Deterministic Scheduling for Low-latency Wireless Transmissions with Continuous Channel States.

High energy efficiency and low latency have always been the significant goals pursued by the designer of wireless networks. One efficient way to achieve these goals is cross-layer scheduling based on the system states in different layers, such as queuing state and channel state. However, most existing works in cross-layer design focus on the scheduling based on the discrete channel state. Little attention is paid to considering the continuous channel state that is closer to the practical scenario. Therefore, in this paper, we study the optimal cross-layer scheduling policy on data transmission in a single communication link with continuous state-space of channel. The aim of scheduling is to minimize the average power for data transmission when the average delay is constrained. More specifically, the optimal cross-layer scheduling problem was formulated as a variational problem. Based on the variational problem, we show the optimality of the deterministic scheduling policy through a constructive proof. The optimality of the deterministic policy allows us to compress the searching space from the probabilistic policies to the deterministic policies.