Transmit Antenna Selection for Security Enhancement in MIMO Wiretap Channels

We propose and analyze transmit antenna selection (TAS) to enhance physical layer security in a wiretap channel with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> antennas at the transmitter, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> antennas at the receiver, and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</sub> antennas at the eavesdropper. We focus on the practical scenario where the transmitter does not have any channel state information (CSI) of the eavesdropper's channel. The transmitter selects a single antenna that maximizes the instantaneous signal-to-noise ratio (SNR) at the receiver. The receiver and the eavesdropper employ either maximal-ratio combining (MRC) or selection combining (SC) to combine the received signals. For the proposed protocols, we derive new closed-form expressions for the probability of non-zero secrecy capacity. We consider Nakagami-m fading with non-identical fading parameters of the main channel, m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> , and of the eavesdropper's channel, m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</sub> . Next, we derive new closed-form expressions for the exact secrecy outage probability, based on which the ε-outage secrecy capacity is characterized. Based on the exact expressions, we derive the asymptotic secrecy outage probability which accurately reveals the secrecy diversity order and the secrecy array gain. We confirm that the proposed protocols achieve identical secrecy diversity orders of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> . An interesting conclusion is reached that this diversity order is independent of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</sub> and m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</sub> . Furthermore, we prove that under the proposed protocols, the secrecy outage probability and the ε-outage secrecy capacity improve with increasing N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> .