  Coexistence of Wi-Fi and LTE-Unlicensed (LTE-U) technologies has drawn
significant concern in industry. In this paper, we investigate the Wi-Fi
performance in the presence of duty cycle based LTE-U transmission on the same
channel. More specifically, one LTE-U cell and one Wi-Fi basic service set
(BSS) coexist by allowing LTE-U devices transmit their signals only in
predetermined duty cycles. Wi-Fi stations, on the other hand, simply contend
the shared channel using the distributed coordination function (DCF) protocol
without cooperation with the LTE-U system or prior knowledge about the duty
cycle period or duty cycle of LTE-U transmission. We define the fairness of the
above scheme as the difference between Wi-Fi performance loss ratio
(considering a defined reference performance) and the LTE-U duty cycle (or
function of LTE-U duty cycle). Depending on the interference to noise ratio
(INR) being above or below -62dbm, we classify the LTE-U interference as strong
or weak and establish mathematical models accordingly. The average throughput
and average service time of Wi-Fi are both formulated as functions of Wi-Fi and
LTE-U system parameters using probability theory. Lastly, we use the Monte
Carlo analysis to demonstrate the fairness of Wi-Fi and LTE-U air time sharing.
