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This paper studies the maximum throughput achievable with optimal schedulingin multi-hop mmWave picocellular networks with Multi-user Multiple-InputMultiple-Output (MU-MIMO) radios. MU-MIMO enables simultaneous transmission tomultiple receivers (Space Division Multiplexing) and simultaneous receptionfrom multiple transmitters (Space Division Multiple Access). The maincontribution is the extension to MU-MIMO of the Network Utility Maximization(NUM) scheduling framework for multi-hop networks. We generalize to MU-MIMO theclassic proof that Maximum Back Pressure (MBP) scheduling is NUM optimal. MBPrequires the solution of an optimization that becomes harder with MU-MIMOradios. In prior models with one-to-one transmission and reception, each validschedule was a matching over a graph. However, with MU-MIMO each valid scheduleis, instead, a Directed Bipartite SubGraph (DBSG). In the general case thisprevents finding efficient algorithms to solve the scheduler. We make MU-MIMOMBP scheduling tractable by assuming fixed power allocation, so the optimalscheduler is the Maximum Weighted DBSG. The MWDBSG problem can be solved usingstandard Mixed Integer Linear Programing. We simulate multi-hop mmWavepicocellular 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.

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