Many shortest link scheduling algorithms adopt non-fading SINR interference model, which assumes that the received signal power will always remain determinate as long as the transmission power of the corresponding sender is fixed. In fact, because environment always influences the propagation of radio signals, the received signal power is by no means a certain value. Rayleigh fading is a statistical model for radio signals propagation. It assumes that the strength of a signal on a receiver is a random variable, varying with the Rayleigh distribution. This paper proposes a shortest link scheduling algorithm under the Rayleigh fading model (SLSRF). The SLSRF partitions the wireless network area into hexagons and colors the hexagons with three different colors such that two neighboring hexagons have different colors. The senders of the links scheduled simultaneously are arranged in hexagons with the same color. The correctness of the SLSRF is proved through theoretical analysis, and the efficiency is illustrated by elaborate simulations. Our simulation results demonstrate that the schedule delay of SLSRF is less than that of some results under the non-fading SINR interference model. Furthermore, we extend the SLSRF to a distributed version, which is suitable for large wireless networks.

许多最短链路调度算法采用非衰落SINR干扰模型，假设只要相应发送方的发射功率固定，接收信号功率将始终保持确定。事实上，由于环境总是会影响无线电信号的传播，因此接收到的信号功率并非一定值。瑞利衰落是无线电信号传播的统计模型。它假设接收器上的信号强度是一个随机变量，随瑞利分布而变化。本文提出了一种基于瑞利衰落模型（SLSRF）的最短链路调度算法。SLSRF 将无线网络区域划分为六边形，并用三种不同的颜色为六边形着色，使得两个相邻的六边形具有不同的颜色。同时调度的链接的发送者排列在相同颜色的六边形中。通过理论分析证明了 SLSRF 的正确性，并通过精心的仿真来说明其效率。我们的仿真结果表明，SLSRF 的调度延迟小于非衰落 SINR 干扰模型下的某些结果。此外，我们将 SLSRF 扩展为分布式版本，适用于大型无线网络。