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International Conference on Communications

Linear MIMO precoding in multi-antenna wiretap channels for finite-alphabet data

Yongpeng Wu, Chengshan Xiao, Zhi Jun Ding, Xiqi Gao, Shi Jin

Published Jun 1, 2012• 0 citations
Publisher

Abstract

In this paper, we investigate the secrecy rate of finite alphabet communications over multiple-input, multiple-output, multiple-antenna eavesdropper (MIMOME) systems. Traditional precoder designs at the transmitter for achieving secrecy capacity (maximum secrecy rate) for MIMOME systems are developed according to the assumption of Gaussian input signals. Such designs may risk substantial secrecy rate loss when Gaussian inputs are replaced by practical finite alphabet inputs. To address this issue, we propose a linear precoding design to directly maximize the secrecy rate for MIMOME systems under the constraint of finite alphabet input. Exploiting convex optimization and matrix calculus, we present necessary conditions required of the optimal precoding design and develop an iterative algorithm for finding an efficient precoder. With finite alphabet input signals, maximum transmission power no longer corresponds to maximum secrecy rate as in the case of Gaussian input. We further derive closed-form results on the optimal transmission design for maximizing secrecy rate in low signal-to-noise ratio (SNR) region and near-optimal transmission power in a high SNR region.

DOI
10.1109/icc.2012.6363783

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In this paper, we investigate the secrecy rate of finite alphabet communications over multiple-input, multiple-output, multiple-antenna eavesdropper (MIMOME) systems. Traditional precoder designs at the transmitter for achieving secrecy capacity (maximum secrecy rate) for MIMOME systems are developed according to the assumption of Gaussian input signals. Such designs may risk substantial secrecy rate loss when Gaussian inputs are replaced by practical finite alphabet inputs. To address this issue, we propose a linear precoding design to directly maximize the secrecy rate for MIMOME systems under the constraint of finite alphabet input. Exploiting convex optimization and matrix calculus, we present necessary conditions required of the optimal precoding design and develop an iterative algorithm for finding an efficient precoder. With finite alphabet input signals, maximum transmission power no longer corresponds to maximum secrecy rate as in the case of Gaussian input. We further derive closed-form results on the optimal transmission design for maximizing secrecy rate in low signal-to-noise ratio (SNR) region and near-optimal transmission power in a high SNR region.
In this paper, we investigate the secrecy rate of finite-alphabet communications over multiple-input-multiple-output-multiple-antenna eavesdropper (MIMOME) channels. Traditional precoding designs based on Gaussian input assumption may lead to substantial secrecy rate loss when the Gaussian input is replaced by practical finite-alphabet input. To address this issue, we investigate linear precoding designs to directly maximize the secrecy rate for MIMOME systems under the constraint of finite-alphabet input. By exploiting the theory of Karush-Kuhn-Tucker (KKT) analysis and matrix calculus, we first present necessary conditions of the optimal precoding design when instantaneous channel-state information (CSI) of the eavesdropper is known at the transmitter. In this light, an iterative algorithm for finding the optimal precoding matrix is developed, utilizing a gradient decent method with backtracking line search. Moreover, we find that the beamforming design in MIMONE systems, which is a secrecy-capacity-achieving approach for Gaussian signaling, no longer provides the maximum secrecy rate for finite-alphabet input data. This case is substantially different from the Gaussian input case. In addition, we derive the closed-form results on the precoding matrix, which maximizes the secrecy rate in the low signal-to-noise ratio (SNR) region, and reveal the optimal precoding structure in the high-SNR region. A novel jamming signal generation method that draws on the CSI of the eavesdropper to additionally increase the secrecy rate is further proposed. The precoding design with only statistical CSI of the eavesdropper available at the transmitter is also considered. Numerical results show that the proposed designs provide significant gains over recent precoding designs through a power control policy and the precoding design with the Gaussian input assumption in various scenarios.
In this paper, we investigate the precoding scheme for multiple-input multiple-output multiple antennas eavesdropper (MIMOME) channels under the constraint of finite-alphabet inputs to ensure secure transmission between the source and the destination in the presence of an eavesdropper. With finite-alphabet inputs, there are no closed-form solutions for mutual information (MI) and its gradient-minimum mean-square error (MMSE) matrix. Therefore traditional precoding schemes based on direct calculation of MI and MMSE matrix through numerical integration involve prohibitive computational burden. To address this problem, this paper first derives asymptotically optimal lower bounds of MI and ergodic MI with which the computational complexity can be significantly reduced compared with the direct computation of MI. With the derived lower bounds, a low-complexity precoding scheme is proposed to maximize the secrecy rate, wherein a gradient descent based algorithm is used to obtain the precoding result. In the low and high signal-to-noise ratio (SNR) regions, we demonstrate that the proposed precoding scheme gives the same result as directly maximizing the secrecy rate, which indicates that the proposed low-complexity precoding scheme is asymptotically optimal.
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This paper considers secure transmission with the aid of a helper for finite alphabet signals in multiple-input-multiple-output multiple antenna eavesdropper networks, where the helper transmits a jamming signal along with the confidential message sent by the source node to confuse the eavesdropper. For the scenario in which the only statistical channel-state-information (CSI) of the eavesdropper links is available at the transmitter, the ergodic secrecy rate lacks closed-form expression, and the evaluation of the ergodic secrecy rate is computationally prohibitive. To address this problem, an accurate approximation of the ergodic secrecy rate is proposed to reduce the computational complexity. Utilizing this approximation of the ergodic secrecy rate, the joint optimization of precoding design and power allocation between the source and the helper is investigated to improve the ergodic secrecy rate. Furthermore, to achieve a tradeoff between computational complexity and performance, low-complexity schemes without iteration are proposed based on the analysis at extreme signal-to-noise ratio (SNR). In the low SNR regime, we prove that it is optimal to transmit confidential messages with full power, and the beamforming design is the first-order optimal precoder. At high SNR, we transform the problem of precoding design into a semi-definite programming problem, which can be efficiently solved by the interior-point method.
This paper investigates the secure precoding design and proposes a closed-form expression for the approximate achievable secrecy rate. It is assumed that the transmitter knows the full channel information at the legitimate receiver, and knows only the statistics of the channel information at the eavesdropper. We design a time-varying precoder so that it can produce time-varying interference to the eavesdropper, which is capable to resist the wiretap from unknown eavesdropper. Furthermore, we address the power-allocation between information and interference transmission to achieve the optimal secrecy performance. The analysis and numerical results show that the secure precoding design provide significant gains over recent precoding designs especially in high signal-to-noise-ratio (SNR) region. Additionally, the derived results can benefit the maximization of secrecy performance.