"I found that the problem is seperation of Logic Ground and Power Ground."

All that they are trying to say is to be careful not to introduce any ground loops that can unintentionally couple high frequency signals to different pins via the power supply. In fact if you deal with PC DAS cards, they have the following grounds PWRGND, DIGND, AIGND, AOGND ! And if you care to see the continuity between these, you get a perfect 0.0 Ohm !

So to put it simply, don't daisy chain a single wire among all the grounds and finally run that wire to your 5V ground - you will have serious problems.

Return each ground with an independent, amply sized short conductor, DIRECTLY to the common power supply ground. Generally called the Star Ground, this could be your starting point in overcoming the multiple ground issue.

Raghu