On the Fairness of the Coexisting LTE-U and WiFi Networks Sharing Multiple Unlicensed Channels

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In this paper, we are the first to analyse the performance of the carrier sense adaptive transmission (CSAT) scheme in the large-scale coexisting LTE-U and WiFi networks (CLWNets) sharing multiple unlicensed channels (UCs). As the capability of idle channel detection (ICD) has significant effect on the medium access probability (MAP) of WiFi access points (WAP), the closed-from MAP of the WAP and the explicit expressions of downlink successful transmission probabilities (STPs) of LTE-U-base-station (LBS) users and WAP users are derived with/without equipping ICD capability in WAPs, where the positions of LBSs and WAPs are modelled following the Matern hard core process. Based on the derived STPs, the fairness between the LTE-U network and the WiFi network, which is defined as the minimum weighted area spectral efficiency (ASE) of LBS and WAP users, is analysed versus the number of UCs, the fairness weighting factor and the densities of LBSs and WAPs. Furthermore, the optimal off-duty-cycle (DC) ratio to maximize the minimum weighted ASE is obtained based on the derived STPs in the on-DC and off-DC durations. Our results show that the fairness between the LTE-U and WiFi networks can be achieved by adjusting the off-DC ratio under low weighting factors. The increase of UC number leads to a decrease of the optimal off-DC ratio, enhancing the transmission duration of LBSs, and the shrink of UC bandwidth only causes negligible reduction in the CLWNets ASE. In addition, the WAP medium access mechanism mode with ICD capability is preferable as it can provide a maximum of $70\%$ ASE enhancement in the CLWNets.