  We design the phase shifts of an intelligent reflecting surface
(IRS)-assisted single-input-multiple-output communication system to minimize
the outage probability (OP) and to maximize the ergodic rate. Our phase shifts
design uses only statistical channel state information since these depend only
on the large-scale fading coefficients; the obtained phase shift design remains
valid for a longer time frame. We further assume that one has access to only
quantized phase values. The closed-form expressions for OP and ergodic rate are
derived for the considered system. Next, two optimization problems are
formulated to choose the phase shifts of IRS such that (i) OP is minimized and
(ii) the ergodic rate is maximized. We used the multi-valued particle swarm
optimization (MPSO) and particle swarm optimization (PSO) algorithms to solve
the optimization problems. Numerical simulations are performed to study the
impact of various parameters on the OP and ergodic rate. We also discuss
signaling overhead between BS and IRS controller. It is shown that the overhead
can be reduced up to $99.69 \%$ by using statistical CSI for phase shift design
and $5$ bits to represent the phase shifts without significantly compromising
on the performance.
