## 3 LoRa Modulation Evaluation
The model is implemented using MATLAB [27] environment and allows the modulation and demodulation of LoRa packets without any in-band noise from other interference sources. With the integration of the possibility of change for the bandwidth of the communication channel and applying the model on different LoRa packets featuring different payloads, the conclusion is that the applicability of the model is greatly extended. Thus, the new model offers the possibility of analysis of the influence of the communication channel bandwidth and of the payload dimension over the level of performance of the LoRa technology, by determining its scalability through the evaluation of the BER parameter. As expected, the worst-case scenario corresponds to when the packet interferes with a packet modulated with the same spreading factor. The limitations of this approach are related to the fact that an empirical method is used, and some limitations of the hardware design of the sensors and of the gateway modules are not taken into account. Moreover, it is important to mention that the assumption of perfect synchronization between transmitter and receiver is considered. Another major difference is in the fact that the LoRa traffic generator that has been developed and tested uses a method that allows the customization of generated packets with an innovative solution, unlike other approaches like the one presented in Reference [26]. Different approaches that are presented in scientific literature make use of a capture technique of a packet sent by a LoRa sensor. This means that the packet is later simply retransmitted. The disadvantage of this approach is the limitation of user options, due to the impossibility of changing the LoRa data packet characteristics. Arguably, the empirical analysis backed by an experimental evaluation represents the main contribution of this work. These results open new directions of research when it comes to sensor networks that use LoRa modulation. Thus, two overlapped transmissions have been considered by a different use of spreading factors in order to evaluate the performance level. Thus, each packet modulated with an SF is overlapped (the observed packets are transmitted on the same channel at random time intervals) with a packet that has been progressively modulated with all other possible SF combinations. This is the emulated communication scenario. Following the implemented model, the correct synchronization between the sensor and GW is implied, the interference packet is randomly generated in time. All these elements make the degradation in performance of maximum importance. Figure 3 depicts the BER parameter when the SF12 spreading factor is used (the most unfavorable case corresponding to the situation when the transmission duration of the packet is maximum being of the order of seconds). In this situation, a 125 kHz bandwidth is used. One can see that at the same time as the SIR (Signal-to-Interference ratio) parameter decreases, the performance level of the LoRa communication suffers a sharp drop. The SIR parameter has been chosen to evaluate performance as accurately as possible, considering the LoRa communication channel. One can observe that for an SIR value of approximative -1 dB, the BER value equals to about 70%. There is still the need to mention the fact that the most unfavorable case is analyzed when all sensors use the same SF12 spreading factor. Moreover, the spreading factor has been modified from SF12, representing the most unfavorable case (with the sensor located at a great distance from the GW) to SF6 corresponding the situation in which the sensor is located at a short distance from the GW. For each analyzed SF, every spreading factor is taken into consideration as possible interference. Obviously, the maximum value is reached when all the other sensors communicate on the same SF as the one undergoing analysis; this situation is also what we refer to as the worst-case scenario.