The hybrid architecture still be the most attractive solution for the analog‐digital beamforming in millimeter wave (mmWave) large‐scale multiple input multiple output (LS‐MIMO) systems, since it provides the best trade‐off between the achievable rate and the power consumption. When maximizing performance metrics, channel knowledge is required to optimally design the hybrid beamforming. The channel estimation (CE) is essential for wideband mmWave LS‐MIMO to substantially enhance data rates, however, is a challenging task. Practically, the antenna number and the bandwidth for such communications are very large. Therefore, the CE scheme should account for the frequency‐dependence of the array response vectors and thereby the beam squint effect. In the first part, this article addresses a structured analysis compressive sensing (CS) for CE in a frequency selective mmWave LS‐MIMO system without neglecting the beam squint effect. Compared to sparse mmWave CE approach that mostly uses on‐grid dictionaries, our proposed approach considers continually distributed angles of arrival and departure. In the second part, we show that the frequency‐selective mmWave MIMO channels share a common sparsity structure within the same subcarrier‐group. Then, we propose a block‐sparsity‐based CS approach that uses the simultaneous orthogonal matching pursuit method to estimate the mmWave channel. Moreover, we prove the partial sparsity structure shared between all the subcarrier‐groups. Hence, we develop our proposed joint subcarrier‐block‐based CE scheme exploiting these two block‐sparsity structures. Numerical results evaluate the performances in terms of normalized mean‐squared error and spectral efficiency to select the most accurate channel estimator with lower overhead.

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