If all you want to do is light LEDs, set yourself up a piece of sheet metal at so many feet off the ground. Run it to a capacitor with a diode in series and ground it. You'll charge the cap from a couple of energy sources: 1) whatever happens to be the dominate frequencies in the local environment and 2) PLUS the "electron leak" energy available in the dipole between earth and sky -- basically like electron leakage across capacitor plates. The higher you raise the metal from the earth, the higher your rate of charge should increase.
If most of the energy comes from the local frequencies, then you can put two caps in parallel each with an opposite facing diode, and you'll be able to get twice as much energy since you're pulling energy from both sides of whatever the dominant frequencies are in the environment. If the dominate energy is coming from the dipole between earth and sky, then only one diode direction should be dominant (at least theoretically. It's been a few years since I ran these kind of experiments).