## 6 Numerical Results  
In this section, \(E=1.\mu=G_{\text{SR}}/G_{\text{RD}}\). Figure 4 presents the OP performance of the TAS scheme. Table 1 gives the parameters employed. From Figure 4, we see that the Monte-Carlo results and analytical results are similar. The OP is improved as \(N_{t}\) increased. Figure 3: The flowchart of the outage probability (OP) performance prediction algorithm. Figure 5 presents the effect of \(N_{\rm t}\) on the OP performance. Table 2 gives the parameters employed. From Figure 5, with \(N_{\rm t}\) increased, the OP decreases. When SNR=12 dB, the OP is \(8.6\times 10^{-2}\) with \(N_{\rm t}=3\), \(3.6\times 10^{-2}\) with \(N_{\rm t}=4\), and \(1.5\times 10^{-2}\) with \(N_{\rm t}=5\). \begin{table}
\begin{tabular}{l l} \hline \(\mu\) & 0 dB \\ \(\gamma_{\rm th}\) & 5 dB \\ \(m\) & 1 \\ \(N_{\rm t}\) & 2 \\ \(N_{\rm t}\) & 3,4,5 \\ \(N_{\rm r}\) & 1 \\ \(L\) & 1 \\ \hline \end{tabular}
\end{table} 
Table 2: The parameters for the TAS scheme. Figure 4: The OP performance of the transmit antenna selection (TAS) scheme. Figure 6 presents the effect of \(K\) on OP performance. Table 3 gives the parameters employed. From Figure 6, with SNR increased, the OP decreases. When \(K\) = 0.5, the OP is \(3.8\times 10^{-2}\) with SNR = 10 dB, \(2.0\times 10^{-4}\) with SNR = 15 dB, and \(9.0\times 10^{-8}\) with SNR = 20 dB. In Figures 7-10, we compare the BP neural network with LWLR [42], SVM [43], and ELM [44] methods. Figure 5: The effect of \(N_{\rm t}\) on OP performance. \begin{table}
\begin{tabular}{l l} \hline \(\mu\) & 0 dB \\ \(\gamma_{\rm th}\) & 5 dB \\ \(m\) & 1 \\ \(N\) & 2 \\ \(N_{\rm t}\) & 2 \\ \(N_{\rm r}\) & 2 \\ \(L\) & 2 \\ \hline \end{tabular}
\end{table} 
Table 3: The parameters for the TAS scheme. Figure 6: The effect of \(K\) on OP performance. The LWLR [42] model is as follows: \[\text{min}f(\theta)=\sum_{k}\phi^{(k)}(y^{(k)}-\theta^{T}X^{(k)})^{2}\] (25) \[\theta =(\theta_{0},\theta_{1},\cdots,\theta_{n})\] (26) \[\phi^{(k)}=\text{exp}\!\left(-\frac{{(X^{(k)}-X)}^{T}{(X^{(k)}-X)}}{2\tau^{2}}\right)\] (27) where \(\theta\) denotes the coefficient vector of the linear equation, \(\tau\) is the bandwidth parameter. 2. The SVM [43] model is as follows \[ \begin{split}\text{min}\frac{1}{2}&\|w\|^{2}+c \sum\limits_{i=1}^{n}\varepsilon_{i}\\ \text{s.t.}& y_{i}\sum\limits_{i=1}^{m}KK(X_{i}^{T},X _{i})\geq 1-\varepsilon_{i}\end{split} \] (28) where \(w\) is the adjustable weight,\(\|w\|^{2}\) is the Euclidean norm of the vector, \(\varepsilon_{i}\) is the slack variable, and \(c\) is the penalty parameter. \(KK()\) is the kernel function, which has an important parameter g. ELM [44]: ELM has the same framework as the BP neural network. The input weight of ELM is subject to random assignment by a certain distribution function, and the output weight is directly calculated via the least squares method. The hidden layer has q neurons. Compared with the BP neural network, the training and recognition processes of ELM are rapid. Figure 7: Actual and predictive outputs of the BP neural network. Figure 8: Actual and predictive outputs of extreme learning machine (ELM). Figure 9: Actual and predictive outputs of support vector machine SVM. The parameters for the four different methods are given in Table 4. The number of train sets is 950, the number of test sets is 50. From Figures 7-10, we see that the MSE of the BP neural network is 0.0018862, which is lower than that of the LWLR, SVM, and ELM methods. Compared to the LWLR, SVM, and ELM methods, our method can consistently achieve higher OP performance prediction results. Table 5 shows the running time and MSE comparison for the four methods. In Table 5, we see that, compared to ELM, BP has a longer running time, but its performance is better than ELM. In addition, compared to SVM and LWLR, BP has a shorter running time and a smaller MSE.