  Low overhead channel estimation based on compressive sensing (CS) has been
widely investigated for hybrid wideband millimeter wave (mmWave) multiple-input
multiple-output (MIMO) systems. The channel sparsifying dictionaries used in
prior work are built from ideal array response vectors evaluated on discrete
angles of arrival/departure. In addition, these dictionaries are assumed to be
the same for all subcarriers, without considering the impacts of hardware
impairments and beam squint. In this manuscript, we derive a general channel
and signal model that explicitly incorporates the impacts of hardware
impairments, practical pulse shaping functions, and beam squint, overcoming the
limitations of mmWave MIMO channel and signal models commonly used in previous
work. Then, we propose a dictionary learning (DL) algorithm to obtain the
sparsifying dictionaries embedding hardware impairments, by considering the
effect of beam squint without introducing it into the learning process. We also
design a novel CS channel estimation algorithm under beam squint and hardware
impairments, where the channel structures at different subcarriers are
exploited to enable channel parameter estimation with low complexity and high
accuracy. Numerical results demonstrate the effectiveness of the proposed DL
and channel estimation strategy when applied to realistic mmWave channels.
