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.

中文翻译：

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用于非授权频谱中 LTE-U 和 WLAN 共存的在线频谱划分

长期演进 (LTE) 和无线局域网 (WLAN) 通常被视为对立的技术。因此，频谱资源的有效划分对于在未授权频谱带上实现这些资源的共存至关重要。在本文中，我们首先开发了一种在线频谱划分算法，该算法在协调管理器和网络之间需要很少的信号传输和交换。然后，我们专注于在线频谱划分算法的收敛性分析，该算法由于无线信道时变而困难。为了克服这一挑战，我们将算法和网络动力学建模为随机微分方程 (SDE)，并表明算法收敛性等效于由 SDE 构建的虚拟随机动态系统的随机稳定性。然后，给出了时变信道状态信息（CSI）外生变化下算法收敛的充分条件和频谱划分算法的跟踪误差上界。基于对时变CSI对算法收敛性影响的认识，提出了一种在线补偿频谱划分算法来抵消时变CSI扰动引起的跟踪误差。通过性能评估，我们表明共存性能效率将以较低的算法复杂度和信号开销为代价。基于对时变CSI对算法收敛性影响的认识，提出了一种在线补偿频谱划分算法来抵消时变CSI扰动引起的跟踪误差。通过性能评估，我们表明共存性能效率将以较低的算法复杂度和信号开销为代价。基于对时变CSI对算法收敛性影响的认识，提出了一种在线补偿频谱划分算法来抵消时变CSI扰动引起的跟踪误差。通过性能评估，我们表明共存性能效率将以较低的算法复杂度和信号开销为代价。