  In this work, we analyze the secrecy outage performance of a dual-hop relay
system composed of multiple-input-multiple-output radio-frequency (RF) links
and a free-space optical (FSO) link while a multiple-antenna eavesdropper
wiretaps the confidential information by decoding the received signals from the
resource node. The channel state information (CSI) of the RF and FSO links is
considered to be outdated. We propose three transmit antenna selection (TAS)
schemes to enhance the secrecy performance of the considered systems. The
secrecy outage performance with different TAS schemes is analyzed and the
effects of misalignment and detection technology on the secrecy outage
performance of mixed systems are studied. We derive the closed-form expressions
for probability density function (PDF) and cumulative distribution function
(CDF) over M\'alaga channel with imperfect CSI. Then the closed-form
expressions for the CDF and PDF of the equivalent signal-to-noise ratio (SNR)
at the legitimate receiver over Nakagami-$m$ and M\'alaga channels are derived.
Furthermore, the lower bound of the secrecy outage probability (SOP) with
different TAS schemes are derived. Besides, the asymptotic results for SOP are
investigated by exploiting the unfolding of Meijer's $G$-function when the
electrical SNR of FSO link approaches infinity. Finally, Monte-Carlo simulation
results are presented to testify the correctness of the proposed analysis. The
results illustrate that the outdated CSI shows a strong effect on the secrecy
outage performance. In addition, increasing the number of antennas at the
source cannot significantly enhance the secrecy performance of the considered
systems.
