  This paper considers the deployment of a hybrid wireless data/power access
point in an 802.11-based wireless powered IoT network. The proportionally fair
allocation of throughputs across IoT nodes is considered under the constraints
of energy neutrality and CPU capability for each device. The joint optimization
of wireless powering and data communication resources takes the CSMA/CA random
channel access features, e.g. the backoff procedure, collisions, protocol
overhead into account. Numerical results show that the optimized solution can
effectively balance individual throughput across nodes, and meanwhile
proportionally maximize the overall sum throughput under energy constraints.
