a non-convex optimization problem. Particularly, it can be shown that the objective function of (P1) is non-concave over $\bar{\boldsymbol{\phi}}$; moreover, the variables $\bar{\boldsymbol{\phi}}$ and $\boldsymbol{p}$ are coupled in the objective function, which makes their joint optimization difficult. To overcome the above challenges, in the following, we propose an alternating optimization algorithm to find an approximate solution to (P1), by iteratively optimizing one of $\boldsymbol{p}$ and $\bar{\boldsymbol{\phi}}$ with the other fixed at each time. In addition, we devise a customized method to obtain an initial solution of $\bar{\boldsymbol{\phi}}$, denoted by $\bar{\boldsymbol{\phi}}_0$, as the starting point of the proposed alternating optimization algorithm.

Power Allocation Optimization Given IRS Coefficients {#sec:pa}
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Note that given a set of IRS coefficients $\bar{\boldsymbol{\phi}}$ with the CSI estimates, the CFR can be estimated as $\hat{\boldsymbol{v}}=\boldsymbol{F}_N\left(\hat{\boldsymbol{h}}_d+\hat{\boldsymbol{V}}'\bar{\boldsymbol{\phi}}\right)$. The optimal BS transmit power allocation $\boldsymbol{p}$ is thus given by the well-known water-filling (WF) solution [@goldsmith], i.e., $$\label{eqn:p1}
    p_n=\left(\frac{1}{c_u}-\frac{1}{c_n}\right)^+,\quad\forall n\in\mathcal{N},
$$ where $\left(x\right)^+\triangleq\max\left(0,x\right)$, $c_n=|\hat{v}_n|^2/(\Gamma\sigma^2)$ is the effective channel-to-noise power ratio (CNR) for SC $n$, and $c_u$ is the cut-off CNR that satisfies $$\begin{aligned}
    \sum_{n=0}^{N-1} \left(\frac{1}{c_u}-\frac{1}{c_n}\right)^+=P.\label{eqn:p2}\end{aligned}$$

IRS Coefficient Optimization Given Power Allocation
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Given power allocation, Problem (P1) is simplified as $$\begin{aligned}
\mathrm{(P1.1)}:\mathop{\mathtt{maximize~~}}_{\bar{\boldsymbol{\phi}}~}  &~\sum_{n=0}^{N-1} \log_2\left(\!1\!+\!\frac{|\boldsymbol{f}_n^H\hat{\boldsymbol{h}}_{d}\!+\!\boldsymbol{f}_n^H\hat{\boldsymbol{V}}'\bar{\boldsymbol{\phi}}|^2p_n}{\Gamma\sigma^2} \!\right)   \nonumber\\
    \mathtt{subject\; to}
&~~|\bar{\phi}_k|\leq 1, \quad 