I don't know exactly what type of jack the PSP has, but if it has a standard one you should be able to plug it in your active sound system (if there is a sound out jack available). If not you can always go at the source and plug them directly into your sound board.
You need an adapter that splits the 3 channel jack on the PSP headset into one stereo headphone jack and a mono microphone jack. There are DIY tutorials available (search).