reflected by the IRS more than once have negligible power due to severe path loss and thus are ignored. We consider a quasi-static block fading channel model for all channels involved and focus on one particular fading block where the channels remain approximately constant.

Similar to conventional OFDM-based systems, the total bandwidth of the system is equally divided into $N$ orthogonal SCs, denoted by the set $\mathcal{N}=\{0,\dotsc,N-1\}$. Moreover, let $\boldsymbol{p}=[p_0,\dotsc,p_{N-1}]^T\in\mathbb{R}^{N\times 1}$, where each $p_n\geq 0$ denotes the power allocated to the $n$-th SC at the BS. Assume the total transmission power available at the BS is $P$. Thus, the power allocation should satisfy $\sum_{n=0}^{N-1} p_n\leq P$. Let $\boldsymbol{h}_{d}=[\bar{h}_{0},\dotsc,\bar{h}_{L-1},\boldsymbol{0}_{1\times\left(N-L\right)}]^T\in\mathbb{C}^{N\times 1}$ denote the zero-padded $L$-tap baseband equivalent multipath channel for the BS-user direct link. Moreover, there exists an $L_0$-tap baseband equivalent multipath channel for the BS-IRS-user link, through which the signals transmitted by the user are reflected by the IRS before arriving at the BS. Specifically, let $\boldsymbol{h}_m\in\mathbb{C}^{L_1\times 1}$ denote the $L_1$-tap baseband equivalent BS-IRS channel for the $m$-th reflecting element at the IRS, $m\in\mathcal{M}$. Similarly, let $\boldsymbol{g}_m\in\mathbb{C}^{L_2\times 1}$ denote the $L_2$-tap baseband equivalent channel of the IRS-user link for the $m$-th reflecting element, $m\in\mathcal{M}$. At the IRS, each element re-scatters the 