Why is radio still the method of communication from the ground to air? If i'm not mistaken, cellular services should be much better in quality and reliability
Cellular communication has multiple issues:
When a plane is up more than a few thousand feet, a cell phone would see, and try to talk to, multiple cell towers at once. At best, this is inefficient and overloads the cell network. At worst, the network can get confused and drop calls. (not something you want when trying to get ATC directions)
When a plane is moving rapidly, it will change cell towers frequently. This has the same problems as above.
Cell communications is designed for Person-to-Person during a single call. Aviation radio is designed so that everyone can hear everyone else's communications. Even if an ATC instruction is not specifically for me, I can get a mental picture of what other planes are nearby and what they are doing. This is not so easy with cellular.
In many rural areas, cell phone coverage is limited.
As mentioned in comments radiocommunication includes all forms of radio links, hence includes cellular networks.
A cellular network covering any land is not realistic, not mentioning water areas. Given the size of a cell, at most 20 km for GSM (1G/2G), and much less for UMTS/LTE (3G), this would lead to prohibitive costs:
Continents represent about 150 millions km², a GSM cell covers about 10 km² (in large cities a cell usually covers less than 1 km²).
15 millions cells would be required, still lands are only 30% of Earth's area.
User's motion speed
If we used the existing cellular network, the current cell size would be impractical for fast mobiles.
With small cells, fast users would constantly hop (handoff) from a cell to another. The network would be overloaded and the efficiency of the mobile node would also decrease a lot as cell transfer has some overhead, including frame replication by all cells in sight. Actually an assumption for the design of a phone cellular network is infrequent handoffs during a communication.
A more suited size would be about 100+ km, which is impossible in urban areas due to cells overlapping to try cover shadowed areas.
GSM and UMTS standards limit user's equipment power to 2 W (33 dBm) and 125 mW (21 dBm) respectively.
If the cell size is increased this power must be increased too (see here a link budget for UMTS). Each time the cell size doubles, the power used must be be multiplied by 4. As @jamesqf pointed out, the cell size impacts the phone set running time. The user's equipment would need larger batteries to maintain the same running time, or the running time would be divided by 4 each time the cell size doubles.
If the cell size is increased, there are more users in the same cell. The combination more users + more power would need important changes in the cellular network technology to prevent interferences.
Current antennas are oriented towards ground for efficiency and noise reduction. In practical a base station is barely reachable by an aircraft flying at 10 km altitude.
We would need a 180° beam versus the current 10° beam. As the cell is now a cube instead of a disc, power must be increased to reach the top corners, which can be done at the price of increasing cell overlap at ground level and higher cross-cell interference.
There is a master thesis on this exact topic:
- Feasibility study of a WCDMA direct air-to-ground link in the UMTS licensed band, by Dora Swamy Naidu Raghavarapu.
From the section Conclusions and Outlook:
[...] Some aircraft specific constraints, such as Doppler shift, propagation delay, handover and interference have been identified and analyzed. Doppler shift occurs in terrestrial networks on a much smaller scale, since mobile stations on the ground move at much lower speeds. However, WCDMA receivers are equipped with powerful frequency acquisition circuits, capable of counteracting this effect. We have also shown that propagation delay has no significant effect on the power control mechanism. Finally, we have seen how UMTS networks can perform handover procedures between remote parts of the network.
[...] we have focused much of our study on analyzing the possibility of using UMTS terrestrial frequencies for an aircraft component. It can be observed from the simulation results shown in chapter(6), that an aircraft component transmitting at these frequencies would degrade the performance of the existing network to an intolerable extent due to interference.
[...] In order for the aircraft to degrade the performance of the terrestrial network only to a tolerable extent, it would need to transmit at extremely low power. The airspace cells would then have to be so small that the system would be impractical.
Future solution is already broadly defined and satellite-based
Using the phone cell network is impractical, and has few advantages over other solutions. If a radio network had to be build for aviation, it would be a satellite one to cover oceans. It would be cheaper (relative) than building an equivalent on the ground.
Could such satellite network be built in spite of its cost? Well, it is already under construction!
The need for constant radio exchanges between aircraft and ground has increased a lot since 15 years:
ACARS can already use satellites, and it's a matter of choice for an airline to use this kind of link in addition of VHF/HF.
Airlines start to offer Internet access in flight. Wi-Fi access points are installed in the cabin and the local traffic is routed to a satellite which relays it to a ground station connected to the Internet.
Airlines also start to allow cellular phones in flight, using the same satellite technology.
In this numeric world, ATC voice communication is just another data flow, very small compared to ACARS, Wi-Fi and cell phone. There will be little difficulty to reuse data channels for voice transfer, just like IP phones have replaced traditional fixed phones in countries with a broadband Internet backbone.
GSM only works for a relative speed between the handset and the base station of 250 kph max (130 kph max for 1800 MHz). UMTS is slightly better, but it too maxes out at 500 kph. Many planes fly faster than that. Airliners regularly cruise at 800 kph+ groundspeed, with a nice tailwind, they may achieve 1000 kph. That's twice as fast as the maximum possible relative speed for UMTS, and almost 8 times faster than the maximum possible relative speed for GSM 1800 MHz.