Spreading factor: time and sensitivity

Time doubles every step

The spreading factor sets how many starting points a symbol has, and so how long it takes. At a bandwidth of 125 kHz a symbol lasts 2^SF divided by the bandwidth: 1.024 ms at SF7, 2.048 ms at SF8, and 32.768 ms at SF12. Every step up doubles the time. The symbol carries one more bit, so the nominal bit rate does not halve, but it falls to a little more than half: about 5.47 kbit/s at SF7 and 0.293 kbit/s at SF12, before any of the packet's own overhead.

What the time buys

At the same transmit power, a longer symbol carries more signal energy. The demodulation limit, the weakest signal-to-noise ratio the receiver can still read, falls by about 2.5 dB a step, from about minus 7.5 dB at SF7 to minus 20 dB at SF12. Added to the noise in the band, that gives the nominal sensitivity on the bench: about 12.5 dB better at SF12 than at SF7. The numbers are nominal. They are computed from the thermal noise in 125 kHz, an assumed 6 dB receiver noise figure and the limit, and a chip's datasheet differs from them by a dB or two.

What it costs

The price is time on the air. The six byte soil report of lesson 1 takes about 124 ms at SF9 and close to a second at SF12. Over the day that is battery. At the moment of sending it is also a longer window in which another packet can overlap, and on a shared channel a long packet is hit more often than a short one.

Not a promise of range

A higher spreading factor gives a receiver that can read a weaker signal. It does not make the signal stronger, and whether the signal is that strong at the gateway depends on transmit power, antennas, the path and the hill. Range is the link budget: power, antennas and path, with a margin for conditions that vary. The bench has no distance on it, and it is meant to.

Common mistakes

• Saying a higher spreading factor travels farther. It hears weaker signals, at the cost of airtime and energy. The distance is a result of the whole link.
• Reading the dBm figures as a chip's sensitivity. They are nominal, worked out from the noise in the band. The datasheet for the module in your hand is the reference.
• Raising the spreading factor to be safe. Every step doubles the time on the air, which spends battery and raises the chance of an overlap.