# Spreading Factor, Bandwidth, Coding Rate and Bit Rate in LoRa (English)

In the previous article, I discussed about several basic Spread Spectrum concepts while specifically talking about LoRa modulation and touching the topic regarding several parameters in LoRa. Those parameters in question are Spreading Factor, Bandwidth, and Coding Rate. The three parameters will determine how sensitive the LoRa receiver will perform and how fast the data transmission speed will be. I will shortly discuss them in this article, hoping that the readers will be able to understand the concept and implement it in a LoRa-based system

# Symbol

As discussed before, LoRa is a chirp spread spectrum modulation. The transmitted data, which is a symbol, will be represented by a chirp signal with a frequency range from $f_{min}$ to $f_{max}$, which is shown in Figure 1. In LoRa modulation, we can configure the symbol by changing the Spreading Factor and Bandwidth parameters. According to Application Note Semtech AN1200.22, one symbol will take $T_S$ of second to transmit, which is a function of Bandwidth and Spreading Factor can be shown with the equation below: $\displaystyle T_S = \frac{2^{SF}}{BW}$

# Bandwidth

Bandwidth is the frequency range of the chirp signal used to carry the baseband data. In Figure 1, the Bandwidth can be seen from the width of frequency used between $f_{min}$ to $f_{max}$. Aside from that, Bandwidth can also represent chip rate from LoRa signal modulation $R_C = BW$

The value of Spreading Factor (SF) determines how many chips used to represent a symbol. The higher the SF value is, the more chips used to represent a symbol, which means there will be more processing gain from the receiver side. This will allow receiver to accept data signals with negative SNR value $\displaystyle R_S = \frac{BW}{2^{SF}}$

Spreading Factor shows how many chips used to represent a symbol, with an exponential factor of 2. 1 symbol may consist of N chip where $N = 2^{SF}$. A cyclic shift can be done to represent a bit and sent symbol. If there is N amount of chips, then the resulting symbol value may range from 0 to N-1, or that 1 symbol may represent SF bits $\displaystyle R_b = SF * \frac{BW}{2^{SF}}$

# Coding Rate

LoRa modulation also adds a forward error correction (FEC) in every data transmission. This implementation is done by encoding 4-bit data with redundancies into 5-bit, 6-bit, 7-bit, or even 8-bit. Using this redundancy will allow the LoRa signal to endure short interferences. The Coding Rate (CR) value need to be adjusted according to conditions of the channel used for data transmission. If there are too many interference in the channel, then it’s recommended to increase the value of CR. However, the rise in CR value will also increase the duration for the transmission $\displaystyle R_b = SF \frac{\big[\frac{4}{4+CR}\big]}{\big[\frac{2^{SF}}{BW}\big]}$