# Research on Transmission Task Static Allocation Based on Intelligence Algorithm
## 2 Preliminaries
### Model of TTSA
#### 2.1.1 Input Data  
According to the functional characteristics of the transmission equipment, the transmission frequency range of the equipment is described as \([Fr_{min},Fr_{max}]\): the operating frequency of each piece of equipment is divided into \(m\) frequency bands. According to the  
Figure 1: Framework model for TTSA.  
actual situation, it can be assumed that the transmitting effect of the equipment performing tasks on the frequencies within the frequency band range is consistent. The mathematical model of frequency band division is as follows:  
\[FreqR=\{Fr_{1},Fr_{2},\ldots,Fr_{i},\ldots Fr_{m-1}\},\quad Fr_{i}\in\ [Fr_{min}, Fr_{max}] \tag{1}\]  
where \(m\) is the number of frequency bands and \(Fr_{i}\) is the frequency boundary value between the (\(i-1\))th and \(i\)th frequency bands.  
For the medium- and short-wave transmitter performing the transmission task, the transmission task command parameters include the working frequency, power level, and working type. The values of the working type and other parameters are independent of the optimal allocation of the task. In order to simplify the mathematical model, different transmission tasks are only distinguished according to the transmission frequency. At the same time, the transmission task set consists of n frequencies, and the transmission task can be described as:  
\[Task=\{Freq_{1},Freq_{2},\ldots,Freq_{i},\ldots Freq_{n}\}\ Freq_{i}\in[Fr_{ min},Fr_{max}] \tag{2}\]  
where \(n\) is the number of transmission tasks, and \(i\) is the \(i\)th task expressed by the frequency value.  
The working frequency of the task belongs to the working frequency band divided by the model, and the calculation formula is as follows:  
\[TaFr_{i}=\left\{\begin{array}{ll}0,&Freq_{i}\in[Fr_{min},Fr_{1}]\\ k,&Freq_{i}\in(Fr_{k},Fr_{k+1}]\\ m,&Freq_{i}\in(Fr_{m},Fr_{max}]\end{array}\right. \tag{3}\]  
Through the calculation of Formula (3), the set \(TaFR\) of the working frequency band of the task is obtained, which can be described as follows:  
\[TaFR=\{TaFr_{1},TaFr_{2},\ldots,TaFr_{i},\ldots TaFr_{n}\},TaFr_{i}=0,1,\ldots,m \tag{4}\]  
where \(n\) is the number of transmission tasks, and \(i\) is the segment code obtained by dividing the \(i\)th task by frequency segment.  
The implementation effect of the evaluation task on the equipment is obtained through data quantitative calculation. The rated power of the transmitting equipment is recorded as \(R_{max}\). When the equipment is set to transmit at full power, the monitoring data collected by the receiving equipment are: forward power, recorded as \(R\); reverse power, recorded as \(r\). The transmission effect evaluation in this paper is mainly based on the transmission standing wave ratio (\(SWR\)), and the transmission effect calculation formula is as follows:  
\[SWR=\frac{\sqrt{R}+\sqrt{r}}{\sqrt{R}-\sqrt{r}} \tag{5}\]  
According to the characteristics of the transmitting equipment, the minimum value of the transmitting \(SWR\) is not less than 1.0, and the closer it is to 1.0, the better the effect. The formula is as follows:  
\[Va=\frac{1}{SWR} \tag{6}\]To sum up, _ValueMatrix_ can be obtained through the transmission test run of each piece of transmission equipment in each frequency band, which can be described as:  
\[\textit{ValueMatrix}=\begin{bmatrix}Va_{11}&Va_{12}&\cdots&Va_{1i}&\cdots&Va_{1m }\\ Va_{21}&Va_{22}&\cdots&Va_{2i}&\cdots&Va_{2m}\\ \cdots&\cdots&\cdots&\cdots&\cdots&\cdots\\ Va_{i1}&Va_{i2}&\cdots&Va_{ij}&\cdots&Va_{im}\\ \cdots&\cdots&\cdots&\cdots&\cdots&\cdots\\ Va_{n1}&Va_{n2}&\cdots&Va_{nj}&\cdots&Va_{nm}\end{bmatrix} \tag{7}\]  
where \(n\) is the number of transmission tasks. In this paper, the number of transmission equipment items \(n\) is the number of frequency bands divided, and \(m\) is the evaluation value of the transmission effect of the \(i\)th transmission equipment working in the \(j\)th frequency band when considering the optimal allocation of tasks in the same period.