  Decoupling uplink (UL) and downlink (DL) is a new architectural paradigm
where DL and UL are not constrained to be associated to the same base station
(BS). Building upon this paradigm, the goal of the present paper is to provide
lower, albeit tight bounds for the ergodic UL capacity of a decoupled cellular
network. The analysis is performed for a scenario consisting of a macro BS and
a set of small cells (SCs) whose positions are selected randomly according to a
Poisson point process of a given spatial density. Based on this analysis simple
bounds in closed form expressions are defined. The devised bounds are employed
to compare the performance of the decoupled case versus a set of benchmark
cases, namely the coupled case, and the situations of having either a single
macro BS or only SCs. This comparison provides valuable insights regarding the
behavior and performance of such networks, providing simpler expressions for
the ergodic UL capacity as a function of the distances to the macro BS and the
density of SCs. These expressions constitute a simple guide to the minimum
degree of densification that guarantees the Quality of Service (QoS) objectives
of the network, thus, providing a valuable tool to the network operator of
significant practical and commercial value.
