  In this work, we investigate the performance of a millimeter waves (mmWaves)
cellular system with free space optical (FSO) backhauling. MmWave channels are
subject to Nakagami-m fading while the optical links experience the Double
Generalized Gamma including atmospheric turbulence, path loss and the
misalignment between the transmitter and the receiver aperture (also known as
the pointing errors). The FSO model also takes into account the receiver
detection technique which could be either heterodyne or intensity modulation
and direct detection (IM/DD). Each user equipment (UE) has to be associated to
one serving base station (BS) based on the received signal strength (RSS) or
Channel State Information (CSI). We assume partial relay selection (PRS) with
CSI based on mmWaves channels to select the BS associated with the highest
received CSI. Each serving BS decodes the received signal for denoising,
converts it into modulated FSO signal, and then forwards it to the data center.
Thereby, each BS can be viewed as a decode-and-forward (DF) relay. In practice,
the relay hardware suffers from nonlinear high power amplification (HPA)
impairments which, substantially degrade the system performance. In this work,
we will discuss the impacts of three common HPA impairments named respectively,
soft envelope limiter (SEL), traveling wave tube amplifier (TWTA), and solid
state power amplifier (SSPA). Novel closed-forms and tight upper bounds of the
outage probability, the probability of error, and the achievable rate are
derived. Capitalizing on these performance, we derive the high SNR asymptotes
to get engineering insights into the system gain such as the diversity order.
