The security of a wireless channel between a transmitter and legitimate user(s) in the presence of eavesdroppers can be improved by the addition of artificial noise (AN) transmission. In the case where the channel state information of the eavesdroppers is not known, some AN schemes transmit multiple uncorrelated noise signals via distinct orthogonal beamforming vectors. The vectors are designed to avoid affecting the legitimate links, and mutual orthogonality increases the likelihood that the AN signals are received at the eavesdroppers with high power. Applications in massive-MIMO, where hardware is constrained, motivate us to design vectors whose elements have arbitrary phases but equal magnitudes [1].This work proposes an algorithm that generates multiple such phase-only beamforming vectors via a single optimization problem and significantly increases the number of vectors which can be found compared to the previous work [2]. Consequently, our results demonstrate substantially higher lower-bounds on maximum achievable secrecy rate via this approach compared to the previous work [2] for similar scenarios.
The security of a wireless channel between a transmitter and legitimate user(s) in the presence of eavesdroppers can be improved by the addition of artificial noise (AN) transmission. In the case where the channel state information of the eavesdroppers is not known, some AN schemes transmit multiple uncorrelated noise signals via distinct orthogonal beamforming vectors. The vectors are designed to avoid affecting the legitimate links, and mutual orthogonality increases the likelihood that the AN signals are received at the eavesdroppers with high power. Applications in massive-MIMO, where hardware is constrained, motivate us to design vectors whose elements have arbitrary phases but equal magnitudes [1].This work proposes an algorithm that generates multiple such phase-only beamforming vectors via a single optimization problem and significantly increases the number of vectors which can be found compared to the previous work [2]. Consequently, our results demonstrate substantially higher lower-bounds on maximum achievable secrecy rate via this approach compared to the previous work [2] for similar scenarios.
Artificial noise (AN) transmission can enhance the secrecy in multiantenna wireless channels by superimposing judiciously constructed synthetic noise signals over information signals during transmission. Motivated by the large-scale multiple-input multiple-output systems, we study AN transmission under a constraint that all elements (weights) in each beamforming vector must have a constant magnitude, but can have arbitrary phases. For the special case of one AN beamforming vector and one legitimate receiver, we derive a necessary and sufficient condition for finding a beamforming vector in the null space of the legitimate receiver's channel and provide a geometric interpretation. For the independent identically distributed Rayleigh fading channel, we derive an approximate expression for the probability of failing to find such a beamforming vector, and show that it decreases exponentially in the square of the number of transmit antennas. For the general case, we propose a numerical algorithm for obtaining a set of mutually orthogonal AN beamforming vectors in the null space of all the receivers. Our approach involves reducing the problem to an unconstrained nonlinear programming problem, which is then solved using the Gauss-Newton method. We show numerically that our proposed algorithm performs significantly better than a heuristic relaxation approach. Finally, for a multiantenna system with multiple RF chains, we show numerically that the secrecy rate achieved by our proposed approach is close to that achieved by the AN transmission with unconstrained beamforming, when the number of transmit antennas is sufficiently large.
Artificial noise (AN) transmission is a physical layer security technique in multi-antenna wireless communication systems. Synthetic noise is broadcast to all receivers except designated legitimate users via beamforming in the legitimate users' null space. We consider AN transmission employing a single RF chain and analog beamforming, where beamforming vectors maintain constant magnitude while allowing arbitrary phases. Our primary objective is to design a constant-magnitude vector capable of nullifying multiple users' channel vectors simultaneously. To tackle this zero-forcing problem, we propose a novel successive partition zero-forcing (SPZF) scheme, which transforms the multi-user zero-forcing task into optimizing channel partitioning to minimize outage probability. The SPZF scheme can be generalized to any number of users, but our analysis focuses on the two-user case. Theoretical analysis reveals that our proposed SPZF scheme can attain arbitrarily low outage probability in the limit of large number of transmit antenna. We present three partition algorithms (random, iterative, and genetic) to minimize the outage probability. The outage probabilities and secrecy rates of the three partition algorithms are compared via numerical simulations. We find that the more advanced partition algorithms (iterative and genetic) achieve higher secrecy rates than the random algorithm, particularly under conditions of high signal-to-noise ratio (SNR), large number of eavesdroppers, or small number of transmit antennas.
