  We present a generalization of the notoriously unwieldy second-order
scattering fading model, which is helpful to alleviate its mathematical
complexity while providing an additional degree of freedom. This is
accomplished by allowing its dominant specular component associated to
line-of-sight propagation to randomly fluctuate. The statistical
characterization of the newly proposed model is carried out, providing
closed-form expressions for its probability and cumulative distribution
functions, as well as for its generalized Laplace-domain statistics and raw
moments. We exemplify how performance analysis can be done in this scenario,
and discuss the role of the fading model parameters on system performance.
