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Table Of Integrals Series And Products

As a complement to high-layer encryption techniques, physical layer security has been widely recognized as a promising way to enhance wireless security by exploiting the characteristics of wireless channels, including fading, noise, and interference. In order to enhance the received signal power at legitimate receivers and impair the received signal quality at eavesdroppers simultaneously, multiple-antenna techniques have been proposed for physical layer security to improve secrecy performance via exploiting spatial degrees of freedom. This paper provides a comprehensive survey on various multiple-antenna techniques in physical layer security, with an emphasis on transmit beamforming designs for multiple-antenna nodes. Specifically, we provide a detailed investigation on multiple-antenna techniques for guaranteeing secure communications in point-to-point systems, dual-hop relaying systems, multiuser systems, and heterogeneous networks. Finally, future research directions and challenges are identified.

A Survey on Multiple-Antenna Techniques for Physical Layer Security

Millimeter wave (mmWave) communication technologies have recently emerged as an attractive solution to meet the exponentially increasing demand on mobile data traffic. Moreover, ultra dense networks (UDNs) combined with mmWave technology are expected to increase both energy efficiency and spectral efficiency. In this paper, user association and power allocation in mmWave-based UDNs is considered with attention to load balance constraints, energy harvesting by base stations, user quality of service requirements, energy efficiency, and cross-tier interference limits. The joint user association and power optimization problem are modeled as a mixed-integer programming problem, which is then transformed into a convex optimization problem by relaxing the user association indicator and solved by Lagrangian dual decomposition. An iterative gradient user association and power allocation algorithm is proposed and shown to converge rapidly to an optimal point. The complexity of the proposed algorithm is analyzed and its effectiveness compared with existing methods is verified by simulations.

Energy Efficient User Association and Power Allocation in Millimeter-Wave-Based Ultra Dense Networks With Energy Harvesting Base Stations

Millimeter wave (mmWave) communication technologies have recently emerged as an attractive solution to meet the exponentially increasing demand on mobile data traffic. Moreover, ultra dense networks (UDNs) combined with mmWave technology are expected to increase both energy efficiency and spectral efficiency. In this paper, user association and power allocation in mmWave based UDNs is considered with attention to load balance constraints, energy harvesting by base stations, user quality of service requirements, energy efficiency, and cross-tier interference limits. The joint user association and power optimization problem is modeled as a mixed-integer programming problem, which is then transformed into a convex optimization problem by relaxing the user association indicator and solved by Lagrangian dual decomposition. An iterative gradient user association and power allocation algorithm is proposed and shown to converge rapidly to an optimal point. The complexity of the proposed algorithm is analyzed and the effectiveness of the proposed scheme compared with existing methods is verified by simulations.

Energy Efficient User Association and Power Allocation in Millimeter Wave Based Ultra Dense Networks with Energy Harvesting Base Stations

In this letter, we propose intelligent reflecting surface (IRS) aided multi-antenna physical layer security. We present a power efficient scheme to design the secure transmit power allocation and the surface reflecting phase shift. It aims to minimize the transmit power subject to the secrecy rate constraint at the legitimate user. Due to the non-convex nature of the formulated problem, we propose an alternative optimization algorithm and the semidefinite programming (SDP) relaxation to deal with this issue. Also, the closed-form expression of the optimal secure beamformer is derived. Finally, simulation results are presented to validate the proposed algorithm, which highlights the performance gains of the IRS to improve the secure transmission.

Intelligent Reflecting Surface Aided Multi-Antenna Secure Transmission

In this paper, we study different secrecy rate optimization techniques for a multiple-input–multiple-output (MIMO) secrecy channel, where a multiantenna cooperative jammer is employed to improve secret communication in the presence of a multiantenna eavesdropper. Specifically, we consider two optimization problems, namely, power minimization and secrecy rate maximization. These problems are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To circumvent these nonconvexity issues, we alternatively design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. For a given transmit covariance matrix at the cooperative jammer, we solve the power minimization and secrecy rate maximization problems based on a Taylor series expansion. Then, we propose two iterative algorithms to solve these approximated problems. In addition, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploiting S-Procedure , we show that these robust optimization problems can be formulated into semidefinite programming. Moreover, we consider the secrecy rate maximization problem based on game theory, where the jammer introduces charges for its jamming service based on the amount of the interference caused to the eavesdropper. This secrecy rate maximization problem is formulated into a Stackelberg game where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game, Stackelberg equilibrium is analytically derived. Simulation results have been provided to validate the convergence and performance of the proposed algorithms. In addition, it is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate. Finally, the Stackelberg equilibrium solution has been validated through numerical results.

