  This paper considers an intelligent reflecting surface (IRS) aided
multiple-input single-output communication system, where statistical channel
state information (CSI) is exploited for transmit beamforming and IRS
beamforming. A tight upper bound is derived for the ergodic capacity of the
system. Based on which, the joint optimization of transmit beam and IRS beam
are studied. Depending on whether a line-of-sight path exists between the
access point and user, two different cases, namely, Rician fading and Rayleigh
fading, are separately treated. Specifically, for the Rician fading case, an
iterative algorithm is proposed, which is guaranteed to converge. For the
Rayleigh fading case, closed-form designs are obtained for the transmit beam
and IRS beam. Simulation results show the proposed beamforming scheme achieves
similar performance as the benchmark algorithm requiring instantaneous CSI.
