## 5 Simulation Analysis
### LoRa  
LoRa is a communication protocol that uses a spread-spectrum technique and this protocol utilizes unlicensed ISM groups, i.e., 433 MHz in Asia, 868 MHz in Europe, and 915 MHz in North America [36]. The consequent signal has low noisy levels, engaging high check adaptability, and is difficult to stick or recognize [6]. Some works highlight the LoRa innovation and detailed data about LPWAN innovation and the PHY layer are represented by different parameters such as Code Rate (CR), Bandwidth (BW) Spreading Factor (SF), and Transmission power. Further, messages transmitted using particular spreading components can be gotten simultaneously by LoRa base stations [37]. LoRaWAN offers bi-directional availability over multi-kilometers go and with a bit rate between 0.3 kbps to 50 kbps. The frequency in the spectrum band is presented as BW, and it is selected from one of three bands: 125 kHz, 250 kHz, & 500 kHz. A large bandwidth indicates faster transmission while a small bandwidth denotes long-distance transmission. The key parameter of the LoRa modulation is BW. The 2\({}^{SF}\) chirps that comprise the complete frequency band are symbolized as the LoRa symbol. At first, it commences with a series of upward chirps; if the highest frequency band is attained, then the frequency is covered and there will be an increase in the frequency yet again from the lowest frequency. Bit Rate/data rate is defined as the rate at which bits are transferred from one location to another location. The bit rate (_Rbit_) of LoRa is expressed as:  
\[Rbit=\frac{SF*BW}{2^{SF}*BW} \tag{5}\]  
Sensitivity refers to a system's capacity to extract information from signals. It may also be measured as the lowest feasible signal strength that will cause the system to packet resolution. The first term is generated by thermal noise in 1 Hz of bandwidth and can only be controlled by adjusting the receiver's temperature. The receiver bandwidth is denoted by the second term, _BW_. _NF_ is the noise figure of the receiver and is fixed for certain hardware implementation. Finally, _SNR_ denotes the signal-to-noise ratio demanded by the underlying modulation strategy. The signal-to-noise ratio (_SNR_) and bandwidth are the design factors accessible to the LoRa designer. The LoRa receiver sensitivity (S) is calculated as follows:  
\[S=-174+10\log_{10}BW+NF+SNR \tag{6}\]  
where \(S\) = receiver sensitivity in dB, _BW_ = Bandwidth in KHz, _NF_ = Noise Figure of a receiver in dB, and _SNR_ = Signal-to-Noise Ratio. A link budget, also known as received power, is the total of all losses and gains from the transmitter to the receiver over free space [32]. The link budget can be calculated by adding transmitter power (_PTX_), receiver sensitivity (_Rx_), antenna gain, and free space path loss (_FSPL_). The link budget is expressed as:  
\[PR_{X}\ =PT_{X}\ -FSPL+GT_{X}\ +GR_{X} \tag{7}\]  
where _PRX_ implies received power or link budget (dBm), _PTX_ implies transmitter power (dBm), _GTX_ implies transmitting antenna gain (dB), _GRX_ implies as receiver antenna gain (dB), and _FSPL_ implies free space path loss (dB). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Average Data** \\ \hline Queuing size & 0.5 \\ Queuing delay & 0.01 s \\ Throughput (bits/Second) & 45,000 bits/s \\ Retransmission Attempts (Packets) & 0.5 packets \\ Packet Delivery ratio & 90\% \\ End-to-end delay (Sec) & 0.013 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results. The behavior of the network is evaluated by varying certain parameters such as SF, bandwidth, and CR. The analysis of bit rate, link budget, and LoRa sensitivity are presented below:  
(a) Bit rate:  
The data rate/bit rate is well-defined as the number of bits that are transported during transmission between transmitter and receiver. We utilized Equation (5) for calculating the bit rate of the LoRa. To compute the bit rate of LoRa, the input parameters, such as SF, BW, and CR are included in the equation. Figure 15 presents the bit rate of LoRa from SF 7 to SF 12.