Interference Relay Channels - Part II: Power Allocation Games

In the first part of this paper we have derived achievable transmission rates for the (single-band) interference relay channel (IRC) when the relay implements either the amplify-and-forward, decode-and-forward or estimate-andforward protocol. Here, we consider wireless networks that can be modeled by a multi-band IRC. We tackle the existence issue of Nash equilibria (NE) in these networks where each information source is assumed to selfishly allocate its power between the available bands in order to maximize its individual transmission rate. Interestingly, it is possible to show that the three power allocation (PA) games (corresponding to the three protocols assumed) under investigation are concave, which guarantees the existence of a pure NE after Rosen [3]. Then, as the relay can also optimize several parameters e.g., its position and transmit power, it is further considered as the leader of a Stackelberg game where the information sources are the followers. Our theoretical analysis is illustrated by simulations giving more insights on the addressed issues. Index Terms Cognitive radio, game theory, interference relay channel, Nash equilibrium, power allocation games, relay channel, Stackelberg game.