  In this paper, we propose a trainable least squares (LS) approach for
reducing the peak-to-average power ratio (PAPR) of orthogonal frequency
division multiplexing (OFDM) signals in a hybrid beamforming (HBF) system.
Compared to digital beamforming (DBF), in HBF technology the number of antennas
exceeds the number of digital ports. Therefore, PAPR reduction capabilities are
restricted by both a limited bandwidth and the reduced size of digital space.
The problem is to meet both conditions. Moreover, the major HBF advantage is a
reduced system complexity, thus the complexity of the PAPR reduction algorithm
is expected to be low. To justify the performance of the proposed trainable LS,
we provide a performance bound achieved by convex optimization using the CVX
Matlab package. Moreover, the complexity of the proposed algorithm can be
comparable to the minimal complexity of the digital ``twin'' calculation in
HBF. The abovementioned features prove the feasibility of the trained LS for
PAPR reduction in fully-connected HBF.
