Introduction
| LoRa Parameter | Region/Country Specific |
| 900MHz ISM Freq Band | North America (902-928MHz) Europe (863-870MHz) |
| R Data Rate | US(902-928): 980bps – 21900bps EU(863-870): 250bps – 11000bps |
| Bandwidth | US(902-928): 125KHz, 500KHz EU(863-870): 125KHz, 250KHz |
| Tx Power | US(902-928): 2dBm – 28dBm EU(863-870): 2dBm – 16dBm EIRP |
| SF Spreading Factor | 7,8,…..12 |
| Number Symbols 2^SF | 128(2^7),……4096(2*12) |
LoRa (Long Range) is a very popular protocol for long range communication between low powered battery operated devices (Ref.1). In the last post, I looked at sending a packet using LoRa on a pair of 915MHz transceivers (Ref.2). Previous to that, I examined how to create LoRa symbols using Scicos (Ref.3). In this post I look at how a receiver distinguishes between the various possible LoRa symbols, and the amazing spread spectrum performance for reception at SNRs < 0dB!
Chirp Symbol Correlation
| SNR = 20log10[Vp2p_sig]/[Vp2p_noise] | S11=S1x(closest) |
| noise=0.0 | S11=2.7, S17=1.4 |
| noise=0.1, -1.0V/-0.8V=0.2Vp2p SNR=20log10(2V/0.2)=20dB | S11=2.7, S17=1.45 |
| noise=0.3, +0.0V/-1.0V=1.0Vp2p SNR=20log10(2V/1.8V)=6.0dB | S11=2.7, S17=1.8 |
| noise=1.0, +2.3V/-2.0V=4.3Vp2p SNR=20log10(2V/4.3V)=-6.7dB | S11=2.6, S17=2.6 Threshold |
Figure 2 shows the ScicosLab code used to generate two Symbol structures: V1=S1,S2,..,S8 and V2=S1,S1..,S1. These structures are read into the Scicos model as shown in Figure 3. Simulated channel noise is added to V2 and then the symbols are correlated by multiplication and integration for various noise values. For no noise, Symbol 1 correlated with itself produces a peak clearly distinguishable from all the other possibilities as in Figure 4. Figure 5 shows noise at 0.3 and Symbol 1 correlation with itself still strong. When noise is 1.0, Symbol 1 correlation with itself cannot be distinguished from say Symbol 1 with Symbol 7. This is not an exact BER vs. SNR curve, but just used to illustrate the correlation procedure. Figure 8 summarizes the result. So for SF=3 (SF=7…12 in practice) at SNR=-6.7db many errors will start to occur.
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References
#1. – “LoRa Alliance”
https://resources.lora-alliance.org/technical-specifications/rp002-1-0-4-regional-parameters
#2. – “LoRa 915MHz Transceiver Packet Test”
https://jeremyclark.ca/wp/telecom/lora-915mhz-transceiver-packet-test/
#3. – “LoRa Scicos Simulation_a”
https://jeremyclark.ca/wp/telecom/lora-scicos-simulation_a/
