# Sum Rate Optimization Scheme of UAV-Assisted NOMA under Hardware Impairments
## 1 Introduction
### Related Works and Motivation  
The joint NOMA and UAV technology was investigated in [13; 14; 15; 16; 17; 18; 19; 20] to improve the system's performance further. The study in [13] provided a closed-form expression of outage probability and ergodic capacities in UAV-aided relay NOMA networks. In [14], the sum rate of downlink users was maximized by jointly optimizing the position and power of the UAV. Ref. [15] investigated a multi-user NOMA system with a flying base station (BS). The authors obtained globally optimal solutions to both problems for the placement of UAV and its power allocation. In [16], the authors proposed a path-following method to solve the max-min rate optimization problem in UAV-enabled BS networks. In [17], BS and UAV cooperated to serve ground users simultaneously and employed the method of an iterative algorithm to complete the sum rate maximization problem. Ref. [18] showed an iterative method that could achieve an approximate optimal solution of joint optimization maximization throughput problem in multiple user group NOMA networks with a UAV relay. In [19], a block coordinate descent method was used to solve a minimum energy consumption problem in the uplink NOMA communication for a UAV-assisted base station system. The authors proposed a method combining NOMA and spatial modulation to improve the energy efficiency of UAV in [20]. The aforementioned work in [13; 14; 15; 16; 17; 18; 19; 20] presumed that the hardware condition in the system was ideal.  
In practical UAV-aided NOMA systems, The communication node takes the form of suffering hardware impairments (HIs), which consist of an in-phase/quadrature-phase imbalance (IQI), radio frequency circuit noise, and non-linear amplifiers equivalent noise [21; 22]. The performance analysis was conducted for the UAV communication network under HIs in [23; 24; 25]. In [23], the average sum rate was asymptotically analyzed for UAV-assisted NOMA multi-way relaying networks with hardware impairments in the Nakagami-m fading channel. In [24], the outage probability was derived for the satellite-unmanned aerial vehicle (UAV)-terrestrial networks with a reconfigurable intelligent surface under hardware impairments. In [25], the asymptotic outage behavior was investigated for a hybrid satellite-terrestrial network aided by UAV relays under hardware impairments.  
Although NOMA and UAV have been studied in previous works [23; 24; 25] for performance analysis, very little attention has been paid to the resource allocation problems of the UAV-assisted NOMA communication network. In [26]'s study on the fair allocation of resources for cooperative and cognitive NOMA networks with hardware impairment, the authors derived the closed-form optimal power and time slots allocation. The difference between this paper and [26] is that the UAV relay adopts the decode-and-forward protocol, and the system max-min fair fitness is studied under the assumption that the user channel gain is sorted in advance in [26]. However, in this paper, under the condition of hardware impairments, the UAV adopts the amplify-and-forward protocol and considers the variable order of the user channel gain to study the system sum rate. Our research considers more complex network scenarios and is more in line with the actual situation. A comparison of the related UAV's works is summarized in Table 1.