  We investigate the joint uplink-downlink configuration of an intelligent
reflecting surface (IRS) for multi-user frequency-division-duplexing (FDD) and
time-division-duplexing (TDD) systems. This is motivated in FDD since uplink
and downlink transmissions occur simultaneously and hence an IRS must be
jointly configured for both transmissions. In TDD, while a joint design is not
strictly necessary, it can significantly reduce feedback overhead, power
consumption, and configuration periods associated with updating the IRS. To
compute the trade-off between uplink and downlink rates achieved by a joint
design, a weighted-sum problem is formulated and optimized using a developed
block-coordinate descent algorithm. The resulting uplink-downlink trade-off
regions are investigated by numerical simulation to gain insights into
different scenarios. In all FDD scenarios and some TDD scenarios, the jointly
optimized design significantly outperforms the fixed-uplink (fixed-downlink)
heuristic of using the IRS configuration optimized for uplink (downlink) to
assist downlink (uplink) transmissions. Moreover, the joint design
substantially bridges the gap to the individual design upper bound of allowing
different IRS configurations in uplink and downlink. Otherwise, in the
remaining TDD scenarios, the fixed-uplink and fixed-downlink designs nearly
achieve the individual design performance and substantially reduce overhead
and/or complexity compared to the optimized joint design and individual design.
