  Configuring hybrid precoders and combiners is a major challenge to deploy
practical mmWave communication systems. Prior work addresses the problem of
designing hybrid precoders and combiner, yet focusing on finding solutions
under a total transmit power constraint. The design of hybrid precoders and
combiners in practical system, is constrained, however, by a per antenna
transmit power, since each antenna element in the array is connected to a power
amplifier (PA) that has to operate within its linear region. In this paper, we
focus on the problem of hybrid precoding and combining with per-antenna power
constraints, and under a frequency-selective bandlimited channel model. We
first propose an all-digital solution to this problem, and develop a hybrid
precoding and combining strategy that aims at matching this solution by
minimizing the chordal distance between the all-digital precoders (combiners)
and their hybrid approximations. Finally, since minimizing this metric does not
guarantee that the final spectral efficiency will be maximized, we optimize the
resulting spectral efficiency taking into account the per-antenna power
constraints. Simulation results show the effectiveness of our all-digital and
hybrid solutions, while emphasizing the differences with respect to the
corresponding solution under a total power constraints. As shown in our
numerical results, the proposed all-digital solution performs similarly to the
case in which a total power constraint is considered. Further, our proposed
hybrid solution is also shown to exhibit near-optimum performance, and the
influence of different system parameters is also shown, thereby showing the
suitability of our proposed framework to deploy practical mmWave MIMO systems.
