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.

Twice Simulated Annealing Resource Allocation for mmWave Multi-hop Networks with Interference

“…We adopt as a baseline the Mixed Integer Linear Programming (MILP) link selection algorithm from a prior work [12], which is optimal for the interference-free scheduling problem (4) with fixed power allocation ρ F P (s) = P/N RF , but not for (2). The baseline precomputes the "potential capacity" a link would have if selected, which does not depend on s, as…”

“…For this, the upper layers interface with the scheduler by providing a list of weights that assign a certain value to the delivery of one bit through each link, denoted w n,m (t). This framework permits embedding our scheduler into a wide variety of well-known networking, congestion control, routing and quality of service algorithms for multi-hop networks, such as for example [12]. Due to the fact that at each time t the scheduler makes decisions based only on w n,m (t), in the rest of the paper we will drop the time index indication (t) from our notation.…”

“…where one possible interpretation of existing schedulers for mmWave systems assuming negligible interference such as [10]- [12] is that they implicitly claim that the solution of ( 4) is identical or close enough to the solution of (2).…”

“…Some prior works have studied mmWave under the assumption that interference can be ignored. This assumption is often found in multi-hop scheduling research [10]- [12]. Even though this would be justified under perfect link directivity, separate studies on mmWave single-hop cellular systems suggest that this assumption does not always hold [13].…”

“…The main contribution of this paper is to study the impact of nonnegligible interference on link scheduling and power allocation schemes for mmWave IAB networks with MU-MIMO. We implement a scheduler for the case with interference and compare it with the optimal scheduler for the interferencefree case given in [12]. Our solution employs two separate instances of Simulated Annealing (SA) optimization [14], one to select which nodes transmit or receive and another for power allocation.…”