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Recently, I have been reading about the LoRa modulation and I am curious, why the symbol transmission time (T_symbol) doubles, if the Spreading Factor (SF) is increased by one.

The SF is equal to the number of bits transmitted in a symbol, i.e. the 'SF8' means that one symbol carries 8 bits of information; the 'SF9' means that one symbol carries 9 bits of information. If the SF is changed from the 'SF8' to the 'SF9', the T_symbol doubles.

Secondly, the bandwidth of the signal (BW) has some impact on the T_symbol; T_symbol is inversely proportional to the BW.

Could You provide me an explanation why is it so?

Reference document: "LoRa-LoRaWAN and Internet of Things for beginners" by Sylvain MONTAGNY - page 22

pstr
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  • Please hyperlink the LoRa document that describes the way it assigns SF to the number of bits per symbol. – Andy aka Apr 04 '23 at 09:34

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LoRa modulation uses the spreading factor (SF) as a variable and Bandwidth (B) as a variable to affect transmission rate and receiver sensitivity depending on requirements. From memory there are 6 spreading factors from SF7 to SF12, and three bandwidths from 125 KHz to 500 KHz.

The B variable will affect receiver sensitivity as it does in most receivers, but your question relates to the variation of symbol time Tm for a variation in SF for a fixed B from what I gather.

Since BTm=M where Tm is the symbol time, and we know M=2^SF (samples in each symbol) for SF=8 M=256 and for SF=9 M=512, so you can see that for a fixed B (say 125KHz) your symbol time Tm changes by a factor of 512/256 = 2, for SF=8 compared to SF=10 it would be a factor of 4 etc...

For further details I suggest searching for the article "Understanding LoRa PHY (Long-Range Physical Layer)".

citizen
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  • Yeah, I know this formula, but I wonder, if there is some explanation of how this formula is derived. I would like to gain some intuitive understanding of how it works. – pstr Apr 04 '23 at 10:27
  • Not having read the quoted article entirely, just briefly it looks more like a tutorial for eventual experimental work and/or field application manual etc. So you need to find something more on the theory that gives you the details you're looking for. – citizen Apr 04 '23 at 11:24
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    I've included a brief article on the subject in my answer for searching with your favourite search engine ... – citizen Apr 04 '23 at 11:27