Check your PSP's wireless security setting, and make sure it matches your router's security. https://support.us.playstation.com/app/answers/detail/a_id/1133/
It's possible that your wireless router is set for a security protocol that is not supported by your PSP. The PSP can only connect using the WEP or WPA protocol. If your router is set for WPA2, then your device will not be able to join the network.
You'll need log in to your router and set it for WPA if you want to network your PSP. Do not use WEP since this security protocol is outdated and will leave your network vulnerable to attacks.