A Key Generation Method Based on Atomic Norm Minimization For Reconfigurable Intelligent Surface-Assisted Millimeter Wave MIMO Communication Systems

YANG Lijun; KONG Wenjie; LU Haitao; QI Jin

doi:10.11999/JEIT240885

Volume 47 Issue 4

Apr. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(4): 1066-1075

YANG Lijun, KONG Wenjie, LU Haitao, QI Jin. A Key Generation Method Based on Atomic Norm Minimization For Reconfigurable Intelligent Surface-Assisted Millimeter Wave MIMO Communication Systems[J]. Journal of Electronics & Information Technology, 2025, 47(4): 1066-1075. doi: 10.11999/JEIT240885

Citation:

YANG Lijun, KONG Wenjie, LU Haitao, QI Jin. A Key Generation Method Based on Atomic Norm Minimization For Reconfigurable Intelligent Surface-Assisted Millimeter Wave MIMO Communication Systems[J]. Journal of Electronics & Information Technology, 2025, 47(4): 1066-1075. doi: 10.11999/JEIT240885

Citation:

YANG Lijun, KONG Wenjie, LU Haitao, QI Jin. A Key Generation Method Based on Atomic Norm Minimization For Reconfigurable Intelligent Surface-Assisted Millimeter Wave MIMO Communication Systems[J]. Journal of Electronics & Information Technology, 2025, 47(4): 1066-1075. doi: 10.11999/JEIT240885

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A Key Generation Method Based on Atomic Norm Minimization For Reconfigurable Intelligent Surface-Assisted Millimeter Wave MIMO Communication Systems

doi: 10.11999/JEIT240885 cstr: 32379.14.JEIT240885

YANG Lijun¹,
KONG Wenjie¹,
LU Haitao^{2, 3},
QI Jin^{1
,
,}

1.
School of Internet of Things, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
2.
ZTE Corporation, Shenzhen 518057, China
3.
Shenzhen Key Laboratory of 5G RAN Security Technology Research and Application, Shenzhen 518055, China

Funds: The National Natural Science Foundation of China (62372244, 62172235), The ZTE Industry-university-Research Fund (2023ZTE08-02), The National Key Research and Development Program of China (2021YFB3101100), The Primary Research & Developement Plan of Jiangsu Province (BE2023025), The Natural Science Foundation of Nanjing University of Posts and Telecommunications (NY222132), The Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX23_1056)

