WiFi/LTE-U Coexistence: An Evolutionary Game Approach

We study the spectrum coexistence problem between the long term evolution (LTE)-U and the WiFi technologies using evolutionary game theory. Specifically, we study enabling friendly coexistence mainly by interference reduction through increase in the power transmission cost on each LTE AP
¹
(eNodeB) and WiFi AP and find the conditions under which a long-term coexistence can be established. We model this long-term coexistence by finding the evolutionary stable strategies of the evolutionary game. We analyze the cost functions for the LTE-U and the WiFi APs, and show that the LTE-U AP behavior is more sensitive to the cost than to the number of users, while WiFi is more sensitive to the number of users than to the transmission power cost. To further reduce the interference, we consider the case where the WiFi AP removes users that cannot establish the minimum signal to interference plus noise ratio required to reduce the interference to the LTE-U AP users. Interestingly this creates more interference due to the aggressive/selfish behavior of the WiFi APs. Finally, we extend the game over continuous strategies by formulating a game theoretic model for the coexistence problem, find its Nash equilibrium, and study its stability under the replicator dynamics of the evolutionary game.
¹
For simplicity, we use the term AP to also refer to LTE-U eNodeBs.