Optimal Scheduling for Uncoded and Coded Multicast in Millimeter Wave Networks Leveraging Directionality and Reflections

We investigate the minimum-delay multicast scheduling problem for millimeter wave (mmWave) networks. Salient characteristics of mmWave links, directionality and reflections, are considered under sectored antenna model. We first consider the model where the signal is received at a single Direction-of-Arrival (DoA) with the highest SNR at each node. We identify the property such that the optimal policy can be recursively partitioned into smaller sizes and propose an iterative method based on graphs which finds the optimal schedule in polynomial time. Next, we extend our model where a node leverages signals received at multiple DoAs through reflections. We introduce the concept of receiving direction diversity (RDD) which states that the availability of multiple receiving directions enables opportunistic reduction of multicast delay. We prove NP-hardness of the problem, and propose approximations with performance bounds and heuristics of reduced complexity. Next, we consider multicast scheduling with rateless codes (RCs) which reduces delay by flexible packet reception. For both cases of coded multicast with and without RDD, we formulate linear programming problems and propose greedy algorithms with nearly optimal performance and reduced complexity. By simulation we show the outperformance of our method over conventional ones, and numerically characterize the gain of RDD and RCs.