## 6 Outage Capacity of NDA-EVM-AM in NLOS Scenario  
The outage capacity is the realistic maximum of capacity of NDA-EVM-AM for WSN. It aims to achieve a maximum rate at which data can be transmitted over a fading channel with a certain outage probability \(P_{out}\)[29]. Because the NLOS for WSN can be modeled by \(\eta-\mu\) fading channels, for any \(0\leq\varepsilon<1\), the outage capacity of NDA-EVM-AM of \(\eta-\mu\) fading channels can be expressed as [23]:  
\[\begin{array}{l}C=\max\{R=\log_{2}(M_{\max}):P_{out}(R)\leq\varepsilon\},\\ M_{\max}=\xi_{\eta-\mu,\min}^{-1}[M],\ M=(k+1)^{2}\end{array}. \tag{17}\]  
This reflects the best-case performance of a realistic system in NLOS scenario of WSN. The outage capacity of NDA-EVM-AM calls for the use of the highest modulation order that can tolerate the lowest EVM on the \(\eta-\mu\) fading channels at the receiver (i.e., the lower bound on the NDA-EVM) while achieving the expected SER such that the \(P_{out}\) limit is satisfied.  
NDA-EVM of the \(\eta-\mu\) fading channels is given by  
\[\xi_{\eta-\mu}(k)=\int_{0}^{1}\xi[M]f_{\alpha,\eta-\mu}(\alpha)d\alpha, \tag{18}\]  
which is the \(\eta-\mu\) fading channel's NDA-EVM scaled by the specific probability of the occurrence of each instantaneous \(\alpha\), and averaged by integrating over the range of possible \(\alpha\). To obtain the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Steps** & **NDA-EVM-AM Complexity** & **DA-SNR-AM Complexity** \\ \hline Initialization & \((1)\) & \((n)\) \\ Calculation of the metric & \((M_{m})\) & \((n)\) \\ Calculation of SER & \((M_{m})\) & \((M_{m})\) \\ Adjustment of constellation size & \((1)\) & \((n)\) \\ Complexity of algorithm & \((M_{m})\) & \((M_{m})\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of algorithmic complexity.  
lower bound of the NDA-EVM on the \(\eta-\mu\) fading channels, we can lower bound \(\xi[k]\) by simplifying Equation (14) (as shown in the Appendix B), and it can be shown that  
\[\xi[k]>\frac{\sigma_{n}+bk}{(2\pi)^{1/4}}\exp(-\frac{b^{2}[(1+k)^{2}+2k(1+k)]+b^ {2}k^{2}a^{2}}{4\sigma_{n}^{2}}). \tag{19}\]  
Substituting Equations (4) and (19) into Equation (18), the lower bound of NDA-EVM for a \(\eta-\mu\) fading channel is (the derivation is shown in the Appendix C):  
\[\xi_{\eta-\mu}(k)>\frac{1}{k^{2p}}\tau(k)\beta(k)^{2\mu-p}\frac{\Gamma(2\mu-p )}{\theta_{1}^{\mu}\theta_{2}^{\mu}\Gamma(2\mu)}F_{D}^{(2)}(2\mu-p,\mu,\mu;2 \mu;\frac{-\beta(k)}{\theta_{1}},\frac{-\beta(k)}{\theta_{2}}),k=\sqrt{M}-1. \tag{20}\]  
In Equation (20), by setting the optimal \(p=p^{*}\), we obtain  
\[p^{*}=\arg\max_{\begin{array}{l}p^{*}\in p\\ p\in(0,2\mu)\end{array}}\{\beta(k)^{2\mu-p}\frac{\Gamma(2\mu-p)}{\theta_{1}^{ \mu}\theta_{2}^{\mu}\Gamma(2\mu)}F_{D}^{(2)}(2\mu-p,\mu,\mu;2\mu;\frac{-\beta( k)}{\theta_{1}},\frac{-\beta(k)}{\theta_{2}})\}, \tag{21}\]  
where \(p\in(0,2\mu)\).  
After obtaining the lower bound of the NDA-EVM, by using the relationship between NDA-EVM and SER, the minimum NDA-EVM for a \(\eta-\mu\) fading channel \(\xi_{\eta-\mu,\min}(k)\) and the maximum modulation order \(M_{\max}\) can be confirmed while satisfying the expected outage probability. Using the equations above and Equation (17), the outage capacity of an NLOS scenario for WSN is obtained.