  Future wireless communication calls for exploration of more efficient use of
wireless channel capacity to meet the increasing demand on higher data rate and
less latency. However, while the ergodic capacity and instantaneous capacity of
a wireless channel have been extensively studied, they are in many cases not
sufficient for use in assessing if data transmission over the channel meets the
quality of service (QoS) requirements. To address this limitation, we advocate
a set of wireless channel capacity concepts, namely "cumulative capacity",
"maximum cumulative capacity", "minimum cumulative capacity", and "range of
cumulative capacity", and for each, study its properties by taking into
consideration the impact of the underlying dependence structure of the
corresponding stochastic process. Specifically, their cumulative distribution
function (CDFs) are investigated extensively, where copula is adopted to
express the dependence structures. Results considering both generic and
specific dependence structures are derived. In particular, in addition to
i.i.d., a specially investigated dependence structure is comonotonicity, i.e,
the time series of wireless channel capacity are increasing functions of a
common random variable. Appealingly, copula can serve as a unifying technique
for obtaining results under various dependence assumptions, e.g. i.i.d. and
Markov dependence, which are widely seen in stochastic network calculus.
Moreover, some other characterizations of cumulative capacity are also studied,
including moment generating function, Mellin transform, and stochastic service
curve. With these properties, we believe QoS assessment of data transmission
over the channel can be further performed, e.g. by applying analytical
techniques and results of the stochastic network calculus theory.
