pioneer deh p6000ub background hiss

I recently bought a Pioneer DEH-P6000UB head unit. I like everything about it except for the horrible background noise. At half power (31), it seems to have just as much (if not more) noise than my old Pioneer DEH-P4700MP unit did at full power (62). It's very noticeable and annoying when nothing is playing. It's easily audible during quieter parts of a song, too. I can also hear it when the engine is idling too. The noise does get better at volumes lower than 25 and doesn't seem to increase much past 35. I'm not sure if it does it in Tuner mode, but it does in all other modes; CD, USB, and Auxiliary. It doesn't seem to be alternator noise, the noise is constant regardless of whether or not the engine is running and doesn't vary with the engine speed. I've checked all connections on the wiring harness, everything is good. I did originally have the unit grounded through the factory harness, but I also tried grounding both the chassis and wire directly to the frame, nothing help. I plugged my old unit unit into the same harness and had no noise. The noise does stop for a split second when changing sources, which makes me believe the noise is being generated inside the head unit itself. I don't believe it's the internal pico fuse because I'm using the head unit's internal amp to power my speakers. Do I have a defective unit or is it just designed like that? I've already exchanged this unit once, but both do it. I know Pioneer isn't exactly high-end, but come on.

That's just the thing, I'm not using the RCA outputs, I'm using the internal amp.

Ground one of the RCA jacks on the radio anyway.  Try each set, one at a time.

Didn't help, thanks anyways though. This really sucks, I like everything about this unit, but I can't stand the noise.