# On the Benefits of Listen before Talk Scheme for NB-Fi Networks
## 5 Studied Scenario  
We consider a network that consists of a server, 1000 sensors evenly distributed in a circle of radius \(R\), and a BS located in the center of this circle. The widths of the uplink and downlink channels are 51.2 kHz and 102.4 kHz, respectively. The sensors generate a Poisson flow of frames with a load \(\lambda\) and transmit them to BS. To transmit their frames, sensors use the assigned data rate, and the BS uses the same data rate for acknowledgments. A frame is discarded after seven unsuccessful transmission attempts. Sensors have a buffer that can store up to one frame, and new frames preempt the old ones when they are generated and the buffer is occupied.  
We use the Okumura-Hata model [35] to describe the signal propagation in the uplink channel, and the model from [36] to describe the propagation between sensors. We choose such models because we assume that the sensors are located at the same height, while the BS is at an elevation of 30 m higher than the sensors. Thus, to calculate the signal power at the receiver, we consider that the sensor or the base station transmits the frame with the power of \(P_{o}=14\) dBm, and, at the receiver, the power of this signal equals \(P_{o}-PL(d)\), where \(d\) is the distance between the transmitter and the receiver, and \(PL(d)\) is the path loss corresponding to such a distance. We use function \(PL(d)\) from [35] if the transmitter or the receiver is BS, and from [36] if both the transmitter and the receiver are sensors. The BS receives a frame if the signal to interference and noise ratio (SINR) during its transmission is not less than 7 dB (such an SINR corresponds to a bit error rate of \(10^{-5}\)[4]). Otherwise, the frame is damaged. Table 3 provides the maximal values for the receiving sensitivity \(S\), BS reception distance \(R_{busc}\), and the distance \(R_{sensor}\) at which sensors can sense each others' signals.  
The sensors' energy consumption depends on their state, see Table 4. We consider that the sensor can be in idle, receiving, or transmitting states. In the idle state, the sensor's transceiver is turned off and does not consume additional power. In the receiving state, the sensor can listen to the channel, determine if the channel is idle, and receive packets. In the receiving state, the sensor consumes \(P_{rx}\) power. In the transmitting state, the sensor transmits its frame and consumes \(P_{tx}\) power. According to [34], a sensor is powered by a voltage \(V\) and consumes a current \(I_{rx}\) in the receiving state and a current \(I_{tx}\) in the transmitting one. In its turn, the power source consumes \(I_{s}\) current. Thus, we obtain that the sensor consumes \(P_{tx}=(I_{tx}+I_{s})\times V\) power when transmitting data and  
Figure 3: Schemes of the \(p\)-persistent CSMA.  
\(P_{rx}=(I_{rx}+I_{s})\times V\) when receiving or listening to the channel in LBT mode and when waiting for an acknowledgment. Note that the resulting power consumption values differ from those used in [15] and describe the devices more correctly. Here we consider only the power consumed by the sensor's transceiver and leave the other sources of power consumption out of consideration because they are the same for all the considered kinds of LBT and non-LBT modes.