  In this paper, we investigate the robust outage constrained transmission
design for an intelligent reflecting surface (IRS) aided secure communication
system. We assume that a single-antenna legitimate receiver (Bob) served by a
multi-antenna base station (BS) is overheard by multiple single-antenna
eavesdroppers (Eves), and the artificial noise (AN) is incorporated to confuse
the Eves. In particular, we aim to jointly optimize the transmit beamforming,
the AN spatial distribution at the BS, and the passive beamforming at the IRS,
where the Eve-related channels are assumed to be imperfect due to the channel
estimation errors and their concealment. Two scenarios with partial channel
state information (CSI) error of only cascaded BS-IRS-Eve channel and full CSI
errors of both cascaded BS-IRS-Eve channel and direct BS-Eve channel are
investigated under the statistical CSI error model. An outage-constrained power
minimization problem is formulated by limiting the maximum allowable data rate
of Eves and ensuring the minimum data rate requirement of Bob. To solve it, the
Bernstein-type inequality and alternating optimization strategy are exploited,
and artful mathematical manipulations are performed to facilitate the
optimization on the phase shifts of the IRS. Simulation results confirm the
performance advantages of the proposed algorithm.
