RIS-Assisted MIMO CV-QKD at THz Frequencies: Channel Estimation and SKR Analysis

TL;DR

This work tackles secure key distribution for THz RIS-aided MIMO wireless links using continuous-variable QKD. The authors implement a practical least-squares channel estimation at the receiver, enable CSI feedback to the transmitter, and analyze the secrecy performance under a collective Gaussian attack with an eavesdropped feedback channel. They derive a closed-form secret-key-rate expression that accounts for channel estimation overhead and the noise introduced by imperfect CSI, for both homodyne and heterodyne detection at the receiver, and they quantify the impact of RIS element count and phase configurations. Numerical results show that RIS can significantly boost SKR, especially at longer distances, and identify optimal RIS phase configurations that depend on pilot power and geometry, with heterodyne generally advantageous at lower pilot powers. Overall, the paper provides a tractable framework for designing RIS-assisted THz CV-QKD systems under realistic CSI imperfections and eavesdropping threats.

Abstract

In this paper, a multiple-input multiple-output (MIMO) wireless system incorporating a reconfigurable intelligent surface (RIS) to efficiently operate at terahertz (THz) frequencies is considered. The transmitter, Alice, employs continuous-variable quantum key distribution (CV-QKD) to communicate secret keys to the receiver, Bob, which utilizes either homodyne or heterodyne detection. The latter node applies the least-squared approach to estimate the effective MIMO channel gain matrix prior to receiving the secret key, and this estimation is made available to Alice via an error-free feedback channel. An eavesdropper, Eve, is assumed to employ a collective Gaussian entanglement attack on the feedback channel to avail the estimated channel state information. We present a novel closed-form expression for the secret key rate (SKR) performance of the proposed RIS-assisted THz CV-QKD system. The effect of various system parameters, such as the number of RIS elements and their phase configurations, the channel estimation error, and the detector noise, on the SKR performance are studied via numerical evaluation of the derived formula. It is demonstrated that the RIS contributes to larger SKR for larger link distances, and that heterodyne detection is preferable over homodyne at lower pilot symbol powers.

Figures (6)

• Figure 1: (a) The considered RIS-assisted MIMO CV-QKD wireless communication system at THz frequencies; (b) The feedback channel designed to transfer the estimated MIMO channel at Bob's side to Alice, which is eavesdropped by Eve.
• Figure 2: SKR versus the transmission distance between Alice and Bob for $N_{T}= N_{R}=\{32, 128, 256\}$, $f_c = 15$ THz, $K = 100$, and $\phi = \pi/4$, with Bob employing homodyne and heterodyne measurements for secret key detection.
• Figure 3: SKR versus the pilot power $V_p$ for $N_{T}= N_{R}= \{128, 256, 512\}$ MIMO configurations, $f_c = 15$ THz, $d=100$ m, $K = 100$, and $\phi = \pi/4$, with Bob employing homodyne and heterodyne measurements for secret key detection.
• Figure 4: SKR versus the pilot length $L_p$ for $N_{T}= N_{R}= \{32, 128, 256\}$ MIMO configurations, $f_c = 15$ THz, $d=30$ m, $K = 100$, $\phi = \pi/4$, with Bob employing homodyne and heterodyne measurements for secret key detection.
• Figure 5: SKR versus transmission distance $d$ between Alice and Bob for a $32 \times 32$ MIMO configuration, $f_c=15$ THz, $\phi = \pi/4$ for $K = \{25, 225, 400, 1600\}$ RIS elements, with homodyne detection at Bob's side.