Communication - 2 Battery Powered Circuits, 1 Conductor, no common ground

My friends and are are building a fencing box to score matches (The kind of fencing with swords). Competitive fencing is scored electronically by using a sword rigged with a button and jackets made of conductive material. We want to improve on the existing designs available today.

To make a long story short, we need to be able to communicate over one "wire" (the sword) between two Arduinos. Our plan was to use the Arduino PWM generators to generate tones that can then be detect by FFT of the analog inputs on the other side. We got all that working great. The problem is what happens when we go to batteries and no common ground. The PWM signal goes from 5V peak to peak to 1.2V peak to peak. I don't understand why this is happening. Any enlightenment here would be appreciated.

Can anybody recommend a circuit design for transmitting a wave over 1 conductor between two systems with no common ground? I'm thinking it's going to have to be similar to radio technology. Alternativly I can try to take what I've got and feed it into some sort of amplifier and see if I can run with that.