  Grant Free Random Access (GFRA) is a popular protocol in the Internet of
Things (IoT) to reduce the control signaling. GFRA is a framed protocol where
each frame is split into two parts: device identification; and data
transmission part which can be viewed as a form of Frame Slotted ALOHA (FSA). A
common assumption in FSA is device homogeneity; that is the probability that a
device seeks to transmit data in a particular frame is common for all devices
and independent of the other devices. Recent work has investigated the
possibility of tuning the FSA protocol to the statistics of the network by
changing the probability for a particular device to access a particular slot.
However, power control with a successive interference cancellation (SIC)
receiver has not yet been considered to further increase the performance of the
tuned FSA protocols. In this paper, we propose algorithms to jointly optimize
both the slot selection and the transmit power of the devices to minimize the
outage of the devices in the network. We show via a simulation study that our
algorithms can outperform baselines (including slotted ALOHA) in terms of
expected number of devices transmitting without outage and in term of transmit
power.
