This document discusses LoRa modulation parameters and interference. It describes: 1. The main LoRa modulation parameters including spreading factor, bandwidth, frequency range, and how the symbol rate and bit rate are calculated from these parameters. 2. How LoRa symbols are generated by varying the frequency within each symbol time according to the minimum and maximum frequency and slope. 3. The two types of interference in LoRa - co-spreading factor (Co-SF) and inter-spreading factor (inter-SF) which can occur when signals with the same or different SFs overlap in time and frequency. It provides an equation to calculate the total multiple access interference (MAI) from both types.

1. LoRa interference
Mina Yonan
m.yonan@aucegypt.edu

2. LoRa Symbol Generation
LoRa Modulation Main Parameters :
• Spreading Factor (7- 12)
• The minimal and maximal frequency (𝑓 𝑚𝑖𝑛, 𝑓𝑚𝑎𝑥)
• Scalable Bandwidth 𝐵 = 125, 250, 500 𝑘𝐻𝑧
• Starting frequency 𝑓𝑖𝑛𝑖𝑡𝑖𝑎𝑙
𝑐ℎ𝑖𝑝 𝑟𝑎𝑡𝑒 𝑅 𝑐 = 𝐵
𝑁𝑜. 𝑜𝑓 𝑆𝑡𝑎𝑟𝑡𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡𝑠 =
𝐵
𝑁𝑜. 𝑜𝑓 𝑠𝑦𝑚𝑏𝑜𝑙𝑠
=
𝐵
2 𝑆𝐹
𝑓𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝑓 𝑚𝑖𝑛 + 𝑛
𝐵
2 𝑆𝐹

3. LoRa Symbol Generation
𝑠𝑦𝑚𝑏𝑜𝑙 𝑟𝑎𝑡𝑒 (𝑅 𝑠) = 𝑅 𝑐 ∗ 2 𝑆𝐹 =
2 𝑆𝐹
𝐵
𝐵𝑖𝑡 𝑟𝑎𝑡𝑒 𝑅 𝑏 = 𝑅 𝑠 ∗ 𝑆𝐹 = 𝑆𝐹 ∗
2 𝑆𝐹
𝐵
𝑓(𝑡) = ቊ
𝑓𝑚𝑎𝑥+𝑚(𝑡 − 𝑛𝑇𝑐) 𝑖𝑓 𝑛𝑇𝑐 > 𝑡 ≥ 0
𝑓 𝑚𝑖𝑛 + 𝑚(𝑡 − 𝑛𝑇𝑐) 𝑖𝑓 𝑇𝑠 > 𝑡 ≥ 𝑛𝑇𝑐
𝑚 (𝑠𝑙𝑜𝑝𝑒) = 𝑓𝑚𝑎𝑥 − 𝑓 𝑚𝑖𝑛/𝑇𝑠

4. LoRa Symbol Generation

5. LoRa Interference
Co-SF and inter-SF Interference
• The same or different SFs can overlap in time and
frequency.
• The demodulator output can be indistinct depending on
the isolation threshold and the processing gain of the SFs.
• The SIR of the desired signal is above the isolation
threshold
• Each element 𝛿𝑖𝑗 [dB] in ∆ is the SIR margin that a packet
sent at 𝑆𝐹𝑖 must have in order to be decoded correctly if
the colliding packet is sent at 𝑆𝐹𝑗.

6. LoRa Interference
Co-SF and inter-SF Interference
• Each element 𝛿𝑖𝑗 [dB] in ∆ is the SIR margin that a packet
sent at 𝑆𝐹𝑖 must have in order to be decoded correctly if
the colliding packet is sent at 𝑆𝐹𝑗.

8. LoRa Interference
𝑀𝐴𝐼 = 𝐼 𝐶𝑜−𝑆𝐹 + 𝐼𝑖𝑛𝑡𝑒𝑟−𝑆𝐹
= ෍
𝑖 ∈𝑥 𝐶𝑜− 𝑐𝑜𝑙𝑙𝑖𝑠𝑜𝑛
𝐸𝑖𝑙
𝑙𝑖𝑠
𝑇𝑖,𝑜𝑣𝑒𝑟𝑙𝑎𝑝
𝑙 𝑠
+ ෍
𝑗∈𝑥 𝑖𝑛𝑡𝑒𝑟−𝑐𝑜𝑙𝑙𝑖𝑠𝑜𝑛
𝐸𝑖𝑙
𝑙𝑖𝑠
𝑇𝑖,𝑜𝑣𝑒𝑟
𝑙 𝑠