  Terahertz (THz) frequency bands can be promising for data transmissions
between the core network and access points (AP) for next-generation wireless
systems. In this paper, we analyze the performance of a dual-hop THz-RF
wireless system where an AP facilitates data transmission between a core
network and user equipment (UE). We consider a generalized model for the
end-to-end channel with an independent and not identically distributed
(i.ni.d.) fading model for THz and RF links using the $\alpha$-$\mu$
distribution, the THz link with pointing errors, and asymmetrical relay
position. We derive a closed-form expression of the cumulative distribution
function (CDF) of the end-to-end signal-to-noise ratio (SNR) for the THz-RF
link, which is valid for continuous values of $\mu$ for a generalized
performance analysis over THz fading channels. Using the derived CDF, we
analyze the performance of the THz-RF relayed system using decode-and-forward
(DF) protocol by deriving analytical expressions of diversity order, moments of
SNR, ergodic capacity, and average BER in terms of system parameters. We also
analyze the considered system with an i.i.d. model and develop simplified
performance to provide insight on the system behavior analytically under
various practically relevant scenarios. Simulation and numerical analysis show
a significant effect of fading parameters of the THz link and a nominal effect
of normalized beam-width on the performance of the relay-assisted THz-RF
system.
