  The current body of research on terahertz (THz) wireless communications
predominantly focuses on its application for single-user backhaul/fronthaul
connectivity at sub-THz frequencies. First, we develop a generalized
statistical model for signal propagation at THz frequencies encompassing
physical layer impairments, including random path-loss with Gamma distribution
for the molecular absorption coefficient, short-term fading characterized by
the $\alpha$-$\eta$-$\kappa$-$\mu$ distribution, antenna misalignment errors,
and transceiver hardware impairments. Next, we propose random access protocols
for a cell-free wireless network, ensuring successful transmission for multiple
users with limited delay and energy loss, exploiting the combined effect of
random atmospheric absorption, non-linearity of fading, hardware impairments,
and antenna misalignment errors. We consider two schemes: a fixed transmission
probability (FTP) scheme where the transmission probability (TP) of each user
is updated at the beginning of the data transmission and an adaptive
transmission probability (ATP) scheme where the TP is updated with each
successful reception of the data. We analyze the performance of both protocols
using delay, energy consumption, and outage probability with scaling laws for
the transmission of a data frame consisting of a single packet from users at a
predefined quality of service (QoS).
