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I'm a NYC based director.

What is the best way to avoid feedback from wireless mics in a Theater in the Round layout or in an environmental immersive staging?

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The biggest thing is going to be careful EQing and using microphones as close to the actor's mouthes and as directional as possible. Feedback occurs when the amount of amplification applied to the microphone signal becomes enough that the background noise that the microphone picks up from the speaker is louder than the signal it is amplifying, thus forming a loop that makes it keep growing louder.

You prevent the loop by either increasing the source signal, thus reducing the amount of amplification needed or by reducing the amount of the signal picked up in the background from the speaker. The first is accomplished by micing closer to the source. Sound falls off rapidly with distance, so the closer you can get to the speaker's mouth, generally the stronger it will be (though angle also matters as people project sound outward).

For the second part, directional mics and careful EQing help. Directional mics will pick up more focused in one direction than another. If you can aim them carefully, it can prevent picking up background noise coming from other directions and thus give a cleaner signal more resistant to feedback.

EQing works similarly, though you are limited by the actual sound of your source. Certain frequencies will travel through the room better than others due to various acoustic effects, this is why feedback is generally a single frequency (whichever frequency hits the threshold first). You can alter the EQ to reduce those particular frequencies if it doesn't harm the sound of the speaker's voice too much, thus preventing the loop while still boosting the intended signal.

There are actually feedback suppression devices that you can use that will automatically look for rapidly growing feedback loops and make notch adjustments to EQ to prevent them, however such units will often have a slight negative impact on sound quality if they have to act as they generally don't consider what is needed by the source when eliminating feedback, so they are more of a safety mechanism than an ideal solution.

It may also be helpful to have your system leveled if it has not been. As previously mentioned, rooms have natural frequencies that they amplify more than others. Leveling a system in a room involves playing pink noise through the system at the intended volume level and then measuring how the room alters the sound. Those adjustments are then placed in to a 31 band equalizer that adjusts for the sound of the room in the future. This won't directly prevent feedback, but it will help counteract issues with natural reverberating frequencies in the room.

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AJ is correct on all accounts.

There are a couple more things I'd like to add: speaker placement, aim, and signal route.

Since you have an arena theater setup, think about where to put your speakers, where to aim them, and what signals you want to route to them.

As best as you can, route voices only to speakers facing away from the arena stage. Route track and environmental sounds to all speakers, keeping in mind their proximity to the performers mics. Rule of thumb is to keep the sound going to your audience as much as possible, and keep as little sound as possible going to your stage. The omni-directional wireless mics on your performers will thank you, and not complain with feedback.

If your performers need monitoring, IEM's are a good solution. I use IEM's for our touring theater group. They're lighter equipment to pack and I have no floor wedges to feedback on me. IEM's are a bit more expensive and complicated to setup, but are worth it.

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