While an i Phone 4 running i OS 4 firmware can update to i OS 7, it cannot update wirelessly; it requires a wired connection to i Tunes on a computer.
If you have not had success updating your operating system, your i Tunes may be out of date.
According to Tech Advisor website, the update requires at least 1.4GB of free space.
The space is used primarily during the installation process to store the temporary file.
Apple’s support page for specific errors on i Tunes isn’t all that helpful.