I thought this was an interesting article and probably behind the 40% increase in battery life claim. I had previously thought the 40% increase might have been exaggerated though after October, we'll get some real world results.
This new chip is called an envelope tracker, and Qualcomm says that it reduces the amount of power the Galaxy Note 3 uses to maintain an LTE connection by 30%. LTE requires a high-powered amplifier to keep its signal clean enough to use. The mobile signal waveform oscillates, though, and current devices output a wide, linear envelope that can catch its highest peaks. Qualcomm