Q: software update

If you are using iTunes to update your iPhone, make sure iTunes is up to date on your computer > Get the latest version of iTunes - Apple Support

Are you attempting to check for this update OTA (over the air on the phone) or via iTunes? Do you have a good internet connection? If iTunes, are you using the latest version of iTunes?

Restart your router, restart your iPhone, then try again.

tt2

See Get help with over-the-air iOS updates - Apple Support

You said you want to do a wireless updated, but is there a particular reason that you cannot backup your device to iTunes and then use iTunes to perform the update? If you don't use a computer then is your iCloud backup up to date?

tt2

This is an excerpt from the link that turingtest2 provided regarding the OTA update.

"If the issue happens again, try updating with iTunes."

You own an iPhone. You ought to have iTunes on your computer. You ought to have a backup of the state of the device which you refresh from time to time, a backup of the media that is on your device in an iTunes library ready so that it could be restored in case of corruption or loss and replacement, and also a further backup of the library in case your computer's hard drive fails. See Recover your iTunes library from your iPod or iOS device and Backup your iTunes for Windows library with SyncToy for suggestions.

tt2