far away from the BS (e.g., in a cell-edge user scenario). Our considered scenario corresponds to practical multiuser wireless systems based on either time division multiple access (TDMA) or orthogonal frequency division multiple access (OFDMA) with a given set of OFDM subcarriers (SCs) assigned to the user of interest. As the IRS is usually equipped with a large number of reflecting elements, how to jointly design their reflection coefficients (i.e., phase shifts and amplitude attenuations) so as to achieve the optimal constructive superposition of the signals reflected by the IRS and those from other paths at the receiver is crucial to maximizing the link achievable rate. However, this is a non-trivial problem to solve under our considered setup due to the following reasons. First, the BS-IRS-user channels for all the IRS elements need to be estimated for designing their reflection coefficients, for which the required channel training overhead is proportional to the number of IRS reflecting elements, thus may be prohibitive or even unaffordable in practice. Second, under the frequency-selective channel with multiple paths, the reflection coefficients of the IRS need to cater to the channel gains and delays of all paths to the receiver, including both the reflected paths 