  We introduce a new class of fading channels, built as the superposition of
two fluctuating specular components with random phases, plus a clustering of
scattered waves: the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel.
The MFTR model emerges as a natural generalization of both the fluctuating
two-ray (FTR) and the $\kappa$-$\mu$ shadowed fading models through a more
general yet equally mathematically tractable model. This generalization enables
the presence of additional multipath clusters in the purely ray-based FTR
model, and the convenience of the new underlying fading channel model is
discussed in depth. Then, we derive all the chief probability functions of the
MFTR model (e.g., probability density function (PDF), cumulative density
function (CDF), and moment generation function) in closed-form, having {a
mathematical complexity similar to} other fading models in the
state-of-the-art. We also provide two additional analytical formulations for
the PDF and the CDF: (i) in terms of a continuous mixture of $\kappa$-$\mu$
shadowed distributions, and (ii) as an infinite discrete mixture of Gamma
distributions. Such expressions enable to conduct performance analysis under
MFTR fading by directly leveraging readily available results for the
$\kappa$-$\mu$ shadowed or Nakagami-$m$ cases, respectively. The performance of
wireless communications systems undergoing MFTR fading is exemplified in terms
of a classical benchmarking metric like the outage probability, both in exact
and asymptotic forms, and the amount of fading.
