# On the Benefits of Listen before Talk Scheme for NB-Fi Networks
## 7 Numerical Results
### Results for a Circle with Radius of 0.4 km
#### 7.1.1 Plr  
Figure 4 shows the dependencies of PLR on the load for different data rates and six sensor operating modes: Aloha, non-persistent CSMA, persistent CSMA, non-persistent CSMA with frequency hopping, and \(p\)-persistent CSMA with \(p=0.1\) and \(p=0.01\). Interestingly, depending on the data rate, the result may align with or contradict the conclusions of the classic works on CSMA because of the peculiarities of the NB-Fi technology. Let us consider them in detail.  
Figure 3(a),b show results for the 3.2 kbps and 25.6 kbps rates. We do not show the dependence for non-persistent CSMA with frequency hopping for the data rate of 25.6 kbps: with such a bitrate and the 51.2 kHz-wide uplink channel, all sensors transmit in the same subchannel located in the center of the channel. For the 3.2 kbps and 25.6 kbps data rates, the PLR values for CSMA modes are significantly lower than for the Aloha mode, which aligns with the classic results [12]. At these data rates, CSMA efficiently avoids collisions and thus decreases the PLR. Another result predicted from classic CSMA analysis is that at low loads, the difference in the PLR between various CSMA modes is hardly noticeable because, to avoid collision, it is enough not to transmit while the channel is occupied, which is what sensors do in all the considered CSMA modes. However, at high loads, we see a significant difference in the performance of various types of CSMA.  
Figure 4: PLR, R = 0.4 km, rates: (**a**) 25,600 bps, (**b**) 3200 bps, (**c**) 400 bps, (**d**) 50 bps.  
The persistent CSMA is the most inefficient because in this mode, a sensor listens to the channel and waits until it becomes idle, but when several other sensors generate frames during transmission and plan to transmit in overlapping subchannels, they start their transmissions simultaneously after the end of the current transmission, and a collision occurs. The other CSMA modes do not have such a drawback and thus achieve a slightly lower PLR. Let us also note that at a load greater than 100 packets per second, the PLR comes close to 1, which is caused by the high contention for channel access and the limitations of the buffers at the sensors. Specifically, if the sensor cannot transmit its frame as soon as it is generated, at a high load, the frame with a high probability is preempted by a newly generated frame and thus is lost.  
Figure 4c,d show the results for the data rates of 50 and 400 bps. We can see that the PLR of different types of CSMA barely differs from the PLR in Aloha mode. Such a result contradicts the classic results of studies of CSMA and Aloha but is explained by the peculiarities of the NB-Fi technology. Specifically, at such data rates, the transmissions use very narrow subchannels, and the sensors rarely select overlapping subchannels. Therefore, listening to the channel only provides a tiny gain in PLR over the Aloha mode.  
From the obtained results, we can conclude that the lowest PLR can be obtained with P-persistent or non-persistent CSMA at the highest data rate. The difference between these two types of CSMA is hardly noticeable.