This isn't correct, the car key fob is NOT constantly transmitting.
Instead, it is the car that constantly transmits, the key fob just listens in order to preserve battery life. When it detects a signal from the car it is paired with, it will respond with an encrypted code and if it is correct, the car will unlock.
I know you linked to an article that mentioned it but it is wrong.
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Smart key - Wikipedia
en.wikipedia.org
"The key becomes activated if it is sufficiently close and it transmits its ID back to the vehicle via RF (Radio frequency >300 MHz) to a receiver located in the vehicle. If the key has the correct ID, the PASE module unlocks the vehicle."
In terms of usefulness to this case, then in theory somebody could build a transmitter that transmits exactly the same encrypted codes as NB's car and literally walk around until it got a response. The key would only answer if the transmitter used to search was transmitting the exact same codes as NB's car, otherwise, it would ignore an incorrect code. This would need Mercedes techs to build such a thing.
If the key has been in the river for this long then unlikely it is still working. If it is buried underground, the signal strength might not be enough for it to respond to.
Typically remote unlock only occurs within about 10 feet of the vehicle even though the transmitted signal travels much further (maybe up to 500ft as per other posts) but both the car and the key measure the signal strength to determine how close the key is before making an unlock decision.
So depending on the technology in use on that particular keyless entry, the key may only respond when the signal is of specific strength even though it can detect a signal from much further away - and therefore might need to be 10ft or less from a transmitter before it responds, closer if underground.
In other words, a needle in a haystack finding the car keys.
Thanks for this. So it works very similar to blue tooth radio. The remote device listens for the controlling device