and IRS coefficient designs generally achieve improved rate performance compared to systems without using IRS or with random IRS reflection coefficients, for both cases of perfect and estimated CSI. Moreover, it is shown that the proposed initialization scheme is already able to achieve comparable performance to that of the iterative algorithm, thus is suitable for low-complexity implementation in practice. Furthermore, by comparing the performance of the proposed grouping with different group size and at high or low signal-to-noise ratio (SNR) values, it is unveiled that there generally exists an optimal group size that maximizes the achievable rate considerably, with a given channel coherence time, by optimally striking the balance between minimizing the training overhead and maximizing the IRS passive beamforming flexibility.

The rest of this paper is organized as follows. Section \[sec:sysmodel\] presents the system model of the IRS-enhanced OFDM communication and illustrates the proposed IRS elements grouping. Section \[sec:ce\] proposes a practical transmission protocol with channel estimation based on the proposed grouping scheme. Given grouping and channel estimates, Section \[sec:pfsol\] formulates the joint optimization problem of the OFDM power allocation and IRS reflection coefficients to maximize the achievable rate, and proposes an iterative algorithm to obtain a suboptimal solution 