Two-Way Relay Strategies With a Multiaccess Uplink and Queue Stability Constraints

In this paper, we consider energy usage in a three-node, two-way relay system with stochastic data arrivals and Gaussian channels. Specifically, we allow for a set of transmission modes, assuming a multiaccess uplink transmission with the relay as an optimal multiuser receiver, and find the optimal allocation of time and energy resources to the modes. In the downlink, we introduce three transmission strategies, namely, orthogonal transmission of a digital network-coded message and the remainder of the longer source message over time, superposition coding of the digital network-coded message and the remainder of the longer message, and superposition of the two source messages. We then minimize total energy usage subject to queue stability constraints at all nodes for a given pair of average packet arrival rates. The total energy usage of these three strategies in the downlink is compared, and it is found that it is best to use superposition of the network-coded message and the remaining bits in the downlink. To study stability, we present an analysis of the queues at each node under a random scheduling protocol that closely approximates the theoretical design through a Markov chain model.