John Oliver jokes about CNN parent company AT&T (T) aside, 4G will probably work better on the moon than it does here -- it won't have any trees, buildings or TV signals to interfere with the 4G signal. The moon's cellular network will also be specially designed to withstand the particularities of the lunar surface: extreme temperature, radiation and space's vacuum. It will also stay functional during lunar landings and launches, even though rockets significantly vibrate the moon's surface.
Bell Labs said astronauts will use its wireless network for data transmission, controlling of lunar rovers, real-time navigation over lunar geography (think Google Maps for the moon), and streaming of high-definition video. That could give us stuck on Earth a much better shot of astronauts bouncing around on the lunar surface: Buzz Aldrin was a great cameraman, but he didn't have an iPhone.
The 4G network on Earth is supported by giant cell towers with enormous power generators and radios. But Bell Labs helped create small cell technology that's more limited in range but uses far less power than traditional cell towers and is significantly easier to pack into a rocket ship. That small cell tech is currently being deployed for 5G networks across the world.