LORA

Experiment sandbox for playing with CHIRP modulation and developing some intuition for it.

Shannon-Hartley theorem

C = B log₂( 1 + S/N )

C : Channel capacity (theoretical maximum information rate, bit/s) [sometimes as I]
B : Bandwidth (passband width, Hz)
S : Mean power over the bandwidth (W / V²) [sometimes as C]
N : Average noise power (same units as S)
S/N : Signal-to-noise ratio

Frequency-shift CHIRP modulation: The LoRa Modulation (IEEE doc #8067462)

Duration of a chip = T = 1 / B

Duration of a chirp = Tₛ = 2^SF T = 2^SF / B

Frequency shift per chip = B / 2^SF

i.e. frequency = [ ⌊t / T⌋ (B / 2^SF) ] mod B

So to transmit a symbol s, we just offset the shift by the symbol index:

chip = (⌊t / T⌋ + s) mod 2^SF

Δf = B / 2^SF

frequency = chip Δf

Reading

• Good explanations of the basics
• Maths
• Chirp compression