This work investigates the effect of limiting source signals to finite-alphabet on the secrecy rate of a multi-antenna wiretap system. Existing works have characterized maximum achievable secrecy rate or secrecy capacity for single- and multi-antenna systems based on Gaussian source signals and secrecy code. Despite the impracticality of Gaussian source, its compact closed-form expression of mutual information motivated broad use of Gaussian input assumption. For practical consideration, we study the effect of finite discrete-constellation on instantaneous and ergodic secrecy rate of multiple-antenna wire-tap channels. Our results demonstrate substantial difference between systems involving finite-alphabet inputs and systems with Gaussian inputs. Results from Gaussian inputs serve as upper-bound of secrecy rate for practical systems with finite alphabet inputs.
This work investigates the effect of limiting source signals to finite-alphabet on the secrecy rate of a multi-antenna wiretap system. Existing works have characterized maximum achievable secrecy rate or secrecy capacity for single- and multi-antenna systems based on Gaussian source signals and secrecy code. Despite the impracticality of Gaussian source, its compact closed-form expression of mutual information motivated broad use of Gaussian input assumption. For practical consideration, we study the effect of finite discrete-constellation on instantaneous and ergodic secrecy rate of multiple-antenna wire-tap channels. Our results demonstrate substantial difference between systems involving finite-alphabet inputs and systems with Gaussian inputs. Results from Gaussian inputs serve as upper-bound of secrecy rate for practical systems with finite alphabet inputs.
This work investigates the effect of finite-alphabet input constraint on the secrecy rate of a multi-antenna wiretap channel. Most existing works have characterized maximum achievable secrecy rate or secrecy capacity for single and multiple antenna systems based on Gaussian source signals and secrecy code. For practical considerations, we study the effect of finite discrete-constellation on the achievable secrecy rate of multiple-antenna wire-tap channels. Our proposed precoding scheme converts the underlying multi-antenna system into a bank of parallel channels. Based on this precoding strategy, we develop a decentralized power allocation algorithm based on dual decomposition to maximize the achievable secrecy rate. In addition, we analyze the achievable secrecy rate for finite-alphabet inputs in low and high SNR regions. Our results demonstrate substantial difference in secrecy rate between systems given finite-alphabet inputs and systems with Gaussian inputs.
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.
Abstract—We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary. Index Terms—Information-theoretic security, multiple-input multiple-output (MIMO), multiple antennas, secrecy capacity,
Providing secure communications over the physical layer with the objective of achieving secrecy without requiring a secret key has been receiving growing attention within the past decade. The vast majority of the existing studies in the area of physical layer security focus exclusively on the scenarios where the channel inputs are Gaussian distributed. However, in practice, the signals employed for transmission are drawn from discrete signal constellations such as phase shift keying and quadrature amplitude modulation. Hence, understanding the impact of the finite-alphabet input constraints and designing secure transmission schemes under this assumption is a mandatory step toward a practical implementation of physical layer security. With this motivation, this paper reviews recent developments on physical layer security with finite-alphabet inputs. We explore transmit signal design algorithms for single-antenna as well as multi-antenna wiretap channels under different assumptions on the channel state information at the transmitter. Moreover, we present a review of the recent results on secure transmission with discrete signaling for various scenarios including multi-carrier transmission systems, broadcast channels with confidential messages, cognitive multiple access and relay networks. Throughout the article, we stress the important behavioral differences of discrete versus Gaussian inputs in the context of the physical layer security. We also present an overview of practical code construction over Gaussian and fading wiretap channels, and discuss some open problems and directions for future research.
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.