In GSM, something like the following happens:
1) User submits SMS to their mobile phone.
2) Phone starts paging on a random access channel (no synchronization, lots of phones trying to talk at the same time - limited resources for phones to transmit, and limited chance for base station to receive an intact message). Increased load on these channels require operator to have increased capacity, and thus increased spectrum, increased hardware to handle peak throughput (even if network is idle most of the time - one reason prices may not drop as the network's popularity increases)
3) Base station manages to hear an intact access request, allocates a dedicates timeslot on a control channel (a timeslice of spectrum dedicated entirely to one particular handset - the number of available slices in a given area is more likely measured in the 10s, not the 100s), uses yet more spectrum to inform phone of allocation.
4) Phone indicates desire via dedicated control channel to start SMS transaction.
[half a second of allocated time on a licensed band elapses]
5) Phone transmits message.
6) Phone retransmits message due to poor network visibility.
7) Network signals SMS received, closes transaction.
[resources used within network to route, store and forward message, payment made to peering network to which the target phone is connected to]
8) Remote network begins paging target handset on a camping timeslot it shares with a bunch of other phones, on frequencies covered by a second billion dollar spectrum license.
9) Remote phone wakes up, begins placing load on random access channel.
[lots of retries and corrupting of other users' random access requests later]
10) Remote network allocates control timeslot, and begins attempting to inform target phone of its allocation.
[another few second of allocated spectrum go here]