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IEEE Transactions on Communications

Hybrid Beamforming Assisted OTFS-Based CV-QKD Systems for Doubly Selective THz Channels

Xin Liu, Chao Xu, Stephen Wang, Soon Xin Ng, Lajos Hanzo

Published Jul 3, 2025• 1 citation
Publisher

Abstract

Continuous-variable quantum key distribution (CV-QKD) maps information onto the quadrature components of electromagnetic waves, so that off-the-shelf wireless transceivers can be utilized. This motivates the move from optical to Terahertz (THz) bands. However, wireless THz channels suffer from severe path loss, while the mobility of wireless users imposes doubly selective fading. Against this background, we propose a new CV-QKD regime that relies on hybrid beamforming (HBF) assisted multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) system, where the channel’s transmissivity and robustness against double selectivity are overcome by HBF and OTFS, respectively. Secondly, in order to provide channel state information (CSI) for both the transmitter (CSI-T) and receiver (CSI-R), practical channel estimation methods are conceived. They operate in the time-frequency domain for OFDM and in the delay-Doppler domain for OTFS. Thirdly, soft-decision detection is devised for our MIMO OFDM/OTFS aided multi-dimensional reconciliation (MDR) scheme. Low-density parity-check (LDPC) coding is invoked for further improving secure CV-QKD transmission distance in the THz band. Our simulation results demonstrate that the proposed HBF MIMO OTFS-based CV-QKD system relying on realistic estimated CSI is capable of achieving an adequate secret key rate (SKR) and secure transmission distance in hostile doubly selective THz channels.

