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IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)

A Lightweight Preprocessing Scheme for Secret Key Generation from MmWave Massive MIMO Channel Measurements

Lijun Yang, Xinchao Ge, Qianyi Zhu, Lin Guo

Published May 20, 2023• 0 citations
Publisher

Abstract

Due to the new channel characteristics, previous preprocessing methods for physical layer key generation cannot be directly applied in mmWave massive MIMO systems. Actually, due to the intolerable high computation complexity and time consumption caused by large dimension of massive MIMO channel, even the previous optimal preprocessing method principal component analysis (PCA) is not suitable. To address the problem, in this paper, we propose a lightweight preprocessing approach called beamspace refinement, which is suitable for mmWave massive MIMO channel by exploiting its channel characteristics namely sparsity. The proposed scheme brings the following advantages. 1) It is lightweight. The computational complexity is quiet low. Unlike the PCA scheme, the proposed scheme does not involve the exponential calculation of the number of antennas, which makes it very suitable for mmWave massive MIMO channel. 2) It is robust against noise. Thus, it can be used to generate secret key with quiet high-entropy and high bit agreement ratio even in low SNR regimes. Numerical results show that the proposed approach outperforms the previous method DCT, WT and PCA in terms of bit agreement ratio, and is on par with PCA in terms of key capacity. Besides, the increase of the antennas number can improve key agreement ratio in our scheme, which is beneficial for massive MIMO system.

