The only way to control your NAT is through your router. The optimal NAT is "Open." Anything less than that and you will likely have problems with the game in some form or another. The most common problem is the inability to party up with friends. Of course, you will also observe a much higher frequency of lag or "wtf" moments if you are on anything less than Open NAT.
There are several threads that explain how to achieve Open NAT. Activision Support also has a page that deals with NAT issues. If you are unable to find any of those, let me know and I will post links in this thread for you.
Oh, and as far as the chat cutting in and out issue, I have been experiencing the same issue in Ghosts while playing Extinction with a fellow Extinction player. I had that issue in the past when trying to party up with my brother. Before we opened his NAT, chat would cut in and out and even completely disconnect us at times. We also had enormous problems trying to party up. Fixing my brother's NAT to open solved 100% of those issues. The current fellow Extinction player, I know, is aware of potential NAT issues. My NAT is open, has been open for years, and always remains open. One thing I've done in the last few months, though, was to forward all the necessary COD ports.
The issues with the ability of my friend and I to connect is on his end, not mine. Because he is a well-versed gamer, I don't have the nerve to tell him so.
My point is that if you already have Open NAT and your ports are forwarded, the issues you are having may be the result of friends with inadequate connection settings. There may not be anything else further you can do.