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IEEE Internet of Things Journal

Phase-Shift Matrices Optimization in STAR-RIS-Aided Physical-Layer Key Generation

Yufan Song, Liquan Chen, Jiaorui Shen, Peng Zhang, Qingyao Gu

Published Sep 4, 2024• 5 citations
Publisher

Abstract

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.

DOI
10.1109/jiot.2024.3454291

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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.
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.
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.
The key generation rate (KGR) of physical layer key generation (PLKG) is severely restricted in quasi-static environments due to a lack of entropy. To address the problem, a reconfigurable intelligent surface (RIS) is introduced. In this letter, we consider the design of phase shift matrix with vector quantization to fully exploit the randomness of the RIS. In order to reduce the bit disagreement ratio (BDR), we design a vector quantizer to fully exploit the quantization range of the RIS channel. Additionally, we provide the design strategy for the phase shift matrix that aligns with the vector quantizer. Furthermore, we present a closed-form solution for the phase shift matrix. Meanwhile, to balance the tradeoff between high KGR and low BDR, we calculate the BDR in different quantization orders and propose an adaptive quantization order selection. Simulations validate that our proposed scheme obtain a higher KGR than the existing schemes under a certain BDR threshold.
Abstract In quasi-static environment, the performance of physical-layer key generation (PKG) is limited by low entropy. Deploying reconfigurable intelligent surface (RIS) is a mainstream method to solve this problem. However, the secret key performance (SKP) is generally insufficient at low signal-to-noise ratio (SNR). In this paper, we propose an RIS-assisted adaptive PKG scheme. Specifically, we design phase based uniform quantization to enhance the randomness of the RIS channel while simplifying computations. Then, we present an RIS phase shift matrix design based on rejection sampling to adapt the quantization algorithm, which can reduce bit disagreement rate (BDR) and improve key generation rate (KGR). Furthermore, to balance the system’s requirements for low BDR and high KGR, we derive a theoretical model for estimating the BDR probability. By computing the theoretical BDR, we determine the maximum quantization order for different SNRs. Combined with a discard strategy, this enables adaptive selection of the quantization order. Simulation results demonstrate that the proposed scheme achieves lower BDR and higher KGR than existing approaches. Moreover, it does not require complex algorithms, making it suitable for resource-constrained internet of things scenarios. (RIS_Assist_PKG: https://github.com/GQQ1206/RIS_Assist_PKG )
In quasi-static environments, the key generation rate (KGR) of wireless physical layer key generation (PLKG) can be greatly limited. In this paper, we aim to improve the KGR by reconfigurable intelligent surface (RIS) and jointly design the quantizer and phase shift matrix. We give a reconfiguration strategy able to quantify both real and imaginary parts at the same time and give its closed-form solution of the phase shift matrix. To reduce the bit disagreement ratio (BDR), we design a quantizer suitable for RIS-assisted PLKG which uses non-uniform quantization. To achieve high KGR while maintain low BDR, we analyze the BDR in different quantization levels and realize an adaptive quantization selection. Meanwhile, the simulation results verify that the KGR of the proposed scheme is more than twice that of the existing scheme under a certain BDR threshold.
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.