Things to keep in mind before reading this:
I do not like cheating, and I do not support it in any way.
Did he cheat? I do not know, I do not have any proof.
Why may he cheat? To beat Carlsen, because he was the strongest player in the tournament.
Let's imagine for this answer that he did cheat, to make things easier for us. How then?
Hauptideal mentioned "anal beads" and called it "absurd". Why?
What do you really need in order to cheat as a GM?
Well, yes, there was that 15 minute delay, but after Carlsen's game, not in advance of it.
So we ignore that delay for now (but that is not a huge problem, just send the GM the moves for the 5 most probable reactions of the other player).
Let's think a bit:
We need something to calculate good moves for us. No problem, we can take any powerful enough PC and run an engine on it, no matter where it is at that moment.
Then we need to somehow tell the GM the move. Firstly we can use the public internet to bring the move close to him (like within a kilometer).
Then we need to get it right to him. Again, no problem, let's use LoRa (see Wikipedia article). This technology uses low power and covers a reasonable distance. The downside is that it is really slow. Really really slow. According to Wikipedia, it can transmit 292 bit/s up to 50 kbit/s. But that's more than enough: you can even transmit multiple possible moves within one second (each move needs two numbers between 1 and 64, that would be 2 * 6 bits per move).
The device to do that can use WIFI or the normal cellphone network to connect to the internet, and would be as small as a pack of matches (including a battery). You can hide it literally anywhere within one kilometer (the range is theoretically higher, but let's say we limit it to a one kilometer range, to make sure it definitely works).
So we can send the move to the GM.
But how can he receive it, without getting flagged by the scanners?
Firstly, he does not need to transmit anything: his receiver has only to be a receiver. So RF scanners are completely useless.
Secondly: The device must be quite small. Let's come back to the "anal beads". These are more or less small. You can easily fit a vibrator inside one - look at the ones used in smartphones: they are tiny, but quite powerful. Just need a little microcontroller, a tiny battery and an antenna. That's it.
If the metal detectors are not so sensitive, that is not a problem. Build the receiver out of plastic, and only the parts which really need to be metal out of metal, and you should not have a problem.
The receiver can have any size from a small ball up to the size and shape of a USB drive. If it is not bigger than this, you can even swallow it (there are tiny cameras with batteries you can swallow, which then transmit pictures of your digestive system to the doctor).
You just need to find a way to make it silent enough, but that should be doable as well...
Only way to find it is Xray.
Then use morse code or binary code or something.
Done. You just cheated.
How realistic is that?
I think it is definitely doable. Doable enough that I could build it without any problem. I could not use it, because I would lose during the opening of the game, and this would show its potential during long thinking periods (mid-game, end-game).
Ways to prevent that (you need all of them):
Not broadcasting the game at all.
Putting the players in a completely enclosed metal box.
The arbiters must be unbribable.
You have to prevent any RF transmissions (RF jammer, but you will get in trouble with police than).
EDIT: https://www.youtube.com/watch?v=5uDM3fPeNFM this is a build of such a device (not by me). I think, you can build it even smaller, if you want to.