This is basically how it works which means you must buy a compatible wifi card to play with your Psp on Kai: you can replace the Wifi max or the Planex in the picture by any other compatible wifi cards reported below.
Routers are not compatible with Kai (except the Linksys reported in the adapters setup guides): you could get your Psp connected to them as much as you want, they will not allow Kai to recognize it.
May you find here different guides which provide you step by steps through the setup process of your adapter, some tips to let you play in the best conditions as possible and everything else you need to know.
Where you will find some brief explanation about the computing's process, the tunneling, exploited by Kai.
Where you will find recommendations to get your adapter.
Where you will find the step by steps to set up the main adapters for Kai on various operating systems.
Where you will find some information to run the few games which require you more than just getting connected to a single SSID. Dissidia is one of those.
Where you will find the complete list of adapters you can use for Kai and check if yours is compatible or not.
Where you will find tips to reduce your lag and to prevent random disconnections while you are playing, Portforwarding being the first of them.