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 to 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 defend 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 −62 dbm, we classify the LTE-U interference as strong or weak and establish mathematical models accordingly. Te 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.

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