to achieve reasonably good beamforming performance. In general, there has been very limited work on how to design an efficient channel estimation strategy specifically catered to the IRS-based passive array systems. Moreover, it is worth noting that prior works on IRS-aided wireless systems [@qqtwc; @qqicassp; @debtwc; @debtwc2; @mmwre; @irsstatscsi] have mainly considered frequency-flat (non-selective) fading channels for narrowband communications, where the IRS reflection coefficients are designed to align the phase of the BS-IRS-user reflected link with that of the BS-user direct link for constructive superposition. However, when frequency-selective channels are considered, the IRS reflection coefficients need to cater to all signal paths at different delays, for which the underlying optimization problem is thus more challenging to solve. Notwithstanding, the design of IRS passive array coefficients over frequency-selective fading channels for broadband communications has not been addressed yet, to the authors’ best knowledge.

![An IRS-enhanced wireless system.[]{data-label="fig:irs"}](IRS_diag_su.eps "fig:"){width="0.6\linewidth"} .

Motivated by the above challenges, in this paper, we investigate an IRS-aided orthogonal frequency division multiplexing (OFDM)-based wireless system over frequency-selective channels, as shown in Fig. \[fig:irs\]. We consider point-to-point communication between a BS and a single user in the vicinity of an IRS, where the IRS and the user are both 