: List of Main Variables and Their Physical Meanings

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System Model and IRS Elements Grouping Design {#sec:sysmodel}
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We consider a single-user OFDM-based wireless system, wherein an IRS is employed to enhance the communication between a BS and a user, as illustrated in Fig. \[fig:irs\]. For the purpose of exposition, we assume that the BS and the user are both equipped with a single antenna. The IRS is assumed to comprise $M$ passive reflecting units, denoted by the set $\mathcal{M}=\{1,\dotsc, M\}$, and is connected to a controller, which adjusts the IRS pattern for desired signal reflection. Without loss of generality, we focus on uplink communication from the user to the BS in this paper, where pilot symbols are sent from the user and reflected by the IRS, based on which the BS estimates all the involved channels, computes the optimal design parameters, and then informs the IRS via a separate wireless control link (details to be given in Section \[sec:ce\]). For downlink communication, by assuming channel reciprocity and leveraging TDD, the design parameters can be similarly optimized at the BS based on the channel information obtained during the uplink training. It is further assumed that the signals that are 