Optimal Link Scheduling in Millimeter Wave Multi-hop Networks with MU-MIMO radios

Abstract: This paper studies the maximum throughput achievable with optimal scheduling in multi-hop mmWave picocellular networks with Multi-user Multiple-Input Multiple-Output (MU-MIMO) radios. MU-MIMO enables simultaneous transmission to multiple receivers (Space Division Multiplexing) and simultaneous reception from multiple transmitters (Space Division Multiple Access). The main contribution is the extension to MU-MIMO of the Network Utility Maximization (NUM) scheduling framework for multi-hop networks. We generalize to MU-MIMO the classic proof that Maximum Back Pressure (MBP) scheduling is NUM optimal. MBP requires the solution of an optimization that becomes harder with MU-MIMO radios. In prior models with one-to-one transmission and reception, each valid schedule was a matching over a graph. However, with MU-MIMO each valid schedule is, instead, a Directed Bipartite SubGraph (DBSG). In the general case this prevents finding efficient algorithms to solve the scheduler. We make MU-MIMO MBP scheduling tractable by assuming fixed power allocation, so the optimal scheduler is the Maximum Weighted DBSG. The MWDBSG problem can be solved using standard Mixed Integer Linear Programing. We simulate multi-hop mmWave picocellular networks and show that a MU-MIMO MBP scheduler enables a 160% increase in network throughput versus the classic one-to-one MBP scheduler, while fair rate allocation mechanisms are used in both cases.