The use of multiple‐antenna arrays has attracted much attention for the physical layer security of wireless systems, where the so‐called artificial‐noise solution can be applied to enhance the communication confidentiality. In the first part of this study, the authors consider secure communication over a multiple‐input single‐output Rayleigh‐fading channel in the presence of a multiple‐antenna eavesdropper – referred to as a multiple‐input single‐output multiple‐eavesdropper (MISOME) wiretap channel. Specifically, secure beamforming with artificial noise is treated when the transmitter has access to full channel state information (CSI) of a legitimate channel but only partial CSI of an eavesdropper channel. First, the optimal power allocation between the information‐bearing signal and artificial noise (or simulated interference) is derived to maximise the achievable secrecy rate in the presence of a weak or strong eavesdropper. Then, the first‐order optimal power allocation strategy is developed in a switched fashion by selecting the best of weak‐ and strong‐eavesdropper solutions for a general eavesdropping attack, and a closed‐form expression is derived for the ergodic secrecy rate achieved by secure beamforming with this switched power allocation in the MISOME wiretap channel. The numerical results show that the switched power allocation is a simple but effective approach that nearly achieves the optimal secrecy rate.

The authors consider secure beamforming with artificial noise in a multiple‐input single‐output multiple‐eavesdropper (MISOME) wiretap channel, where a transmitter has access to full channel state information (CSI) of a legitimate channel but only partial CSI of eavesdropper channels. In the second part of this study, the authors first put forth a new notion of symbol error probability (SEP) for confidential information – called the ‘ δ ‐secrecy SEP’ – to connect the reliability and confidentiality of the legitimate communication in MISOME wiretap channels. For single‐antenna colluding and non‐colluding eavesdroppers, the authors then quantify the diversity impact of secure beamforming with artificial noise on the δ ‐secrecy SEP and show that the artificial ‐noise strategy with n t transmit antennas preserves the secrecy diversity of order n t − n e for n e colluding eavesdroppers and n t − 1 for n e non‐colluding eavesdroppers, respectively. In addition, the authors determine the optimal power allocation between the information‐bearing signal and artificial noise to minimise the δ ‐secrecy SEP in the presence of weak or strong eavesdroppers, and further develop the switched power allocation for general eavesdropping attacks.

Recursive convolution has been used in conjunction with rational function approximation to significantly improve the efficiency of the transient analysis of lossy coupled transmission lines. However, the algorithm has been mainly limited to distinct real poles. This paper presents a general algorithm for recursive convolution that includes complex conjugate pole pairs and high order real poles. These cases arise in the computation of the rational function approximations for lossy coupled transmission lines.>