  In this letter, some applications of wireless communication systems over
$\alpha-\eta-\kappa-\mu$ fading channels are analysed. More specifically, the
effective rate and the average of both the detection probability and area under
the receiver characteristics curve of energy detection based spectrum sensing
are studied. Furthermore, highly accurate method to truncating the infinite
summation of the probability density function of $\alpha-\eta-\kappa-\mu$
fading conditions for a certain number of terms is provided. To this end, novel
mathematically tractable exact expressions are derived in terms of the Fox's
$H$-function (FHF). The asymptotic behaviour is also explained to earn further
insights into the effect of the fading parameters on the system performance. A
comparison between the numerical results and Monte Carlo simulations is
presented to verify the validation of our analysis.
