IPSW files are essentially just packages to deliver updates to your i Phone, i Pad, and i Pod touch including the baseband and firmware.
Anytime you update your device i Tunes will grab a new IPSW from Apple’s servers.
We know this isn't possible for everyone, especially if the network you're having issues with isn't your own or may even be a corporate one.
If none of the above steps are remedying your Wi-Fi issues, you may need to visit an Apple Store in order to either have your i Phone or i Pad serviced or exchanged.
If you need more space for a wireless update, you can update using i Tunes or delete content manually from your device.
Whether you use i Tunes or update wirelessly, you'll have the same amount of free space on your device after you update.
If all else fails, try completely restoring your i Phone using i Tunes.
I'd suggest restoring it new and then trying Wi-Fi before bringing down all of your stuff from a backup.
For this reason if you ever need i Phone warranty service, be sure to unjailbreak your i Phone before taking it into Apple.