What he is suggesting is a sump that is above the tank. What that is is another tank that is above your circle. You pump water from your circle up to the sump tank, and from the sump, the water flows back down to your circle tank (via holes drilled into the sump, pipes, etc.)
Your sump tank will not be full of water (all you need is a few inches of water to dampen the water fall sound). Above the sump water line (and inside the tank - so no water spills) is your wet dry filter. This can be just a simple perforated box. You fill the box with bioballs & filter media. You adjust your pump output so your water flows evenly over your media (usually some kind of distribution plate) before going into the sump. Since your filter media is actually in the air, there is a tremedeous amount of gas exchange.
You'll need about a gallon or so of space for your bioballs / media. Maybe 3 or 4 gal
of water inside the sump, leave room so water don't splash out ..... maybe a 10 gal
or so container for your sump & filter.
Remember that you will need ventilation in the space where you put your sump ---- to ensure fresh air for gas exchange & to decrease humidity so you don't rot your wall.