# LoRa 2.4 GHz Communication Link and Range
## 4 Path Loss Modeling  
In order to obtain the maximum communication range of a LoRa signal at 2.4 GHz (further denoted as \(d\)), we need to find the maximum link budget for which the signal can be received properly; i.e., at the receiver sensitivity \(P_{RX}\). This receiver sensitivity depends on two key factors: the used spreading factor (SF) and bandwidth (BW). While the SF can range from 5 to 12, the possible bandwidths of LoRa at 2.4 GHz are 203, 406, 812 and 1625 kHz. Furthermore, the combination of a certain SF and BW results in a certain data rate, along with the receiver sensitivity, as shown in Table 2. The raw data rate \(R_{b}\), expressed in kbit/s, can be calculated as  
\[R_{b}=\frac{SF*BW}{2^{SF}}, \tag{8}\]  
with SF and BW as defined in Table 1. As an example, a LoRa signal transmitted with an SF of 8 and a BW of 406 kHz results in a receiver sensitivity of -116 dBm and a data rate of 12.69 kbit/s. The receiver  
Figure 1: Two received Long Range (LoRa) signals constitute eight preamble upchirp symbols at 2.4 GHz with a bandwidth equal to 812 kHz. The spreading factor (SF) of the short signal, which ended after approximately 5 ms, is equal to 9, while the SF of the long-duration signal is equal to 10. Figures (**a**) and (**b**) represent the combined received signals in the time domain and in the spectrogram (i.e., time and frequency) domain, respectively. Figures (**c**) and (**d**) are the cross-correlation functions (6) when the received signals have been cross-correlated with base chirps of the SF equal to 10 and 9, respectively.  
sensitivities and data rates used in this work originate from the datasheet of the Semtech SX1280 LoRa module [5].  
The total link budget of a wireless communication signal propagating from the transmitter to receiver can be represented as [27]  
\[P_{RX}=P_{TX}+G_{TX}-L_{TX}-L_{p}(d)+G_{RX}-L_{RX}, \tag{9}\]  
where \(P_{RX}\) is the received power in dBm, \(P_{TX}\) is the transmission power in dBm, \(G_{TX}\) is the antenna gain at the transmitter in dBi, \(L_{TX}\) is the cable loss in dB, \(L_{p}(d)\) is the path loss in dB in terms of the function from the distance \(d\), \(G_{RX}\) is the antenna gain at the receiver in dB and \(L_{RX}\) is the cable loss at the receiver in dB. Except for the path loss, all these parameters are set to typical values which are commonly used when simulating a wireless communication link between two dipole antennas [27]. The values of these parameters are summarized in Table 1.  
The path loss \(L_{p}(d)\) is defined as the propagation loss caused by the signal traveling from the transmitter to receiver over a distance \(d\). The goal in this research is to maximize \(d\) while still being able to successfully receive the LoRa-modulated signal at the receiver. For the sake of simplicity, the simulated LoRa signal contains eight preamble symbols and no payload bytes.  
Depending on the environment, the path loss should be modeled differently. Therefore, in the next three subsections, we discuss indoor, outdoor (urban) and free space path loss models to translate the propagation loss into a distance between the transmitter and receiver. The parameters required by these models are also summarized in Table 1. No fade margin is taken into account; this is further discussed in Section 6.