For illustration, we consider a rectangular-shaped IRS as shown in Fig. \[fig:irsgroup\] with $\rho=1/4$, where there are $M_x$ and $M_y$ elements in each row and column, respectively. We further assume rectangular-shaped groups with $B_x$ and $B_y$ elements in each row and column, respectively, with $1\leq B_x\leq M_x$ and $1\leq B_y\leq M_y$. Therefore, the number of groups $K$ as well as the grouping ratio $\rho$ can be adjusted by varying $B_x$ and $B_y$. For ease of exposition, given any grouping, we assume the indices of IRS reflecting elements within each group are continuous, namely, the $\left((k-1)B+1\right)$-th to the $\left(kB\right)$-th elements belong to the $k$-th group, as illustrated in Fig. \[fig:irsgroup\]. By considering a common reflection coefficient to the elements of each group, the IRS reflection coefficients can be re-expressed as $$\begin{aligned}
 \boldsymbol{\phi}=\bar{\boldsymbol{\phi}}\otimes {\bf 1}_{B\times 1},\end{aligned}$$ where $\bar{\boldsymbol{\phi}}=[\bar{\phi}_1,\cdots, \bar{\phi}_K]^T\in\mathbb{C}^{K\times 1}$ represents the IRS *group* reflection coefficients, with $\bar{\phi}_k$ denoting the common reflection coefficient for the $k$-th group. With grouping, the concatenation of the BS-IRS channel, IRS reflection, and IRS-user channel in (\[eqn:hr1\]) can be rewritten as $$\begin{aligned}
\boldsymbol{h}_r =[{\boldsymbol{\nu}}_1,\dotsc,{\boldsymbol{\nu}}_M]\bar{\boldsymbol{\phi}}\otimes {\bf 1}_{B\times 1}=[\boldsymbol{\nu}'_1,\dotsc,\boldsymbol{\nu}'_K]\bar{\boldsymbol{\phi}}=\boldsymbol{V}'\bar{\boldsymbol{\phi}},\end{aligned}$$ where $\boldsymbol{\nu}'_k=\sum_{b=1}^{B} {\boldsymbol{\nu}}_{b+(k-1)\times B}$ denotes the combined composite reflecting channel associated with the $k$-th IRS group, $k\in\mathcal{K}$, with $\mathcal{K}=\{1,\dotsc,K\}$, and 