$\boldsymbol{V}'\triangleq[\boldsymbol{\nu}'_1,\dotsc,\boldsymbol{\nu}'_K]\in\mathbb{C}^{N\times K}$ denotes the group composite channel matrix. It is worth noting that with our proposed grouping method, the size of the composite channel matrix associated with the IRS reflected link that needs to be estimated, $\boldsymbol{V}'$, is given by $N\times K$, which is generally smaller than that of the entire composite channel $\boldsymbol{V}$, $N\times M$, due to $K\leq M$. The maximum achievable rate based on the proposed IRS elements grouping is then given by $$\begin{aligned}
    r(\boldsymbol{p},\bar{\boldsymbol{\phi}})\!=\!\frac{1}{N\!+\!N_{\mathrm{CP}}}\!\sum_{n=0}^{N-1}\! \log_2\!\left(\!1\!+\!\frac{|\boldsymbol{f}_n^H\boldsymbol{h}_{d}\!+\!\boldsymbol{f}_n^H\boldsymbol{V}'\bar{\boldsymbol{\phi}}|^2p_n}{\Gamma\sigma^2} \!\right)\!,\label{eqn:rk2}\end{aligned}$$ which is equivalent to (\[eqn:rk\]) if $K=M$. Based on our proposed grouping method, we further propose a practical transmission protocol to approach the theoretical maximum achievable rate shown in (\[eqn:rk2\]) in the next section.

Transmission Protocol with IRS Elements Grouping {#sec:ce}
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In this section, we propose a practical transmission protocol based on the proposed grouping method, as illustrated in Fig. \[fig:Preamble\]. Specifically, each channel coherence block consists of three transmission phases, with $T_c$ denoting the channel coherence time normalized to number of OFDM symbol durations. In the first phase, $K+1$ pilot symbols are transmitted from the user and reflected by the IRS, based on which the BS estimates the channel for both the BS-user direct link (i.e., $\boldsymbol{h}_d$) and the 