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arXiv:2303.12455 · IEEE Transactions on Communications

Reconfigurable Intelligent Surface-Aided Secret Key Generation in Multi-Cell Systems

Lei Hu, Chen K. Sun, Guyue Li, Aiqun Hu, Derrick Wing Kwan Ng

Published Aug 2, 2023• 10 citations
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Abstract

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.

DOI
10.1109/tcomm.2023.3301048

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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.
Physical layer key generation (PLKG) is a promising technique to establish symmetric keys between resource-constrained legitimate users. However, PLKG suffers from a low key rate in harsh environments where channel randomness is limited. To address the problem, reconfigurable intelligent surfaces (RISs) are introduced to reshape the channels by controlling massive reflecting elements, which can provide more channel diversity. In this paper, we design a channel probing protocol to fully extract the randomness from the cascaded channel, i.e., the channels through reflecting elements. We derive the analytical expressions of the key rate and design a water-filling algorithm based on the Karush-Kuhn-Tucker (KKT) conditions to find the upper bound. To find the optimal precoding and phase shift matrices, we propose an algorithm based on the Grassmann manifold optimization methods. The system is evaluated in terms of the key rate, bit disagreement rate (BDR) and randomness. Simulation results show that our protocols significantly improve the key rate as compared to existing protocols. Compared to multiple-antennas systems without a RIS, our proposed method achieves an average 9.51 dB performance gain when the side length of an element is 1/4 wavelength and the Rician factor is 0 dB.
Abstract Reconfigurable intelligent surface (RIS)‐assisted physical layer key generation plays an important role in the eavesdropping problem on a typical multi‐user scenario of wireless networks. Existing RIS‐assisted physical key generation technology mainly solved the security issues in the single‐antenna and multi‐user scenario, which is based on the idealistic assumption of a spatially independent channel model at the RIS. It limits the degrees of freedom and neglects the existence of channel spatial correlation, which would possibly degrade the sum key generation rate (SKGR). To solve the above problem, this paper proposes a secret key generation scheme for RIS‐assisted multiple‐input single‐output multi‐user system. This scheme establishes a spatial correlation channel model, which comprehensively considers the influence of spatial correlation among antennas of the base station (BS), multi‐user, and RIS elements on SKGR. Based on this, a key generation framework is designed to generate a more secure secret key with the maximum SKGR. Specifically, a closed‐form SKGR expression and an optimization problem formulation are obtained to obtain the joint optimal coefficient of the BS and RIS. Then, the difference convex‐successive convex approximation based alternating optimization algorithm is proposed to solve this optimization problem. The simulation results show that the proposed scheme has improved 10‐bit/channel use compared with the randomization scheme of BS precoding and RIS reflection coefficient. It also has an improvement of 12‐bit/channel use compared with the spatially independent scheme.
Channel reciprocity-based key generation (CRKG) has recently emerged as a new technique to address the problem of key distribution in wireless networks. However, as this approach relies upon the characteristics of fading channels, the corresponding secret key rate may be low when the communication link is blocked. To enhance the applicability of CRKG in harsh propagation scenarios, this paper introduces a novel multiuser key generation scheme, which is referred to as RIS-assisted multiuser key generation (RMK) that leverages the reconfigurable intelligent surface (RIS) technology for appropriately shaping the environment and enhancing the sum secret key rate between an access point and multiple users. In the RMK scheme, an RIS-induced channel, rather than the direct channel, serves as the key source. We derive a general closed-form expression of the secret key rate and optimize the configuration of the RIS to maximize the sum secret key rate over independent and correlated fading channels in the presence of multiple users. In the presence of independent fading, we introduce a low-complexity algorithm based on the Karush-Kuhn-Tucker (KKT) condition. In the presence of correlated fading, the optimization problem is non-convex and challenging to solve. To tackle it, we propose a new optimization algorithm based on the semi-definite relaxation (SDR) and successive convex approximation (SCA) methods. Simulation results demonstrate that the proposed RMK scheme outperforms existing RIS-assisted algorithms and achieves a near-optimal sum secret key rate over independent and correlated fading channels.
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.
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.
Reconfigurable intelligent surface (RIS) is a promising technique to enhance the performance of physical-layer key generation (PKG) due to its ability to smartly customize the radio environments. Existing RIS-assisted PKG methods are mainly based on the idealistic assumption of an independent and identically distributed (i.i.d.) channel model at both the transmitter and the RIS. However, the i.i.d. model is inaccurate for a typical RIS in an isotropic scattering environment. Also, neglecting the existence of channel spatial correlation would degrade the PKG performance. In this paper, we establish a general spatially correlated channel model in multi-antenna systems and propose a new PKG framework based on the transmit and the reflective beamforming at the base station (BS) and the RIS. Specifically, we derive a closed-form expression for characterizing the key generation rate (KGR) and obtain a globally optimal solution of the beamformers to maximize the KGR. Furthermore, we analyze the KGR performance difference between the one adopting the assumption of the i.i.d. model and that of the spatially correlated model. It is found that the beamforming designed for the correlated model outperforms that for the i.i.d. model while the KGR gain increases with the channel correlation. Simulation results show that compared to existing methods based on the i.i.d. fading model, our proposed method achieves about 5 dB performance gain when the BS antenna correlationρ\rhoρis 0.3 and the RIS element spacing is half of the wavelength.