  Channel estimation is useful in millimeter wave (mmWave) MIMO communication
systems. Channel state information allows optimized designs of precoders and
combiners under different metrics such as mutual information or
signal-to-interference-noise (SINR) ratio. At mmWave, MIMO precoders and
combiners are usually hybrid, since this architecture provides a means to
trade-off power consumption and achievable rate. Channel estimation is
challenging when using these architectures, however, since there is no direct
access to the outputs of the different antenna elements in the array. The MIMO
channel can only be observed through the analog combining network, which acts
as a compression stage of the received signal. Most of prior work on channel
estimation for hybrid architectures assumes a frequency-flat mmWave channel
model. In this paper, we consider a frequency-selective mmWave channel and
propose compressed-sensing-based strategies to estimate the channel in the
frequency domain. We evaluate different algorithms and compute their complexity
to expose trade-offs in complexity-overhead-performance as compared to those of
previous approaches.
