2A for a 5ms transmission timeslice is 2 x 0.005 coloumbs of charge, ie 10mC
The voltage change across a capacitor = dQ/C, 0.01C / 0.022F = 0.55V, which is still
quite a large voltage droop across the duration of the timeslice (Although the power supply
will provide some of this current, so its more likely to be 0.3V or something).
GSM transmission is done in short timeslices, normally for just 12% of the time, so the ~ 2A peak
current could average at 0.25A, yet a supply of 1.5A won’t work at all (unless such a large
capacitor is employed to bolster it up).
Multimeters only see average, so can be deceptive with this sort of load - they will see the
supply voltage droop a little, but not indicate the transmit slices are dropping out completely.