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EURASIP Journal on Wireless Communications and Networking

STAR-RIS-assisted key generation method in quasi-static environment

Yang Ma, Liquan Chen, Tianyu Lu, Yufan Song, Kailin Cao

Published Jul 15, 2024• 4 citations
Publisher

Abstract

Abstract In this paper, we introduce a new method to solve the low-entropy problem in a quasi-static environment. We utilize a simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS) that transmits and reflects incoming signals to users located on different sides of the surface. Specifically, we design the flow of multi-user channel probing when STAR-RIS is assisted, analyze and derive the analytical expression of the secret key capacity (SKC) of STAR-RIS-assisted system from the perspective of information theory, and finally analyze how to maximize the SKC and sum of all users under three different working protocols of STAR-RIS. The simulation results show that: (1) STAR-RIS can achieve better SKC performance than the conventional reflection/transmission RIS; and (2) the SKC is determined by the number of STAR-RIS elements, correlation coefficient, pilot length and RIS-reflected channel quality, and the time switching protocol can obtain higher SKC than the energy splitting protocol and mode switching protocol.

DOI
10.1186/s13638-024-02388-y

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Abstract In this paper, we introduce a new method to solve the low-entropy problem in a quasi-static environment. We utilize a simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS) that transmits and reflects incoming signals to users located on different sides of the surface. Specifically, we design the flow of multi-user channel probing when STAR-RIS is assisted, analyze and derive the analytical expression of the secret key capacity (SKC) of STAR-RIS-assisted system from the perspective of information theory, and finally analyze how to maximize the SKC and sum of all users under three different working protocols of STAR-RIS. The simulation results show that: (1) STAR-RIS can achieve better SKC performance than the conventional reflection/transmission RIS; and (2) the SKC is determined by the number of STAR-RIS elements, correlation coefficient, pilot length and RIS-reflected channel quality, and the time switching protocol can obtain higher SKC than the energy splitting protocol and mode switching protocol.
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.
To address the problem of low secret key rate (SKR) for quasi-static environments, a secret key generation protocol assisted by Reconfigurable Intelligent Surface (RIS) and artificial noise is proposed. On the one hand, RIS is used to construct the fast-changing channel, and on the other hand, artificial noise is designed to disturb the eavesdropper, both of which boost the SKR. Then, the closed-form expressions for the lower and upper bounds of the secret key capacity of the protocol are derived. Based on this expression, the impact of pilot and artificial noise power allocation on the key capacity is analyzed and the pilot power ratio is optimized. In addition, the influences of RIS elements number, channel correlation coefficient and pilot length on the SKR are further analyzed. Finally, the simulation analysis shows that compared to existing works, the proposed protocol reduces information leakage and further increases the SKR.
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.
We propose a key generation protocol with the aid of a reconfigurable intelligent surface (RIS) to boost secret key rate (SKR) in quasi-static environments. Considering a passive eavesdropper, we derive the closed-form expression of the lower and upper bounds of the SKR. Our findings indicate the SKR is determined by the number of RIS elements, the correlation coefficient, the pilot length and the quality of the reflecting channel. Our protocol fully exploits the randomness from the direct channel and the reflecting channel. Monte Carlo simulations validate the analytical expression of the SKR and demonstrate our protocol outperforms existing work.
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.
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.