WPA2 is a specific type of network encryption used to protect the information being transmitted over wireless Internet networks. In order to connect your computer to a WPA2 network, you need to provide a unique password. If you're attempting to connect your Sony PSP to the network you will still have to provide that password to get the device connected. This is accomplished via a manual configuration of the PSP's network settings.
Turn on your PSP. Select the first option from the console's main menu, labelled "Settings."
Highlight and select "Network Settings."
Select "Infrastructure Mode." This indicates to the console that, instead of connecting to another PSP console (like you would in ad-hoc mode), you are instead connecting to a wireless network.
Select the "New Connection" option. Select "Scan." Locate the name of your WPA2 wireless network. Select it with "X."
Select "WPA-PSK (AES)" from the "WLAN Security Setting" menu. "WPA-PSK (AES)" is the official name of WPA2. Type in the password for your wireless network and select "Next."
Choose the "Easy" connection option. Specify a name for your wireless network on the PSP and select "Save." Your PSP is connected to the WPA2 wireless network.