DOI
10.1109/infocomwkshps57453.2023.10226124

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Due to the new channel characteristics, previous preprocessing methods for physical layer key generation cannot be directly applied in mmWave massive MIMO systems. Actually, due to the intolerable high computation complexity and time consumption caused by large dimension of massive MIMO channel, even the previous optimal preprocessing method principal component analysis (PCA) is not suitable. To address the problem, in this paper, we propose a lightweight preprocessing approach called beamspace refinement, which is suitable for mmWave massive MIMO channel by exploiting its channel characteristics namely sparsity. The proposed scheme brings the following advantages. 1) It is lightweight. The computational complexity is quiet low. Unlike the PCA scheme, the proposed scheme does not involve the exponential calculation of the number of antennas, which makes it very suitable for mmWave massive MIMO channel. 2) It is robust against noise. Thus, it can be used to generate secret key with quiet high-entropy and high bit agreement ratio even in low SNR regimes. Numerical results show that the proposed approach outperforms the previous method DCT, WT and PCA in terms of bit agreement ratio, and is on par with PCA in terms of key capacity. Besides, the increase of the antennas number can improve key agreement ratio in our scheme, which is beneficial for massive MIMO system.
In this work, we present a scheme of physical layer secret key generation for Millimeter wave (mmWave) Massive MIMO system. Our scheme is compatible with current hardware structure and protocols including Analog Beamforming, Massive MIMO, and Beam Sweep. We add a small perturbation angle into the Angle of Arrival (AoA) of the transmitter as the common randomness, which significantly improved the secret key rate without being constrained by the complexity of link initialization protocols and low dynamic of the channel. Therefore, the secret key rate can be enhanced by increasing the number of perturbations. In addition, our scheme can combat co-located eavesdropper (Eve) by utilizing the high directionality of Massive MIMO antenna. Numerical results show that our scheme has a high bit agreement ratio (BAR) between legitimate users while the co-located Eve only gets the BAR around 50%, which indicates that the secrecy of the generated key is well achieved.
Shared secret key generation from wireless channel characteristics has attracted a lot of research attention in recent years due to its low computational overhead and potentials to achieve information-theoretic security. In this paper, for millimeter wave (mmWave) Massive MIMO channel, we propose to use new channel characteristics - virtual AoA (Angle of Arrival) and AoD (Angle of Departure), to generate a shared secret key between two devices. Other than reciprocity, AoA and AoD of the virtual channel present sparsity and their estimation is efficient and robust against noise. Through theoretical analysis and extensive simulations, we show that the proposed key generation using virtual AoA and AoD achieves much higher bit agreement ratio than existing mechanisms directly using channel state information. Our method can achieve above 99% bit agreement ratio even under very low SNR (e.g., -10dB), which is not achievable by the existing mechanisms. Besides, in our proposed mechanism, the bit agreement ratio becomes higher when number of antennas increases, along with higher key generate rates achieved per channel sounding.
Random and high-agreement secret key generation from noisy wideband channels is challenging due to the autocorrelation inside the channel samples and compromised cross correlation between channel measurements of two keying parties. This paper studies the signal preprocessing algorithms to establish high-agreement uncorrelated secret key in the presence of channel independent eavesdroppers. We first propose a general mathematical model for various preprocessing schemes, including principal component analysis (PCA), discrete cosine transform (DCT) and wavelet transform (WT). Among preprocessing schemes, PCA is proved to achieve the optimal secret key rate. Next, PCA with common eigenvector has been found to outperform PCA with private eigenvector in terms of an overall consideration of key agreement, information leakage, and computational expense. Then, we propose a system level design of key generation, including quantization, information reconciliation, and privacy amplification. Numerical results verify that the key generation enhanced by PCA with common eigenvector can achieve secret key with high key generation rate, low key error rate, and good randomness.
This chapter presents a multi-user secret key generation in massive multiple-input multiple-output (MIMO) wireless networks. Physical-layer key generation (PKG) based on channel reciprocity has emerged as a new technique to establish secret keys between devices. However, in future wireless communications, massive antennas will be employed to support multiple users, which bring new challenges to PKG, e.g., low key agreements caused by long-time delay or strong inter-user interference. By harnessing the sparse characteristics of the beam domain channel model, we propose a general channel dimensionality reduction (CDR)-based secret key generation scheme and optimize the parameters of this scheme. The security of this key generation scheme under different user cases of non-overlapping and overlapping beams is then discussed. Some new directions that generalize and improve the basic scenarios for PKG are described. These new directions include multi-cell multi-user secret key generation, PKG in millimeter wave wireless communications, and PKG in frequency division duplexing systems.
Physical layer secret key generation techniques have spurred much recent research interest. In general, the secret key establishment contains four main procedures: channel sounding, quantization, information reconciliation and privacy amplification. However, to overcome the non- reciprocity and correlation problems in key generation from orthogonal frequency division multiplexing (OFDM) channels, a preprocessing procedure is added to prepare inputs for quantization. This paper demonstrates the optimal preprocessing approach in secret key generation and addresses its practical problems in realization. More specifically, we first build the mathematical model of a preprocessing procedure. Then, we identify that principle component analysis (PCA) can achieve the optimal performance in this model from the perspective of secret key capacity. Next, we discuss the realization steps of PCA algorithm and the corresponding procedures to cooperate with it. The parameter design in matrix partitioning and covariance matrix calculation are also analyzed. Numerical results verify that the proposed PCA preprocessing outperforms other tall unitary transforms and thus, it can be used to generate secret key with high key generation rate (KGR), low key error rate (KER) and good randomness.
We investigate group secret key generation in 5G mmWave Massive MIMO networks and intend to improve the efficiency of channel probing for group key generation. In this paper, a new channel probing strategy for star-topology networks is proposed, which relies on the multiplexing of downlink probing signals, enabled by the hybrid precoding. To improve the group key rates per channel probing, a genetic algorithm (GA) based power allocation algorithm is also proposed. What’s more, to estimate the group key rates based on the probing samples, we propose a scheme for the estimation of group key rates based on the maximum likelihood estimator (MLE). The performance of the proposed scheme on group key rates and bits disagreement ratio (BDR) are provided. The numerical results show that the GA-based downlink channel probing scheme can increase the efficiency of channel probing and have higher group key rates compared with the existing channel probing schemes. When the SNR is 25dB, the key rates of GA-based power allocation scheme are 20% higher than the scheme with the conventional channel probing strategy.