This paper considers the secure communication via combining the artificial noise with the masked beamforming scheme. In this scenario, the transmitter is equipped with multi-antenna while each of the eavesdroppers is equipped with only one antenna, and the legitimate receiver has a receiving antenna and a transmitting antenna, respectively. The transmitter simultaneously transmits a beamformed secret information-bearing signal to a legitimate receiver and artificial noise (AN) to the eavesdroppers. The legitimate receiver sends the AN to confuse the eavesdropper while receiving the desired signal from the transmitter. We compare the proposed scheme that combining the AN with masked beamforming with no beamforming vector scheme, and derive that the combined strategy obviously improved the secrecy rate.
We consider secure communications over MISO wiretap channels, in the presence of a passive eavesdropper with multiple antennas. In this scenario, an artificial-noise-resistant (ANR) eavesdropping behavior is introduced to invalidate the artificial noise (AN) scheme proposed by Goel et al. This novel eavesdropper, by exploiting the statistical filter derived from the collected signals, can completely eliminate the influence of AN by using only two receive antennas. In particular, the received signals are firstly syphered to eliminate the power influence of AN by a linear weight which is generated from the statistical estimation for the signal covariance matrix. In comparison with the original legitimate signals, the weighted signals are however imposed by a phase difference which can be then erased by a weight vector inferred from the available information at the eavesdropper. Based on the two filtering processes, we derive a novel expression of achievable secrecy rate and give an analytical expression for the zero-secrecy-rate distance of eavesdropper to the transmitter. Finally, we characterize the expression of maximum achievable secrecy rate (MASR) and show that the optimal power allocation strategy under an ANR eavesdropping behavior is transformed into no allocation of transmission power to AN. Numerical results are presented to illustrate the damage caused by the investigated eavesdropping behavior. Interestingly, the consequence of AN elimination is not influenced even under large number of transmit antennas.
This paper studies secure wireless transmission from a multi-antenna transmitter to a single-antenna intended receiver overheard by multiple eavesdroppers with considering the imperfect channel state information (CSI) of wiretap channel.To enhance security of communication link, the artificial noise (AN) is generated at transmitter.We first design the robust joint optimal beamforming of secret signal and AN to minimize transmit power with constraints of security quality of service (QoS), i.e., minimum allowable signal-to-interference-and-noise ratio (SINR) at receiver and maximum tolerable SINR at eavesdroppers.The formulated design problem is shown to be nonconvex and we transfer it into linear matrix inequalities (LMIs).The semidefinite relaxation (SDR) technique is used and the approximated method is proved to solve the original problem exactly.To verify the robustness and tightness of proposed beamforming, we also provide a method to calculate the worst-case SINR at eavesdroppers for a designed transmit scheme using semidefinite programming (SDP).Additionally, the secrecy rate maximization is explored for fixed total transmit power.To tackle the nonconvexity of original formulation, we develop an iterative approach employing sequential parametric convex approximation (SPCA).The simulation results illustrate that the proposed robust transmit schemes can effectively improve the transmit performance.
This paper studies a secure communication over multiple-input multiple-output multi-antenna eavesdropper (MIMOME) channels which consist of legitimate parities, namely a transmitter and receiver, equipped with multi-antennas and a passive eavesdropper with multi-antennas. For securing the communication between the legitimate parties, we consider an artificial noise (AN) scheme in which the legitimate transmitter sends its secret messages and AN signal together. Meanwhile, it is assumed that the legitimate receiver has a full-duplex capability which enables it to capture the secret message from the transmitter and simultaneously generate a jamming signal to strengthen security. While there have been studies on similar setups, most of them focus on the design of the jamming signal with the assumption of full channel-state information (CSI) and/or system parameter optimization based on numerical evaluations. On the contrary, in this work, we instead introduce a tight lower bound on an achievable ergodic secrecy rate as a versatile analytic tool and derive a closed-form expressions for the bound. To confirm the analytic results, we carry out numerical evaluations of the ergodic secrecy rate which are compared with the proposed lower bound.