## 4 Simulations
### Energy Model  
A different assumption of node characteristics, including energy consumption of the transmitter and receiver, will affect the advantages of different protocols. In our simulations, we apply the same node architecture as shown in Figure 1. According to this architecture, the total energy required for transmitting (\(E_{TX}\)) includes the energy consumed by the active transmitter (\(E_{AX}\)) and that consumed by the passive transmitter (\(E_{PX}\)):  
\[E_{TX}=E_{AX}(m,d,\varphi)+E_{PX}(n) \tag{2}\]  
For simplicity, we assume that energy loss is proportional to the scanning area when using the active transmitter. Thus, power at the active transmitter should be appropriately adjusted to invert this loss so as to ensure a certain power at the receiver. During data transmission, if the number of bits transmitted by the active transmitter is \(m\), then the scanning angle is \(\varphi\), the communication radius is \(d\), and then the energy for the active transmitter is:  
\[E_{AX}\left(m,d,\varphi\right)=\varepsilon\times\varphi\times d^{2}\times m \tag{3}\]  
For the passive transmitter, if the total number of bits transmitted by the CCR is \(n\), and the transmitted energy per bit for the CCR is \(E_{CCR}\), then the energy of passive transmitter is:  
\[E_{PX}\left(n\right)=E_{CCR}\times n \tag{4}\]  
In the receiver, if the received energy per bit is \(E_{R}\), then the total energy for receiving \(k\) bits is:  
\[E_{RX}\left(k\right)=E_{R}\times k \tag{5}\]  
Researchers have designed several energy saving sensor network systems so far. In [4], the estimated energy for \(E_{CCR}\) and \(E_{R}\) is 16 pJ/bit and 69 pJ/bit, respectively. In our simulation, we use the value 16 pJ/bit for \(E_{CCR}\) and set the \(E_{R}\) as 60 pJ/bit for simplicity. The parameter \(\varepsilon\) relies on the required receiver sensitivity and the receiver noise figure as the transmit power needs to be adjusted so that the power at the receiver is above a certain threshold, \(P_{r\text{-}thresh}\). We work backwards to determine the minimum transmit power. If the radio bitrate is \(R_{b}\), then the transmit power in 1 rad \(P_{t}\) is equal to the transmit energy per bit \(E_{AX}\)(1, d, 1) times the bitrate:  
\[P_{t}=E_{AX}\left(1,d,1\right)\times R_{b}=\varepsilon d^{2}R_{b} \tag{6}\]  
The free space model is adopted in our simulation. According to the Friss free space equation, the transmit power is attenuated as follows:\[P_{r}(d)=\frac{P_{r}G_{r}G_{r}\lambda^{2}}{\left(4\pi d\right)^{2}L} \tag{7}\]  
where \(P_{r}(d)\) is the receive power given a transmitter-receiver separation of \(d\), \(P_{t}\) is the transmit power, \(G_{t}\) is the gain of the transmitting antenna, \(G_{r}\) is the gain of the receiving antenna, \(\lambda\) is the wavelength of the carrier signal, \(d\) is the distance between the transmitter and receiver, and \(L\geq 1\) is the system loss factor not related to propagation. Combining Equations (6) and (7), we get:  
\[P_{r}=\frac{\varepsilon R_{s}G_{t}G_{r}\lambda^{2}}{\left(4\pi\right)^{2}} \tag{8}\]  
Thus, \(\varepsilon\) can be determined by setting Equation (8) equal to \(P_{r\text{-}thresh}\):  
\[\varepsilon=\frac{P_{r\text{-}thresh}(4\pi)^{2}}{R_{b}G_{t}G_{r}\lambda^{2}} \tag{9}\]  
We employ the receiver threshold \(P_{r\text{-}thresh}\geq-52\) dBm used in [15], which could achieve a minimum of 30 dB signal-to-noise (SNR) to receive the signal with no error. The whole system works with the following parameters: \(G_{t}=G_{r}=1\), no system loss (\(L=1\)), \(R_{b}=250\) Mbps, 300 GHz radios and \(\lambda=\frac{3.0\times 10^{8}}{300\times 10^{9}}=0.001\,\mathrm{m}\). Then, \(\varepsilon=4\) pJ/m\({}^{2}\) is determined. The parameters in our energy model are summarized in Table 3.