## 3 System Model  
Figure 1 illustrates the assumed wireless sensor networks. A long-range wide-area network (LoRa), which is a low-power wide-area network, is assumed. There is a data center and sensors within the cover area constructed by the data center. Each sensor accesses the data center to inform the sensing data. We assumed that each sensor transmitted data within a certain time period. Figure 2 shows the wireless accessing image of each sensor. Periodic data transmission is suitable for detecting changes in the monitoring environment [42]. In the wireless access scheme, each sensor was assigned an orthogonal time period and/or a frequency-orthogonal channel [43]. In accordance with the specifications of LoRa [44], the access time limitation, which is the duty cycle, is under the 1% and, thus, packet collisions among sensors within the LoRa system rarely occur. Under this assumption, the wireless access of each sensor does not affect that of the other sensors. For simplicity, we assume that the number of sensors is one; it is noted that the extension of the proposed scheme to multiple sensors is straightforward. We assume frequency spectrum sharing between the single-carrier (SC) and LoRa systems, where the example of an SC system is a wireless smart utility network (WiSUN) [6]. Various channels of Wi-SUN are defined. We assume that the channel bandwidth of the SC is approximately equal to or a few tens of percentage points smaller than that of LoRa. We also assume that if packet collision between SC and LoRa occurs, the entire packet of LoRa overlaps with the packet of the SC system. If a partial overlap of packets between LoRa and SC occurs, the estimated signal power of CCI is reduced. We assume the fluctuation of the power of CCI by the shadowing effect. In the performance evaluation, the impact of partial overlap is also considered. Figure 2 shows the image of spectrum sharing between the sensor and SC system in the multiple channel environment. In each channel, the time period of the channel occupied by the SC system is random. In addition, the power of CCI emitted by the SC system depends on the distance between the SC system and the data center, and then it fluctuates in each channel. If the SC system and the sensor simultaneously access the common channel and the power of the CCI is larger than a certain level, the packet collision occurs and, thus, the demodulation of the data from the sensor is failure. If it is not, as in channel 2 of Figure 2, the demodulation of the data from the sensor is successful owing to the capture effect [11]. If each sensor exploits the channel with low COR as well as the low power of CCI, the packet delivery rate (PDR) becomes large. For selecting the suitable channel for each sensor, this paper considers the estimation of the desired signal power, the CCI power, and the COR. The transmitted signal is modulated using a chirp modulation scheme. In the chirp modulation scheme, the carrier frequency cyclically increases or decreases, and the change in carrier frequency is determined by the data bits. The altering pattern of the carrier frequency is defined as the chirp pattern. The number of chirp patterns, \(L\), is \(2^{N_{SF}}\)[12], where \(N_{SF}\) is the spreading factor, which is a parameter for spreading the carrier signal over  
Figure 1: System overview of assumed wireless sensor networks. Frequency spectrum sharing between LoRa and single-carrier systems was considered. Figure 2: Accessing image of the multichannel environment under spectrum sharing between LoRa and the SC system. the frequency domain within one transmitted symbol time. The number of transmitted bits \(B\) is  
\[B=\log_{2}L=\log_{2}2^{N_{SF}}=N_{SF}. \tag{1}\]  
As \(N_{SF}\) increases, the number of bits per modulated symbol also increases. When we define \(W\) and \(T=1/W\) as the occupied bandwidth and sampling periods, respectively, the time length of one modulated symbol, \(T_{s}\), is \(2^{N_{SF}}T\)[12]  
Figure 3 illustrates an image of chirp-modulated symbols.