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LoRa
- 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
- 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