Mobile Phone Coverage in flight
The problem is not at all lack of coverage but too much coverage - at least with GSM.
When you are at altitude you can see many base-stations within the 25km (or 50km with software mods) range of GSM.
There are not that many frequencies available so they they are recycled across base stations and rely on ground level visibility to prevent interference.
In an aircraft all bets are off as there is no physical limitations on signals. This is also seen when in tall buildings. The higher you get the less likely you will get a clean call. I remember hiding in the toilets to blank out most signals and only use the strong local base station.
When considering SMS there may well be moments when the signal is clean but the phone generally won't try and send. The algorithm is for ever increasing delays between retries - sometimes up to days.