# Utility-Based Wireless Routing Algorithm for Massive MIMO Heterogeneous Networks
## 2 Related Work  
Several papers have studied the rate, delay, and interference of wireless backhaul transmission. [PERSON] et al. [4] analyzed the performance and feasibility of full-duplex (FD) BSs. They proposed a theoretical framework that can reflect different interference problems and accurately analyze a scenario of complex interference full-duplex wireless backhauling. [PERSON] et al. [5] focused on the latency and reliability issues of mobile backhaul networks and proposed a distributed load-balancing  
Figure 1: Example of utility-based wireless backhaul routing (UWBR). algorithm for fiber-wireless-enhanced LTE-A HetNets. This method reduced the probability of latency and congestion through distributed load balancing. [PERSON] et al. [6] considered the performance and cost of wireless heterogeneous cellular networks and proposed a superimposed independent homogeneous Poisson point process model for hierarchical networks. In addition, a delay-based access control strategy was proposed to obtain better delay performance. [PERSON] et al. [7] studied the capacity of wireless backhaul networks and proposed a scheme to increase transmission capacity as well as reduce delay. The scheme concatenates small packets into large frames and then use an intelligent channel selection algorithm between adjacent nodes to send large frames. Many studies have been carried out for spectrum allocation of massive MIMO. [PERSON] et al. [8] optimized the channel performance in situations where the number of available pilot sequences cannot satisfy the demand for users in the massive MIMO system. This issue was modeled as a partially observable Markov decision process. [PERSON] et al. [9] studied downlink resource allocation to enhance user experience and improve system performance. In a scenario of cell-free massive MIMO, they proposed an iterative algorithm that can effectively solve the original downlink issue. [PERSON] et al. [2] investigated the total rate gain in the case of time-division duplex transmission brought by power allocation. [PERSON] et al. [10] studied the issue of maximum system energy efficiency in a multiuser and multicell massive MIMO network. They proposed an iterative algorithm to solve the issue of power allocation and optimization of the number of antennas. Moreover, these studies [11; 12; 13; 14] also focused on the spectrum allocation of massive MIMO. [PERSON] et al. [15] proposed a novel approach to decrease the overhead of both uplink and downlink channel estimation in massive MIMO systems. Different from traditional algorithms, they used multiple dimensional parameters to reduce the channel estimation overhead. [PERSON] et al. [16] focus on channel estimation in massive MIMO- Orthogonal Frequency Division Multiplexing (OFDM) systems. In order to reduce the adverse impact on the channel state information (CSI) due to the pilot overhead being too large, they proposed an algorithm named structured sparse adaptive coding sampling matching pursuit (SSA-CoSaMP) to optimize the channel estimation performance. Some studies have focused on wireless backhaul topology. [PERSON] et al. [17] demonstrated that a multihop network is better than a direct backhaul network in a cellular composite network topology. Furthermore, they proposed an algorithm for backhaul routing, that is, determining the switching status of small cell BSs based on traffic allocation. The algorithm can reduce energy consumption while meeting user traffic demands. [PERSON] et al. [18] proposed an algorithm that can improve system efficiency by considering various aspects (i.e., link cross, small angle) of wireless backhaul networks. Moreover, these studies [19; 20; 21] also focused on wireless backhaul routing. To the best of our knowledge, there are no existing studies that focus on the abovementioned issue. In this paper, we introduce the new problem of utility-based wireless backhaul routing (UWBR).