Physical-layer key generation (PKG) in multi-user massive MIMO networks faces great challenges due to the large length of pilots and the high dimension of channel matrix. To tackle these problems, we propose a novel massive MIMO key generation scheme with pilot reuse based on the beam domain channel model and derive close-form expression of secret key rate. Specifically, we present two algorithms, i.e., beam-domain based channel probing (BCP) algorithm and interference neutralization based multi-user beam allocation (IMBA) algorithm for the purpose of channel dimension reduction and multi-user pilot reuse, respectively. Numerical results verify that the proposed PKG scheme can achieve the secret key rate that approximates the perfect case, and significantly reduce the dimension of the channel estimation and pilot overhead.
Physical-layer key generation (PKG) in multi-user massive MIMO networks faces great challenges due to the large length of pilots and the high dimension of channel matrix. To tackle these problems, we propose a novel massive MIMO key generation scheme with pilot reuse based on the beam domain channel model and derive close-form expression of secret key rate. Specifically, we present two algorithms, i.e., beam-domain based channel probing (BCP) algorithm and interference neutralization based multi-user beam allocation (IMBA) algorithm for the purpose of channel dimension reduction and multi-user pilot reuse, respectively. Numerical results verify that the proposed PKG scheme can achieve the secret key rate that approximates the perfect case, and significantly reduce the dimension of the channel estimation and pilot overhead.
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.
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.
With the substantial increase in the number of antennas, polar-domain channel modeling for extremely large-scale antenna array (ELAA) systems has been introduced to capture both angular and distance information in near-field environments. The fine-grained polar-domain channel provides additional sources of randomness, making it well-suited for physical layer key generation (PLKG). To minimize the pilot overhead in multi-user key generation and leverage the randomness from the polar-domain channel paths, we herein design a zero-forcing (ZF)-based precoding scheme to mitigate inter-path and inter-user interference. Using ZF precoding, we derive an analytical expression for the sum secret key rate (SKR) as a function of power allocation variables, and then optimize these variables in the presence of eavesdroppers. Our simulations validate the proposed precoding design and power allocation methods in terms of sum SKR versus the transmit power, antenna configurations, and spatial correlation between legitimate and eavesdropping channels.
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.
Physical-layer key generation (PKG) leverages the reciprocity of wireless channel to distribute a symmetric secret key between two legitimate transceivers. This paper proposes an efficient and standard-compliant PKG scheme in 802.11 MIMO-OFDM (multiple-input multiple-output, orthogonal frequency division multiplexing) networks. Firstly, we propose to extract secret keys from a novel feature referred to relative channel state information (RCSI), which can eliminate the non-reciprocity caused by transceiver mismatch and synchronization errors. Specifically, the RCSIs are derived through dividing the channel state informations (CSIs) of non-reference antennas by those of reference antennas. By setting the spatial mapping matrices of the sounding packets as permutation matrices, the reference antennas are determined implicitly without the need for information exchange. Secondly, based on the 802.11 low-density parity-check code (LDPC), we propose an adaptive information reconciliation algorithm, which is flexible to fit the various scenarios with different key lengths and bit disagreement ratios. At last, the overall PKG procedure with detailed frame format design is provided. The proposed scheme is evaluated through an 802.11ax link-level simulation. Numerical results show that the key generation rate of the proposed scheme can achieve 0.47~14Mbps for practical settings.