No real details needed other than the name of the network! And possibly the maker's name for the phone, which would be a nice bit of scene setting.
Later - thanks to major_clanger and cdybedahl I'm going to go with a Magnavox satellite phone (briefcase sized) in the Inmarsat network. Many thanks to everyone who commented.
Also posted at https://ffutures.dreamwidth.org/2211575.html, where there are comments. Please comment here or there using OpenID.