Received Date: 2024-10-21
Rev Recd Date: 2025-04-02

Available Online: 2025-04-08

Publish Date: 2025-04-01

Abstract

Abstract

Objective The reciprocity, time variability, and unpredictability of wireless channels enable physical-layer key generation, a promising technology for B5G/6G systems due to its independence from third-party involvement and inherent quantum-resistant properties. In millimeter-wave Multiple Input Multiple Output (MIMO) systems, channel sparsity imposes stringent constraints on key capacity, particularly in quasi-static propagation environments. While Reconfigurable Intelligent Surface (RIS) technology enhances channel time variability and increases key capacity, it also leads to an exponential increase in pilot overhead with the number of transceiver antennas and RIS elements. To mitigate pilot overhead, Compressive Sensing (CS) techniques have been employed by leveraging channel sparsity and reformulating channel estimation as a sparse signal recovery problem. However, existing CS-based key generation schemes require prior knowledge of channel sparsity, which may not reflect actual dynamic channel conditions. Additionally, these approaches typically rely on grid-based discrete modeling, where Angles of Departure (AoDs) and Angles of Arrival (AoAs) are quantized into predefined grids, leading to key mismatches. To address these challenges, this study proposes an RIS-assisted key generation scheme based on Atomic Norm Minimization (ANM) for RIS-assisted millimeter-wave MIMO systems. Methods The proposed method presents a novel key extraction approach based on virtual AoDs and virtual AoAs for RIS-assisted millimeter-wave MIMO systems. First, the problem of virtual channel parameter estimation in RIS-assisted millimeter-wave MIMO cascaded channels is formulated as a continuous sparse signal recovery problem. An optimization problem is then constructed using ANM, where ANM serves as the objective function and pilot observation error as the constraint. The Multiple Signal Classification (MUSIC) algorithm is integrated to enhance channel sparsity and achieve super-resolution angle estimation, thereby extracting high-precision virtual AoDs and AoAs as key parameters. Based on these parameters, a comprehensive key generation scheme is proposed, incorporating quantization, information reconciliation, and privacy amplification. Additionally, the key capacity of the proposed scheme is theoretically derived, with a closed-form expression provided based on the distribution of virtual AoDs/AoAs. Finally, Monte Carlo simulations are conducted to validate the effectiveness of the proposed scheme. Comparative analysis with existing schemes demonstrates its advantages in terms of key inconsistency, mutual information per bit, key generation rate, and pilot overhead. Results and Discussions Analysis of the simulation results indicates that the proposed scheme improves pilot overhead, Bit Disagreement Rate (BDR), mutual information per bit, and Secret Key Rate (SKR). These metrics primarily assess channel information extraction and key generation performance. For channel estimation accuracy, the Normalized Mean Square Error (NMSE) of the estimated virtual angles is used as an evaluation metric, where a lower NMSE indicates higher accuracy. Compared to other schemes, the proposed approach consistently achieves a lower NMSE, particularly for short pilot lengths. Even with $ {N_{\text{p}}} = 4 $, the NMSE remains below 0.1 (Fig. 3), demonstrating superior handling of sparse signals. This contributes to reduced pilot overhead and improved estimation accuracy. Key generation performance is evaluated using BDR, mutual information per bit, and SKR. Compared to schemes using the channel response matrix, employing virtual AoAs and AoDs as random keys results in a lower BDR (Fig. 4) and higher bit-wise mutual information (Fig. 6) across various Signal-to-Noise Ratio (SNR) conditions, demonstrating robustness in both high and low SNR environments. This advantage arises from the inherent sparsity of millimeter-wave channels, where primary propagation paths are clearly distinguishable. Unlike the channel response matrix, angle information is less susceptible to environmental factors and minor physical variations, providing a more stable key source. Compared with traditional CS-based schemes, the proposed approach overcomes grid constraints, reducing the key inconsistency rate by 47.7% under low SNR conditions (5 dB). Additionally, when the number of propagation paths remains constant, BDR decreases as the number of antennas increases. Conversely, when the number of antennas is fixed, BDR increases as the number of paths (L) grows (Fig. 5). This occurs because a higher number of paths increases the complexity of distinguishing AoAs and AoDs, leading to greater estimation error. Furthermore, a larger number of paths generates more key bits, causing BDR accumulation across paths, which raises the overall BDR. However, as the number of antennas increases, the sparsity of millimeter-wave MIMO channels becomes more pronounced (L is smaller), further amplifying the advantages of the proposed scheme. Additionally, by utilizing virtual angles as the key source, the proposed scheme maintains a high SKR even under low SNR conditions, further demonstrating its potential for practical applications (Fig. 7). Conclusions The proposed method employs ANM to formulate the cascaded channel estimation problem between the Base Station (BS) and User Equipment (UE) as a gridless sparse signal recovery problem. By integrating the MUSIC algorithm, the method jointly estimates virtual AoDs and AoAs, overcoming traditional grid-based constraints and eliminating the explicit assumption of channel sparsity. Therefore, high-precision channel parameters are extracted as key sources. Simulation results demonstrate that, compared to conventional CS-based methods, the proposed scheme reduces the BDR by 47.7% at an SNR of 5 dB while significantly lowering pilot overhead. Additionally, its performance advantage becomes more pronounced as the antenna array size increases. The proposed scheme offers a robust solution for key generation in RIS-assisted millimeter-wave MIMO systems, eliminating the need for prior sparsity knowledge and mitigating grid quantization errors.
- Physical-layer key generation,
- Millimeter-wave MIMO,
- Reconfigurable Intelligent Surface (RIS),
- Atomic Norm Minimization (ANM)

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References(20)

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