Delay-Optimal Cooperation Policy in a Slotted Aloha Full-Duplex Wireless Network: Static Approach

We consider a cooperative wireless communication network comprising two full-duplex (FD) nodes transmitting to a common destination based on slotted Aloha protocol. Each node has exogenous arrivals and also may relay some of the unsuccessfully transmitted packets of the other node. In this article, we find the optimal static policies of nodes in order to minimize the sum of the average transmission delays, while the average transmission delay of each node is constrained. The static policy of each node specifies the probability of accepting an unsuccessfully transmitted packet of the other node and how the node prioritizes its transmissions. We show that in the optimal policies, just the node with the better link to destination may relay the packets of the other node. We derive optimal acceptance probability of the relaying node in closed form, and show that it should transmit the packets of the other node first. Moreover, we prove that the noncooperation policy is optimal if the ratio of successful transmission rates of nodes does not exceed the Golden ratio. We also show that FD capability of nodes is helpful only when full-acceptance is the optimal policy. Efficiency of the attained optimal policy is illustrated by numerical results.