Abstract: Intelligent reflecting surface (IRS)-assisted millimeter-wave (mmWave) systems have emerged as a promising solution to enhance coverage and spectral efficiency, while wideband transmission and frequency-selective fading lead to high-dimensional channel models, making efficient channel estimation with limited training overhead challenging. This work proposes a low-rank Tucker channel estimator (LR-TCE) framework for channel estimation in IRS-assisted millimeter-wave orthogonal frequency division multiplexing (OFDM) systems, exploiting the cascaded IRS channel´s low-rank structure. The proposed LR-TCE operates by reformulating the received observations into a structured third-order tensor spanning the spatial, temporal, and frequency dimensions, which exposes the intrinsic low-rank structure of the IRS-assisted cascaded channel. Leveraging this representation, the algorithm extracts and iteratively refines dominant low-dimensional subspaces, which are subsequently mapped to array steering vectors to estimate the underlying path delays, angles, and gains. Simulation results demonstrate that LR-TCE achieves significantly lower normalized mean square error (NMSE) with reduced training overhead, consistently outperforming canonical polyadic decomposition (CPD) and compressed sensing baselines. The simulations also show LR-TCE´s robustness to the choice of Tucker ranks and strong estimation accuracy when training resources are evenly allocated across the time and frequency domains.

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