveness of the proposed algorithm by comparing the key generation performance with that of STAR-RISs using the random configuration and conventional reflecting/transmitting-only RISs.

DOI
10.1109/tvt.2024.3362052

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arXiv:2303.12455•IEEE Transactions on Communications•Aug 2, 2023•10 citations
This paper investigates the application of simultaneously transmitting and reflecting reconfigurable surface (STARRIS) in physical layer key generation (PKG), and proposes a novel STAR-RIS-assisted multiuser PKG framework. We formulate a sum secret key rate maximization problem for the proposed framework, by optimizing phase shift and amplitude coefficients for both independent and coupled phase-shift models. To tackle this non-convex problem, we derive the optimal phase shift in the closed form and demonstrate that the coupled phase shifts do not compromise key generation performance. The original problem is thus simplified into an optimization of amplitude coefficients, for which we use the alternating optimization scheme. Simulation results validate the effectiveness of the proposed algorithm by comparing the key generation performance with that of STAR-RISs using the random configuration and conventional reflecting/transmitting-only RISs.
This paper investigates the simultaneously transmitting and reflecting reconfigurable surface (STAR-RIS) assisted physical layer key generation (PKG) for multiuser networks. We propose a novel STAR-RIS-assisted PKG protocol and formulate a sum secret key rate maximization problem by jointly optimizing the active and passive beamforming. To address the non-convex problem, a block coordinate descent (BCD) algorithm is developed, using both semidefinite relaxation (SDR) and successive convex approximation (SCA) methods to optimize active and passive precoding alternately. Simulation results demonstrate the key generation performance of the proposed algorithm outperforms schemes that STAR-RISs using the random configuration and conventional reflecting/transmitting-only RISs.
Due to the limited coverage of reflecting-only reconfigurable intelligent surfaces (RIS), the existing RIS-assisted physical-layer key generation (PKG) scheme limits its overall performance in the full space. This paper proposes a novel simultaneously transmitting and reflecting (STAR)-RIS-assisted PKG protocol for multiple-input multiple-output (MIMO) systems, where the closed-form sum secret key rate is derived in the presence of full-space eavesdroppers. Two optimization problems are formulated to maximize the sum secret key rate by designing the transmit beamforming (TBF) and transmitting and reflecting coefficients (TRCs) for energy splitting (ES) with coupled phase-shift and mode switching (MS) mode. For ES mode with coupled phase-shift, a penalty-based alternating optimization (AO) algorithm is proposed to address its non-convexity. For MS mode, the semidefinite relaxation-successive convex approximation-based AO algorithm is utilized to achieve continuous solutions and then quantize to binary value for the MS mode. Simulation results demonstrate that the coupled phase-shift STAR-RIS incurs a slight KGR loss in comparison to the independent phase-shift STAR-RIS. Additionally, the ES mode outperforms the MS mode in terms of KGR performance. Finally, STAR-RIS can achieve a higher sum secret key rate than traditional reflecting-only RIS.
By exploiting the entropy of wireless channels, physical layer key generation (PLKG) has gained considerable attention in recent years. Due to the characteristic of dynamic controlling of wireless channels, reconfigurable intelligent surface (RIS) can improve the key generation rate (KGR). Simultaneous transmission and reflection reconfigurable intelligent surface (STAR- RIS) can extend the half-space coverage to full-space coverage. This paper proposes a STAR-RIS-assisted physical layer key generation (SRKG) scheme in a multi-user case. The objective is to maximize the sum KGR by jointly designing the transmitting and reflecting coefficients (TARCs). We propose an iterative algorithm based on alternating optimization (AO), utilizing successive convex approximation (SCA) and semi-definite relaxation (SDR) methods, to solve the non-convex optimization problem in the presence of correlated channels. We also propose a low-complexity algorithm based on Lagrange multipliers to jointly optimize TARCs considering independent fading. Finally, the simulation results validate that, compared with the PLKG scheme assisted by traditional RIS (T-RIS), the proposed SRKG scheme can achieve higher sum KGR in a wider range under correlated and independent channel conditions.
Physical-layer key generation (PLKG) is an information-theoretic security technique aimed at addressing key distribution challenges among resource-constrained legitimate users in the Internet of Things (IoT). However, in quasi-static or blocked environments, key generation faces significant limitations owing to its low entropy. To overcome this challenge, we propose leveraging a simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS). In this study, we introduce a STAR-RIS-aided multiuser PLKG framework and formulate an optimization problem focused on minimizing the average bit disagreement ratio through optimal phase-shift matrix adjustments. Initially, we derive closed-form solutions for optimal phase shifts, simplifying the problem to depend solely on amplitude coefficients. We then employ a Newton-Raphson algorithm under the energy-splitting (ES) protocol and a traversal method under the mode-switching (MS) and time-switching (TS) protocols to solve the optimization problem. Simulation results confirm the efficacy of our proposed schemes by comparison with existing benchmark schemes.
The artificial electromagnetic characteristics of reconfigurable intelligent surfaces (RIS) offers new opportunities to increase the secret key rate (SKR) in physical-layer key generation (PKG). However, the existing literature has primarily focused on continuous phase shift designs for RIS to enhance the SKR, while in practice the phase shifts are discrete due to hardware implementations. Hence, the extent to which practical RIS with discrete phase shifts can enhance SKR remains uncertain. Moreover, we have observed that existing optimization methods are not directly applicable to RIS with discrete phase shifts and relying solely on the approximation projection algorithm may lead to certain SKR performance degradation. To address these problems, this paper proposes a RIS-assisted PKG model considering the impact of discrete RIS phase shifts. To maximize the SKR by properly designing the RIS phase shifts, we propose an algorithm utilizing linear conic reformulation (LCR) with alternating difference-of-convex (DC) programming and successive convex approximation (SCA). Simulation results unveil that the proposed LCR-DC algorithm has the capability to achieve the SKR close to the optimal solutions. Furthermore, increasing the number of RIS elements or the number of quantization bits for RIS phase shifts enhances SKR but with diminishing returns. It is worth noting that a small number of discrete phase shifts, e.g., 2-3 quantization bits, is generally sufficient to achieve satisfactory SKR performance.
Physical-layer key generation (PKG) exploits the reciprocity and randomness of wireless channels to generate a symmetric key between two legitimate communication ends. However, in multi-cell systems, PKG suffers from severe pilot contamination due to the reuse of pilots in different cells. In this paper, we invoke multiple reconfigurable intelligent surfaces (RISs) for adaptively shaping the environment and enhancing the PKG performance. To this end, we formulate an optimization problem to maximize the weighted sum key rate (WSKR) by jointly optimizing the precoding matrices at the base stations (BSs) and the phase shifts at the RISs. To address the non-convexity of the problem, we adopt an alternating optimization (AO)-based algorithm that divides the joint optimization problem into two subproblems. For the subproblem of precoding matrices, we apply the Lagrangian dual approach based on the Karush-Kuhn-Tucker (KKT) conditions. As for the subproblem of phase shifts, we adopt a projected gradient ascent (PGA) algorithm. Simulation results validate the effectiveness of the proposed scheme, demonstrating significant gains in WSKR. Moreover, compared with a single-RIS case, deploying multiple RISs offer spatial diversity so as to improve the PKG performance of multicell systems.