  In this article, we provide further asymptotic analysis to the higher-order
statistics (HOS) of the channel capacity over generalized fading channels,
especially by proposing simple and closed-form expressions each of which can be
easily computed as a tight-bound revealing the existence of constant gap
between the actual and asymptotic HOS of the channel capacity in the limit of
both high- and low-signal to noise ratios (SNRs). As such, we show that these
closed-form asymptotic expressions are insightful enough to comprehend the
diversity gains. The mathematical formalism we followed in this article is
illustrated with some selected numerical examples that validate the correctness
of our newly derived asymptotic results.
