iphone 7 will not back up

Try to optimize the range of the mobile network, see this Apple article:

If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

Not sure if this is the cause, see -> iPhone 7 Repair Program for "No Service" Issues

iPhone 7 Repair Program for "No Service" Issues - Apple Support

Then try again, see this Apple article: How to back up your iPhone, iPad, and iPod touch

How to back up your iPhone, iPad, and iPod touch - Apple Support

Read also again -> Related Article -> If you see an error when you update or restore your iPhone, iPad, or iPod

Click here for more support and assistance.