Some thoughts when trying to use a Bandwidth of 31.25 kHz.
Reading this document: AN1200_59_LoRa_Reference_Clock_Selection_V1.2_rev
from the Semtech website, I see these requirements:
The carrier frequency between the Tx/Rx should be within ±25% of BW
Table 2 displays the Xtal accuracy in ppm for various SF and Bw. for US915 band.
Bw 31.25 - 8.5 ppm
Bw 62.5 - 17.1 ppm
Bw 125 - 34.2 ppm
Bw 250 - 68,3 ppm (except SF12 - 50 ppm)
Bw 500 - 136.6 ppm (except SF11 - 100 ppm and SF12 - 50 ppm)
The same document in table 1 tells us that a standard X-tal can deviate +/- 10 ppm over it’s temperature range.
So if one radio is operated outside on a cold winterday and the other is inside in a hot enclosure the total difference can be 20 ppm worst.
There is also the aging effect of +/- 5 ppm for 5 years and +/- 10 ppm for 10 years
So for worst case after more than 5 years there can be a theoretical difference between sender and receiver of almost 40 ppm !!.
We can assume that the usual LoRa_modems are equipped with a standard X-tal, unless the device-documentation claims it has a TCXO.
Taking this in consideration I conclude that using a BW of 31.25kHz is not a good option for normal LoRa modems except if both/all radio’s in the group are equipped with a TCXO (or if all radio’s operate at the same room-temperature ?).
I may be too pessimistic or even wrong but the numbers in the documentation says so.
I believe that (for non-TCXO modems) only BW of 125, 250 and 500 kHz are reliable on the long term.
Maybe the meshtastic documentation should mention that the mode Long-Fast Bw31_25 can only reliable be used if both or all radio’s in the network have a LoRa-modem with TCXO.