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IEEE Access

Power Allocation and Beam Scheduling for Multi-User Massive MIMO Secret Key Generation

Chen K. Sun, Guyue Li

Published Jan 1, 2020• 10 citations
Publisher

Abstract

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.

DOI
10.1109/access.2020.3022052

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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.
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.
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.
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.
Extremely large-scale antenna arrays (ELAA) require near-field spherical wave modeling due to the substantial increase in the number of antennas, which introduces new spatial dimensions to physical layer key generation (PLKG). We investigate multi-user PLKG in near-field environments, where a base station with an ELAA simultaneously generates secret keys with multiple users. We derive an analytical expression for the key rate (KR). By utilizing spatial dimensions of distance and angle in near-field environments, we apply eigenvalue decomposition and singular value decomposition to design precoding matrices to reduce interference among user equipments (UEs) and extract uncorrelated subchannels. Given that the KR is non-convex, we approximate it and optimize the precoding matrix to increase the KR. After precoding design, the KR depends on the transmit power allocated to the subchannels. Two optimization problems are formulated to further optimize transmit power allocation. The first problem focuses on maximizing the sum KR. We apply the Lagrange multiplier method to determine the optimal power allocation variables by searching the Lagrange multiplier. To reduce computational complexity, a supervised feedforward neural network (FNN) is designed to capture the relationship between the power allocation variables and the Lagrange multiplier. The second optimization problem focuses on KR fairness. By introducing a slack variable that is smaller than the KRs of all users, we use the CVX toolbox to find optimal power allocation variables that maximize this slack variable. To further reduce complexity, the Lagrange multiplier method offers an analytical solution for power allocation variables in terms of Lagrange multipliers determined by the slack variable in the high-power case. We employ a bisection algorithm to find the slack variable. Furthermore, we propose an FNN to map transmit power to the slack variable. Simulations demonstrate that the proposed methods efficiently leverage near-field effects for multi-user PLKG, reducing pilot overhead.
For the single-cell massive multiple-input multiple-output (MIMO) downlink transmission, we investigate an artificial noise (AN) assisted secure transmission strategy where the base station has only access to statistical channel state information (CSI) of the legitimate user terminals and the eavesdropper. By maximizing a lower bound of the ergodic secrecy sum rate, we figure out the eigenvectors of the optimal secrecy signal and AN transmit covariance matrices in the closed-form. Notably, such a solution reveals that it is more favorable to transmit both the secrecy signals and the AN in the beam domain, by which we translate the original problem into a simpler power allocation problem in the beam domain. Building on the approaches of sequential optimization and the deterministic equivalent, we further propose an iterative algorithm for power allocation with guaranteed convergence to a local optimum. Numerical results show the superior performance of the proposed approach compared with the traditional one without AN.