On LTE-WiFi coexistence and inter-operator spectrum sharing in unlicensed bands: altruism, cooperation and fairness

The coexistence of LTE-Unlicensed (LTE-U) and WiFi in unlicensed spectrum is studied in the context of airtime sharing. We consider core problem where a set of LTE-U cells from different operators share the same channel as a co-located WiFi access point (AP). We assume that LTE-U cells utilize Listen-Before-Talk (LBT) as the default channel access mechanism. Principally, we deal with the following question: how should an operator's LTE-U cell adjust its contention window in order to provide a fair coexistence both with WiFi and co-located LTE-U cells of other operators? We consider that LTE-U cells behave altruistically both among themselves and to WiFi. Cooperation of LTE-U cells is studied using a coalition formation game framework which is based on the well-known Shapley value. We define a payoff configuration scheme in the coalition game which involves altruism. We prove that the coalitional game is always zero-monotonic, and Shapley value is also max-min fair. We compare airtime sharing performance of Shapley value with weighted proportional fairness via numerical results and show that Shapley value provides much better fairness than proportional fairness as determined by entropy and Jain's index metrics while having roughly equal average airtime.