# Dynamic Cooperative MAC Protocol for Navigation Carrier Ad Hoc Networks: A DiffServ-Based Approach
## 3 System Description and Related Models
### Antenna Model and Communication Modes  
**Assumption 1.** (_Adaptive antenna_): Each node is equipped with an adaptive array antenna system, which has two transmission modes in terms of omni-directional and directional modes, as shown in Figure 2. Moreover, the receiving mode of the antenna system is omni-directional.  
**Assumption 2.** (_Directional beam_): Let the ideal model of the beam coverage region be a spherical sector \(V_{ideal}(\theta)\), where \(R_{dir}(\theta)\) denotes the maximal permission range of sender \(s_{2}\) (\(s_{2}\in\mathbf{C}_{g}\)), \(\theta\) is the beam-width of its main-lobe. Suppose that the main-lobe gain is isotropic, and the gains of side-lobes and back-lobes are ignored. Moreover, the direction of the main-lobe can be rotated adaptively around the three-dimensional detecting region.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Free Space Losses (dB)** & **147.33** & **143.80** & **141.32** & **137.78** \\ \hline
**Frequency (GHz)** & 1 & 1 & 1 & 1 \\
**Distance (km)** & 555 & 370 & 278 & 185 \\
**Data Rate** & 220 kbit/s & 500 kbit/s & 1 Mbps & 2 Mbit/s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Propagation parameters in long-range transmission.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Serial No.** & **Data Rate** & **Threshold** & **Range** \\ \hline
1 & 1 Mbit/s & \(-97\) dBm & 278 km \\
2 & 2 Mbit/s & \(-94\) dBm & 185 km \\
3 & 5.5 Mbit/s & \(-88\) dBm & 92.5 km \\
4 & 11 Mbit/s & \(-83\) dBm & 50 km \\ \hline \hline \end{tabular}
\end{table}
Table 2: Multi-rate setting for NC-NET (\(f_{GHz}=1\) GHz).  
The relationship between omni-directional transmission range \(R_{omni}\) and directional range \(R_{dir}(\theta)\) can be expressed as follows:  
**Lemma 1**.: _Let the transmission be directional and the reception be omni-directional, the transmission range \(R_{dir}(\theta)\) under the given transmission power \(P_{T}\) can be determined from_  
\[R_{dir}(\theta)=\left(\frac{2\pi}{\theta}\right)^{\frac{1}{\lambda}}R_{omni} \tag{2}\]  
_where \(\lambda\) is the path loss exponent, i.e., \(2\leq\lambda\leq 4\)._  
Let \(D\) be \(\left(2\pi/\theta\right)^{1/\lambda}\) and under a given transmission power, the range of directional transmission (DT) is equivalent to \(D\) times of omni-directional transmission (OT). If an omni-directional broadcast request is received, or the azimuth of the destination node is unknown, the transmitter will send a packet in omni-directional mode (denoted by OT). If the azimuth of the destination node is known, or a directional transmission request is received, the transmission node will send a packet in directional mode (denoted by DT). Moreover, to extend the transmission radius, the relay node for retransmission mainly works in DT mode (denoted by DR). Thus, the communication modes can be specified as follows: (a) omni-directional transmission and omni-directional reception (OT-OR), (b) directional transmission and omni-directional reception (DT-OR), and (c) directional transmission, directional relay and omni-directional reception (DT-DR-OR). Let \(d_{\mathrm{mod}-a}\), \(d_{\mathrm{mod}-b}\), and \(d_{\mathrm{mod}-c}\) be the ranges of the three modes, respectively, \(D=2\), and \(R_{omni}=\overline{d}\); the maximal transmission range can be calculated by (2) as \(d_{\mathrm{mod}-a}=\overline{d}\), \(d_{\mathrm{mod}-b}=2\overline{d}\), \(d_{\mathrm{mod}-c}=4\overline{d}\).