# Utility-Based Wireless Routing Algorithm for Massive MIMO Heterogeneous Networks
## 1 Introduction  
Multiple input multiple output (MIMO) refers to the configuration of multiple antennas at the receiving and transmitting terminals to form a system with multiple channels. It is regarded as a promising key technology for fifth-generation (5G) communication systems [1]. Base on MIMO, massive MIMO configures a large number of antennas (hundreds or even thousands) at the transceiver terminals. Massive MIMO has lots of promising benefits, such as high spectral efficiency in a specified number of base stations (BSs) and high data rate [2]. Heterogeneous network (HetNet) is another advantageous concept for wireless backhaul in 5G due to different user equipment (UE) of different network standards allowing access [1]. However, it also has some technical challenges, for example, the strong interference between cells caused by the full frequency multiplex of a large number of users and the limitations of the bandwidth and delay of the wireless backhaul link [3]. Massive MIMO communication within HetNet wireless backhaul with adjustable network topology and the number of transceiving antennas can effectively reduce signal interference and increase channel capacity.  
Typically, base stations in HetNets are connected by a tree-shaped topology because of the following reasons: (1) the explosive growth of traffic requires a large number of access points, so an easy-to-expand topology is needed and a tree topology can easily add new nodes to the network; (2) a multihop tree-shaped network is easier to control because a node is only responsible for those that are directly connected to it (i.e., children nodes). To provide a multihop connection to thewired network, the macro base station (MBS) serves as the root of the tree. However, many possible tree-shaped topologies can be considered, and each of them may result in different antenna allocations and respective performance impact. Each non-MBS shares the total data rate to its child nodes. All non-MBSs dedicate their antennas to their own parent links, while some BSs have some child links and thus have to adjust antennas between multiple links. Figure 1 shows an example where seven BSs form a backhaul network. \(BS_{1}\) serves as the MBS and is connected to the wired network, while each BS uses its respective radio interface to serve UE within their coverage. The topology of the network can be formed according to the red or green tree, while nodes in each tree need to have different links with different numbers of allocated antennas. To decide an optimal tree that can efficiently utilize radio resources and effectively serve each BS, two key issues have to be considered at the same time: topology decision and antenna allocation. Existing topology decision schemes do no support massive MIMO and thus do not consider antenna allocation. On the other hand, existing antenna allocation schemes are established based on a fixed topology. Moreover, the nonlinear nature of the utility gain of each additional antenna makes this problem more challenging. In other words, doubling the number of antennas does not double the utility gain.  
Based on the above, taking into consideration antenna allocation while establishing the topology is a challenge. To tackle this problem, we propose a heuristic algorithm named preallocated sequential routing (PSR). PSR adjusts the link of the BSs according to the distance of the root node. Based on the connection state of the previous step, the initial state of the next connection can be determined until all BSs are successfully connected.  
The rest of the paper is organized as follows. Section 2 analyzes related work. Section 3 introduces models and formally defines the problem. In Section 4, we propose a heuristic algorithm and analyze its performance. Section 5 presents the simulation results. Finally, we present the conclusion and future work of this study in Section 6.