# A QoE-Oriented Uplink Allocation for Multi-UAV Video Streaming
## 3 System Model and Utility Function
### QoE-Based Utility  
As mentioned in Section 2.1, we need to implement resource allocation with the goal of improving QoE. Video QoE metrics can also be called Video Quality Assessment (VQA), which can be divided into subjective assessment and objective assessment [39]. Subjective assessment is mainly conducted by the evaluator in a specific test environment, and the Mean Opinion Score (MOS) is obtained. The method and procedure is time-consuming and expensive, which leads people to predict the video quality through the other way. The objective VQA models based on the error statistics of pixel domain are relatively simple, including PSNR, SSIM, MOVIE, etc. [40; 41; 42]. The models oriented to video features are more complex and more accurate, for example, VQMTQ and Q-STAR [43; 44]. It is hoped that, by means of establishing mathematical models, objective assessment could make the predicted results much more approximate to the real MOS value. On one hand, the video feature-oriented models extract the feature information from the video itself. This is consistent with our method because the analysis in this paper is based on rate ranges and characteristic of each video. On the other hand, the results of the models oriented to video features are closer to real MOS values. Therefore, we start from the model of VQMTQ [43] and further analyze the QoE-oriented utility function. Firstly, from the VQMTQ evaluation method, we can find that the subjective perception quality is closely related to the objective evaluation results PSNR and frame rate, which can be denoted as \(VQMTQ(PSNR,f)=SQF(PSNR)\cdot TCF(f)\). In the scenario of this paper, the video captured by UAV needs to be sent to UCDC for clipping, editing and processing together. Thus, the frame rate of all the videos is the same. The above statement is translated into  
\[QoE_{MOS}=Const_{fps}\cdot\Psi(PSNR), \tag{2}\]  
where \(Const_{fps}\) is the constant related to frame rate, and \(\Psi(\cdot)\) is the mapping function from PSNR to MOS. Some studies suggest that there is a simple linear mapping between PSNR and MOS [45; 46] and it can be formulated as \(MOS= \begin{cases}4.5,&40<PSNR,\\ \frac{3.5*PSNR}{20}-2.5,&20<PSNR\leq 40,\text{ However, Ref. \@@cite[cite]{[\@@bibref{}{Roger2012}{}{}]}}\text{ show that}\\ 1,&0<PSNR\leq 20.\end{cases} \)  
this mapping is much closer to a sigmoid function. Although PSNR is not the most accurate VQA metric, it is most widely used. Much literature directly uses PSNR as the measurement of QoE [49; 50]. Meanwhile, it has the lowest complexity [47] and this makes it more convenient to use in real-time services. Thus, we will apply a simple linear mapping between the PSNR and the MOS:  
\[QoE_{MOS}=Const_{fps}\cdot\Psi(PSNR)=Const_{fps}\cdot(A\cdot PSNR+B). \tag{3}\]  
In addition, then, we could formulate the utility function for each UAV video:  
\[u_{i}=QoE_{MOS}-COST_{i}=Const_{fps}\cdot(A\cdot\mathfrak{F}(r_{i})+B)-COST_{ i}. \tag{4}\]  
For \(\mathfrak{F}(r_{i})\), we use the expression of PSNR in [51] and \(PSNR=\mathfrak{F}(r_{i})=a+b\cdot\sqrt{\frac{r_{i}}{c}}(1-\frac{c}{r_{i}})\). The parameters \(a\), \(b\) and \(c\) are constants and have been discussed in detail in the literature. \(COST_{i}\) represents the payment in the process of transmission. In this paper, two aspects of transmission cost are considered. One is the charge by NSP due to the occupation of channel resources. The charging way is determined by the ratio between the actual video transmission rate and the total uplink channel bandwidth. Thus, \(P(r_{i})=\theta\cdot\frac{r_{i}}{Chand}\), and the constant \(\theta\) is the price factor. For scenarios where the capacity is large enough or the price is not considered, \(\theta\) can be zero. The other is the cost of energy consumption. For all UAVs, the energy consumption of video capturing and encoding is roughly the same. Thus, we mainly consider the energy loss caused by transmission, which is related to the video encoding rate.