Secrecy Rate Optimizations for a MIMO Secrecy Channel With a Cooperative Jammer

This paper investigates simultaneous wireless information and power transfer (SWIPT) for a multiple-input–single-output (MISO) secrecy channel. First, transmit beamforming without artificial noise (AN) is designed to achieve the secrecy rate maximization problem subject to the transmit power and the energy harvesting (EH) constraints. This problem is not convex, but this can be solved by applying a bisection search to a sequence of the associated power minimization problems, each of which can be solved by using a novel relaxation approach. Moreover, we extend our proposed algorithms to the robust case by incorporating channel uncertainties. Then, transmit beamforming with AN is investigated for the secrecy rate maximization problem, where two relaxation approaches are presented, i.e., a two-level optimization algorithm and a successive convex approximation (SCA), to solve the secrecy rate maximization problem. In addition, tightness analyses of rank relaxation are provided to show that the optimal transmit covariance matrix exactly returns rank one. Simulation results are provided to validate the performance of the proposed algorithms.

/pdf/simultaneous-wireless-information-power-transfer-for-miso-39os7cebc2.pdf

Simultaneous Wireless Information Power Transfer for MISO Secrecy Channel

This paper investigates secrecy rate optimization problems for a multiple-input-single-output (MISO) secrecy channel in the presence of multiple multiantenna eavesdroppers. Specifically, we consider power minimization and secrecy rate maximization problems for this secrecy network. First, we formulate the power minimization problem based on the assumption that the legitimate transmitter has perfect channel state information (CSI) of the legitimate user and the eavesdroppers, where this problem can be reformulated into a second-order cone program (SOCP). In addition, we provide a closed-form solution of transmit beamforming for the scenario of an eavesdropper. Next, we consider robust secrecy rate optimization problems by incorporating two probabilistic channel uncertainties with CSI feedback. By exploiting the Bernstein-type inequality and S-Procedure to convert the probabilistic secrecy rate constraint into the determined constraint, we formulate this secrecy rate optimization problem into a convex optimization framework. Furthermore, we provide analyses to show the optimal transmit covariance matrix is rank-one for the proposed schemes. Numerical results are provided to validate the performance of these two conservative approximation methods, where it is shown that the Bernstein-type inequality-based approach outperforms the S-Procedure approach in terms of the achievable secrecy rates.

/pdf/secrecy-rate-optimizations-for-a-miso-secrecy-channel-with-3zlylqzhyw.pdf

Secrecy Rate Optimizations for a MISO Secrecy Channel with Multiple Multiantenna Eavesdroppers

This letter investigates robust secrecy rate optimization techniques for a multiple-input-multiple-output (MIMO) wiretap channel in the presence of a multiantenna eavesdropper. In particular, two robust secrecy rate optimization problems are studied: robust power minimization with an outage secrecy rate constraint and robust secrecy rate maximization subject to the outage secrecy rate and transmit power constraints. Here, it is assumed that the legitimate transmitter has perfect channel state information (CSI) of the legitimate receiver and imperfect CSI of the eavesdropper. Both robust problems are not convex in terms of transmit covariance matrix and the outage secrecy rate constraint. Hence, we propose a conservative approximation approach to reformulate this outage secrecy rate constraint by exploiting the Bernstein-type inequality to obtain a tractable solution for these two robust problems. Numerical results have been provided to validate the convergence and the performance of the proposed robust algorithms.

Robust Outage Secrecy Rate Optimizations for a MIMO Secrecy Channel

We propose a novel iterative decoder for block turbo codes (BTCs). The proposed decoder combines soft-input/softoutput (SISO) and hard-input/hard-output (HIHO) constituent decoders in order to obtain better error performance and reduce the computational complexity compared to classical BTC decoders. We show that the new decoder, called 'hybrid decoder', offers a better complexity/performance tradeoff than a classical BTC decoder.

/pdf/a-hybrid-decoder-for-block-turbo-codes-5bb1ur07t3.pdf

Stephane Y. Le Goff

Papers

Secrecy Rate Optimizations for a MIMO Secrecy Channel With a Cooperative Jammer

Simultaneous Wireless Information Power Transfer for MISO Secrecy Channel

Secrecy Rate Optimizations for a MISO Secrecy Channel with Multiple Multiantenna Eavesdroppers

Robust Outage Secrecy Rate Optimizations for a MIMO Secrecy Channel

A Hybrid Decoder for Block Turbo Codes