  Optical wireless communication (OWC) over atmospheric turbulence and pointing
errors is a well-studied topic. Still, there is limited research on signal
fading due to random fog in an outdoor environment for terrestrial wireless
communications. In this paper, we analyze the performance of a
decode-and-forward (DF) relaying under the combined effect of random fog,
pointing errors, and atmospheric turbulence with a negligible line-of-sight
(LOS) direct link. We consider a generalized model for the end-to-end channel
with independent and not identically distributed (i.ni.d.) pointing errors,
random fog with Gamma distributed attenuation coefficient, double generalized
gamma (DGG) atmospheric turbulence, and asymmetrical distance between the
source and destination. We develop density and distribution functions of
signal-to-noise ratio (SNR) under the combined effect of random fog, pointing
errors, and atmospheric turbulence (FPT) channel and distribution function for
the combined channel with random fog and pointing errors (FP). Using the
derived statistical results, we present analytical expressions of the outage
probability, average SNR, ergodic rate, and average bit error rate (BER) for
both FP and FPT channels in terms of OWC system parameters. We also develop
simplified and asymptotic performance analysis to provide insight on the system
behavior analytically under various practically relevant scenarios. We
demonstrate the mutual effects of channel impairments and pointing errors on
the OWC performance, and show that the relaying system provides significant
performance improvement compared with the direct transmissions, especially when
pointing errors and fog becomes more pronounced.
