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arXiv:2104.06742 · IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

Optimal Downlink Training Sequence for Massive MIMO Secret-Key Generation

François Rottenberg

Published Sep 27, 2021• 2 citations
arXivHTMLPDF

Abstract

In this paper, the secret-key capacity is max-imized by optimizing the downlink training sequence in a time division duplexing (TDD) massive multiple-input-multiple-output (MIMO) scenario. Both single-user and multiple user cases are considered. As opposed to previous works, the optimal training sequence and the related secret-key capacity is characterized in closed-form in the single-user case and the large antenna multiple-user case. Designs taking into account a constraint on the maximal number of pilots are also proposed. In the multiple-user case, both the max-min and the sum capacity criteria are considered, including potential user priorities. In the end, it is shown that massive MIMO boosts the secret-key capacity by leveraging: i) spatial dimensionality gain and ii) array gain. Moreover, in the large antenna case, the multiple-user capacity is obtained with no extra pilot overhead as compared to the single-user case.

DOI
10.1109/spawc51858.2021.9593207

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In this paper, the secret-key capacity is max-imized by optimizing the downlink training sequence in a time division duplexing (TDD) massive multiple-input-multiple-output (MIMO) scenario. Both single-user and multiple user cases are considered. As opposed to previous works, the optimal training sequence and the related secret-key capacity is characterized in closed-form in the single-user case and the large antenna multiple-user case. Designs taking into account a constraint on the maximal number of pilots are also proposed. In the multiple-user case, both the max-min and the sum capacity criteria are considered, including potential user priorities. In the end, it is shown that massive MIMO boosts the secret-key capacity by leveraging: i) spatial dimensionality gain and ii) array gain. Moreover, in the large antenna case, the multiple-user capacity is obtained with no extra pilot overhead as compared to the single-user case.
Physical-layer key generation (PKG) based on channel reciprocity has recently emerged as a new technique to establish secret keys between devices. Most works focus on pairwise communication scenarios with single or small-scale antennas. However, the fifth generation (5G) wireless communications employ massive multiple-input multiple-output (MIMO) to support multiple users simultaneously, bringing serious overhead of reciprocal channel acquisition. This paper presents a multi-user secret key generation in massive MIMO wireless networks. We provide a beam domain channel model, in which different elements represent the channel gains from different transmit directions to different receive directions. Based on this channel model, we analyze the secret key rate and derive a closed-form expression under independent channel conditions. To maximize the sum secret key rate, we provide the optimal conditions for the Kronecker product of the precoding and receiving matrices and propose an algorithm to generate these matrices with pilot reuse. The proposed optimization design can significantly reduce the pilot overhead of the reciprocal channel state information acquisition. Furthermore, we analyze the security under the channel correlation between user terminals (UTs), and propose a low overhead multi-user secret key generation with non-overlapping beams between UTs. Simulation results demonstrate the near-optimal performance of the proposed precoding and receiving matrices design and the advantages of the non-overlapping beam allocation.
In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform toward the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.
Secret key generation in multi-user massive multiple-input multiple-output (MIMO) communication suffers from high computation complexity, pilot overhead, and inter-user interference caused by the large dimension of the massive MIMO channel. To address these problems, this paper proposes a novel key generation approach that exploits the beam domain channel for channel feature extraction. The proposed approach can effectively reduce the channel feature dimension and mitigate the inter-user interference, via the well-designed power allocation and beam scheduling algorithms. Specifically, the multi-user key generation model is built and the design problem of channel feature extraction matrices is formulated as a sum key rate maximization problem. To tackle this problem, we derive an upper bound of the secret key rate and prove that the upper bound maximization is a convex optimization. After solving the upper bound maximization, the base station (BS) obtains the sum beams for all the users. To allocate the selected beams to each user, an efficient beam scheduling algorithm is proposed, which converges to a locally optimal solution with low computational complexity. Numerical results illustrate that in the proposed scheme, the bit disagreement ratio (BDR) of legitimate users achieves 10−2, while that of the eavesdropper tends to 0.5, confirming the feasibility and security of the proposed scheme.
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.
In this paper, we study the design of secure communication for time division duplexing multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with active eavesdropping. We assume that the eavesdropper actively attacks the uplink pilot transmission and the uplink data transmission before eavesdropping the downlink data transmission phase of the desired users. We exploit both the received pilots and data signals for uplink channel estimation. We show analytically that when the number of transmit antennas and the length of the data vector both tend to infinity, the signals of the desired user and the eavesdropper lie in different eigenspaces of the received signal matrix at the base station if their signal powers are different. This finding reveals that decreasing (instead of increasing) the desire user's signal power might be an effective approach to combat a strong active attack from an eavesdropper. Inspired by this result, we propose a data-aided secure downlink transmission scheme and derive an asymptotic achievable secrecy sum-rate expression for the proposed design. Numerical results indicate that under strong active attacks, the proposed design achieves significant secrecy rate gains compared to the conventional design employing matched filter precoding and artificial noise generation.
Kerchoff's principle states that the security of encryption should be based on the key. Thus, increasing the encryption key length has been an essential approach in generating unbreakable ciphers. Recently, physical layer security has gained significant research attention. It allows secure communications between a source and destination without the need to resort to key-based encryption techniques. In this paper, secret key generation using massive multiple input multiple output (MIMO) techniques is investigated. The large number of subcarriers used in orthogonal frequency division multiple access (OFDMA) systems is also used to increase the key length. Several scenarios are investigated and corresponding key lengths are calculated. The combination of massive MIMO and OFDMA also allows to simultaneously implement physical layer security techniques while generating large keys for traditional key-based cryptography.