## 3 Wireless Communication Schemes for Aircraft
### Single-Hop Scheme  
The single-hop scheme is a method of transmitting data from the source node directly to the destination node without help of the relay node. Thus, the received signal which is common with non-cooperative and cooperative schemes except AF, IAF can be expressed at the destination node by:  
\[y_{ij}=\sqrt{P_{i}}h_{ij}x+n_{ij}. \tag{3}\]  
where \(P_{i}\) is the transmitted power from the node, \(h_{ij}\) is the Nakagami-m fading channel coefficient between the nodes, \(x\) is the packet from the source, \(n_{ij}\) with a variance of \(N_{0}/2\) is the additive white Gaussian noise (AWGN) between the nodes, where \(N_{0}\) is the thermal noise power spectral density per Hz. The outage probability occurs when SNR is lower than the SNR threshold, which means that the wireless communication is cut off. And between the source node and destination node it is defined [28] by:  
\[\rho_{SH}=\Pr\left\{\sigma_{SD}<\mu_{0}\right\}\simeq\frac{\Psi\left(m,\frac{ mN_{0}}{P_{i}TSD}\right)}{\Gamma\left(m\right)} \tag{4}\]  
where \(\sigma_{SD}\) is the instantaneous SNR between the source node and the destination node, \(\mu_{0}=2^{R}-1\) is SNR threshold, where \(R\) is the spectral efficiency, \(\Psi\left(s,x\right)=\int_{0}^{x}a^{s-1}\exp\left(-t\right)dt\) is the lower incomplete gamma function, \(\Gamma\left(z\right)=\int_{0}^{\infty}a^{z-1}\exp(-x)dx\) is the complete gamma function, \(m\) is a Nakagami parameter, \(N=N_{0}B\) where \(B\) is bandwidth, and \(\gamma_{SD}\) is the pathloss between the source node and the destination node. In order to represent the total power consumption [29; 30], each power consumption of components of RF circuit at a transmitter and a receiver is considered. Thus, it can be obtained by:  
\[E_{SH}=\frac{\left(P_{AMP}+P_{TX}+P_{RX}\right)\kappa}{R_{b}} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Group** & **Group Name** & \(k\) & \(n\) & \(\mathbf{C_{1}}\) **[dB]** \\ \hline A & Intra-Flight Deck & 2.45 & 2.00 & 189.8 \\ \hline B & Inter-Cabin & 2.09 & 3.46 & 167.5 \\ \hline C & Inter-Cabin-to-Lower Lobe & 1.86 & 2.49 & 124.5 \\ \hline D & Inter-Cabin-to-Exterior & 1.86 & 2.12 & 118.2 \\ \hline E & Inter-Cabin-to-Landing Gear & 1.59 & 1.51 & 77.9 \\ \hline F & Inter-Exterior & 1.95 & 2.31 & 142.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Path loss parameters in the aircraft. where \(R_{b}\) is bit rate, \(\kappa\) is the packet size, \(P_{AMP}=v\,P_{i}\) is energy consumption of the power amplifier when transmitting, \(v=\
icefrac{{7}}{{\omega}}-1\) is power amplifier efficiency, \(\omega=\frac{P_{iR}^{RF}}{P_{i}^{0\omega}}\times 100\%\) is the drain efficiency of the power amplifier, and \(\tau\) is the PAR (peak to average ratio) for BPSK modulation. \(P_{TX}\)[31] is the power consumption when a transmitter sends a packet, and \(P_{RX}\) is the power consumption when a receiver processes the received packet, which can be expressed by:  
\[P_{TX}=P_{BAS}+P_{MIX}+P_{SYN}+P_{FIL}+P_{DAC}, \tag{6}\]  
\[P_{RX}=P_{BAS}+P_{MIX}+P_{SYN}+P_{LNA}+P_{FIL} \tag{7}\]  
where \(P_{BAS}\), \(P_{MIX}\), \(P_{SYN}\), \(P_{FIL}\), and \(P_{DAC}\) mean power consumption on baseband, mixer, synthesizer, filter, and digital-to-analog converter (DAC) from the transmitter respectively. Furthermore, in Equation (7) \(P_{LNA}\), \(P_{IFA}\), and \(P_{ADC}\) mean power consumption on low noise amplifier, intermediate frequency amplifier, and analog-to-digital converter (ADC) from the receiver respectively when operating.