How to turn on LED using RF as a catalyst?
You first need to make sure that the signal your antenna receives is the signal you intend.


So a band-pass filter is needed for getting only your (maybe also others..) 
produced frequency.  
You need to amplify this signal significantly for it to be workable, so you will need op-amps (or another amp topology like "class A"). 
In the schematic the op-amp will not recreate the negative part of the incoming radio sine-wave. 
The amplified signal can be fed to a comparator. The comparators output is ON if the positive terminal is higher than the negative terminal. 


There will be a lot of tuning of the values to get this to work :) 







simulate this circuit &ndash; Schematic created using CircuitLab