Abstract
Long-term evolution (LTE) and wireless local area network (WLAN) are often presented as opposing technologies. Hence, efficient partitioning of the spectrum resources carries critical importance for achieving the coexistence of these on the unlicensed spectrum band. In this paper, we firstly develop an online spectrum partitioning algorithm, which needs little signal transmission and exchange between coordination manager and networks. Then, we focus on the convergence analysis of the online spectrum partitioning algorithm, which is difficult due to the time-varying wireless channels. To overcome this challenge, we model the algorithm and network dynamics as the stochastic differential equations (SDE) and show that the algorithm convergence is equivalent to the stochastic stability of a virtual stochastic dynamic system constructed by the SDEs. Then, we give the sufficient condition about the algorithm convergence and the upper bound on the tracking error of the spectrum partitioning algorithm under exogenous variations of time-varying channel state information (CSI). Based on the insights of the impact of time-varying CSI on algorithm convergence, an online compensative spectrum partitioning algorithm is developed to offset the tracking error caused by the disturbance of time-varying CSI. Through performance evaluation, we show that the coexistence performance efficiency will come at low expense of algorithm complexity and signal overhead.