DOI
10.1109/tcomm.2025.3585501

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Continuous-variable quantum key distribution (CV-QKD) maps information onto the quadrature components of electromagnetic waves, so that off-the-shelf wireless transceivers can be utilized. This motivates the move from optical to Terahertz (THz) bands. However, wireless THz channels suffer from severe path loss, while the mobility of wireless users imposes doubly selective fading. Against this background, we propose a new CV-QKD regime that relies on hybrid beamforming (HBF) assisted multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) system, where the channel’s transmissivity and robustness against double selectivity are overcome by HBF and OTFS, respectively. Secondly, in order to provide channel state information (CSI) for both the transmitter (CSI-T) and receiver (CSI-R), practical channel estimation methods are conceived. They operate in the time-frequency domain for OFDM and in the delay-Doppler domain for OTFS. Thirdly, soft-decision detection is devised for our MIMO OFDM/OTFS aided multi-dimensional reconciliation (MDR) scheme. Low-density parity-check (LDPC) coding is invoked for further improving secure CV-QKD transmission distance in the THz band. Our simulation results demonstrate that the proposed HBF MIMO OTFS-based CV-QKD system relying on realistic estimated CSI is capable of achieving an adequate secret key rate (SKR) and secure transmission distance in hostile doubly selective THz channels.
The feasibility of continuous variable quantum key distribution (CV-QKD) is considered in the Terahertz (THz) band, experiencing time-varying and frequency-selective fading. Advanced multi-carrier modulation is required for improving the secret key rate (SKR). However, the hostile quantum channel requires powerful classical channel coding schemes for maintaining an adequate reconciliation performance. Against this background, for the first time in the open literature, we propose a multi-carrier quantum transmission regime that incorporates both orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) transmission over doubly selective fading THz channels. Furthermore, we propose a modified multi-dimensional reconciliation algorithm for CV-QKD, facilitating the integration of OFDM/OTFS quantum transmission with low-density parity check (LDPC) coded key reconciliation. Moreover, we harness multiple-input multiple-output (MIMO) beamforming for mitigating the severe THz path loss. Our SKR analysis results demonstrate that the proposed OTFS-based and LDPC-assisted CV-QKD system is capable of outperforming its OFDM counterpart in mobile wireless scenarios. Moreover, we also demonstrate that increasing the MIMO dimension reduces the transmission power required for achieving the secure transmission distance target.
Continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) offers robust protection against side-channel and detector manipulation attacks by outsourcing the detection process to a third party. In this work, we propose a multiple-input multiple-output (MIMO) CV-MDI-QKD system for time-varying and frequency-selective fading terahertz (THz) channels based on orthogonal time frequency space. The information bit mapping symbols are mapped into a two-dimensional plane in the 'delay-Doppler domain,' enhancing resistance to multi-path and Doppler effects, without relying on trusted measurement devices. Moreover, we increase the secret key rate and transmission distance by leveraging MIMO beamforming to mitigate free-space path loss at high THz frequencies. We calculate the secret key rate under a framework of strict composable security, including finite-size effects. Simulation results verify that by integrating OTFS modulation with MIMO beamforming, the proposed system achieves higher secret key rates and longer secure transmission distances, while maintaining strong security against optimal collective Gaussian attacks. This work is of great significance in driving the advancement of wireless communication technology in the 5G and post-5G eras.
Although quantum key distribution (QKD) enables information-theoretically secure key distribution, it is mainly designed for point-to-point communication and cannot directly support multi-user collaborative scenarios. To address this limitation, quantum secret sharing (QSS) has been proposed to enable secure multiparty key sharing. However, most existing QSS protocols rely on a single-input single-output (SISO) channel, which limits the achievable secret key rate (SKR) and transmission distance. This paper proposes a continuous-variable (CV) QSS protocol based on a multiple-input multiple-output (MIMO) architecture operating in the terahertz (THz) band. In the proposed scheme, transmit-receive beamforming decomposes the MIMO channel into multiple parallel SISO subchannels, thereby improving both the SKR and transmission distance. We describe the QSS transmission procedure and derive the SKR expressions for eight protocol variants under Gaussian collective attacks. Specifically, Gaussian modulation and passive modulation are considered at the transmitter, while homodyne and heterodyne detection are considered at the receiver. Both asymptotic and composable finite-size SKR formulas are derived to characterize the ideal upper-bound performance and the achievable performance under finite resources, respectively. Simulation results show that, under ideal assumptions including perfect channel state information, perfect phase synchronization, and ideal beamforming, the Gaussian-modulation protocol with a 32 x 32 antenna configuration and the passive-modulation protocol with a 1024 x 1024 antenna configuration achieve transmission distances of 14.99 m and 160 m in the atmospheric channel, respectively. These results provide an idealized theoretical benchmark for evaluating the potential performance gains of MIMO-assisted THz CV-QSS in indoor and short-range outdoor wireless networks.
Quantum key distribution (QKD) provides information-theoretic security by leveraging quantum mechanical principles, while Terahertz (THz) communications offer unprecedented data rates for next-generation networks. We sketch out an evolutionary pathway for bridging these domains by critically appraising THz-based continuous-variable QKD (CV-QKD) systems conceived for wireless environments like space-air-ground integrated networks (SAGINs) and vehicle-to-everything (V2X) scenarios, where time-varying frequency-selective fading poses critical challenges. To address these issues, we elaborate on the feasibility of THz based CV-QKD applications from a wireless perspective. Specifically, we commence by highlighting a typical CV-QKD protocol. Then present three sophisticated CV-QKD system designs.Firstly, we propose a codeword-based – rather than syndrome-based – reconciliation scheme capable of accommodating diverse forward error correction (FEC) codes, imposing a similar complexity on the transmitter and receiver. As a further improvement, we demonstrate that powerful irregular convolutional codes (IRCCs) attain a near-capacity performance, thus offering longer secure distance and/or improved secret key rate (SKR).Secondly, the secure boundaries derived for the optical and THz band – even down to microwave frequencies – demonstrate the feasibility of short-distance THz CV-QKD systems. Furthermore, multiple-input multiple-output (MIMO) schemes are harnessed for improving the SKR performance.Thirdly, an orthogonal time frequency space (OTFS) modem-based CV-QKD system is conceived for time-varying frequency-selective THz fading channels. Finally, we conclude by identifying several promising research directions for CV-QKD systems.
The feasibility of cost-effective simultaneous quantum and classical communication (SQCC) transmitting both the quantum key and classical information via a superimposed coherent state is investigated both in optical and Terahertz (THz) bands. Since the existing THz SQCC schemes assume single-carrier (SC) transmission over flat fading channels, we embark on investigating SQCC in realistic frequency-selective multipath THz fading channels. We then propose an orthogonal frequency division multiplexing (OFDM) based SQCC system for time-invariant frequency-selective THz scenarios, supported by low-density parity-check coded (LDPC) multidimensional QKD reconciliation schemes. Our simulation results demonstrate that the OFDM-based SQCC scheme is capable of achieving a practical secret key rate (SKR) over a wide range of power sharing scenarios between the classical and quantum signals. By contrast its single-carrier counterpart requires the classical signal to be at least 100 times stronger than the quantum signal in THz SQCC.
We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.