We investigate the joint uplink-downlink design for time-division-duplexing (TDD) and frequency-division-duplexing (FDD) multi-user systems aided by an intelligent reflecting surface (IRS). We formulate and solve a multi-objective optimization problem to maximize uplink and downlink rates as a weighted-sum problem (WSP) that captures the trade-off between achievable uplink and downlink rates. We propose a resource allocation design that optimizes the WSP by jointly optimizing the beamforming vectors, power control and IRS phase shifts where the same IRS configuration is used for assisting uplink and downlink transmissions. In TDD, the proposed IRS design reduces the overhead associated with IRS configuration and the need for quiet periods while updating the IRS. In addition, a joint IRS design is critical for supporting concurrent uplink and downlink transmissions in FDD. We investigate the effect of different user-weighting strategies and different parameters on the performance of the joint IRS design and the resultant uplink-downlink trade-off regions. In all FDD scenarios and some TDD scenarios, the joint design significantly outperforms the heuristic of using the IRS configuration optimized for uplink (respectively, downlink) to assist the downlink (respectively, uplink) transmissions and substantially bridges the gap to the upper bound of allowing different IRS configurations in uplink and downlink.
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