It is nearly impossible to get type 1 NAT.. for that you have to pass the public IP to the PS4.
Please read the info so you understand.
http://www.playstationing.com/ps4/how-to-change-your-nat-type-on-ps4-and-ps3/839
It says..
NAT Type 1 (Open) – You are either NOT behind a router/firewall OR you have already DMZ enabled.
To NOT be behind a router.. means you are plugged directly into the internet.
OR you have DMZ which means ALL ports are open.
For most people you have
NAT Type 2 (Moderate) –Your PS3/PS4 is connected properly and you shouldn’t run into any issues.
That means all the required ports are open.. the list is there .. on the playstation reference.
You need to open up the following ports in both directions TCP & UDP:
- 80
- 443
- 465
- 983
- 3478-3480
- 3658
- 5223
- 6000-7000
- 9293
- 10070-10080
This still only gives you type 2 NAT.
So to answer your title question literally.
Plug your broadband modem directly into your PS4.
You will not achieve Type 1 NAT through any NAT router.
You can put the PS4 in what is the equivalent of DMZ in the Airport.
On the Network tab put the PS4 as the default host. Where I have 192.168.2.253 put the IP of the PS4 there.