are typically equipped with more than tens and up to thousands of elements [@metasurcell]). The number of involved channel coefficients therein is therefore much larger than that for conventional OFDM systems without the IRS, which leads to increased overhead and higher complexity for channel training and estimation to obtain all of them.

![Illustration of the IRS reflect array and proposed elements grouping.[]{data-label="fig:irsgroup"}](IRS_grouping.eps "fig:"){width="0.5\linewidth"} .

To address the aforementioned issues, in this paper, we propose an *IRS elements grouping* method to reduce the training overhead and estimation complexity. Specifically, note that since the IRS elements are usually tightly packed [@metasurcell], the channels for *adjacent* elements are practically *correlated*. Therefore, we propose to group the adjacent IRS elements that form a small block, as illustrated in Fig. \[fig:irsgroup\], based on which we estimate the combined channel of each group and consider a common reflection coefficient in the same group. Let $K$ denote the number of groups, with $1\leq K\leq M$. Without loss of generality, we assume equal size (number of IRS elements) of each group, which is given by $B=M/K$.[^4] We further define the *grouping ratio* as $\rho=1/B=K/M$, where $0<\rho\leq 1$; thus, a smaller grouping ratio implies more elements in each group. 