GSM is a circuit-switched system that divides each 200kHz channel into eight 25kHz time-slots. GSM operates in the 900MHz and 1.8GHz bands in Europe and the 1.9GHz and 850MHz bands in the US. The 850MHz band is also used for GSM and 3GSM in Australia, Canada and many South American countries. GSM supports data transfer speeds of up to 9.6 kbit/s, allowing the transmission of basic data services such as SMS (Short Message Service).
Moh Smith, AFAIK there is not one equation that leads to this number. It is a design constraint influenced by multiple aspects. Oftentimes, Doppler shift is mentioned, but also multipath fading characteristics, GSM's Timing Advance mechanism and handovers are affected by high speeds.
independent of interference, fading, multitrajectory, doppler effect, antenna diversity techniques, etc. I think you should first keep in mind the frequency at which the system under study works, what is determined through of
Λ = c/f , that will allow you to know if the wave travels more or less, following the losses by propagation and consequently the speed of the link and the interference in the band according to the occupation of the channel, This is closely related to the capacity of the channel (SHANNON) C=2BT log M, which regardless of the method of access to the medium, tdma, fdma, etc and the number of slots to use. is directly related to the bandwidth to be used and the modulation index, that’s why the first GSM systems used GMSK, then 8PSK, 16 QAM, 32QAM, etc appeared, achieving higher speed by increasing the bandwidth of communication systems or by increasing the rate of modulation with other types of quadrature modulation.
The mobile systems was designed with three speed modes defined - Stationary, Pedestrian and Vehicle Speed. I did not know there was a number but 250 km/h seems reasonable in that design.
Of course, this is relative speed so a micro cell on an airplane will function for passengers on that aircraft (as the downlink is by satellite).
The highest speed of the user during the communication session is determined by the maximum allowed doppler shift variations as the Doppler shift causes fast fading in the channel. This fast fading can be equalized up to some extent and so one has to limit speed of the vehicles to make the distortion affordable and the quality of service acceptable.