## Sectorized mmWave Networks

Future wireless networks and systems including 5G/6G and next generation Wi-Fi will use the widely available spectrum in the millimeter-wave (mmWave) frequency bands to deliver multi-Gbps data rates. Since radio signals at mmWave frequencies experience significantly higher path loss compared to signals at lower frequencies (e.g., sub-6 GHz), mmWave radios employ directional antennas and the beamforming technology based on phased arrays to compensate for the high signal path loss. Despite recent deployments of commercial 5G mmWave networks, it has been shown that mobile mmWave networks have a spotty coverage, due to the fact that mmWave signals are vulnerable to environmental changes introduced by user mobility and/or blockage. However, mmWave networks in fixed deployments, such as fixed wireless access (FWA) and backhaul networks have been proven to be successful.

In a mmWave backhaul network that can provide fiber-like data rates, each mmWave node is usually composed of a number of sectors, each of which is equipped with a phased array with beamforming capability and a limited field-of-view (FoV) (e.g., ±60◦ degrees). Such a sectorized mmWave node can not only mitigate potential interference from/to neighboring nodes through highly directional transmission, but also allow for multiple concurrent outgoing/incoming data streams to be carried by different sectors of the same node.

In this thrust, we focus on the modeling, analysis, and optimization of sectorized mmWave backhaul networks, where sectorized mmWave nodes with beam-steering capabilities form a multi-hop mesh network for data forwarding and routing. In particular, we present the model of a backhaul infrastructure network consisting of a number of (fixed) sectorized mmWave nodes. Based on this sectorized network model and its connectivity graph, we describe the link interference model and characterize the capacity region of the these networks. For a sectorized mmWave network, we introduce a latent structure of its connectivity graph, called the auxiliary graph, which captures the underlying structural property of the network as a function of the sectorization of each node. We show that the capacity region of a sectorized mmWave network can be described by the matching polytope of its auxiliary graph.