  Machine-type-communications (MTC) are being crucial in the development of
next generation mobile networks. Given that MTC devices are usually battery
constrained, wireless power transfer (WPT) and energy harvesting (EH) have
emerged as feasible options to enlarge the lifetime of the devices, leading to
wireless powered networks. In that sense, we consider a setup where groups of
sensors are served by a base station (BS), which is responsible for the WPT.
Additionally, EH is used to collect energy from the wireless signals
transmitted by other sensors. To characterize the energy obtained from both
procedures, we model the sporadic activity of sensors as Bernoulli random
variables and their positions with repulsive Mat\'ern cluster processes. This
way, the random activity and spatial distribution of sensors are introduced in
the analysis of the energy statistics. This analysis can be useful for system
design aspects such as energy allocation schemes or optimization of idle-active
periods, among others. As an example of use of the developed analysis, we
include the design of a WPT scheme under a proportional fair policy.

Signal Processing