To be honest, I'm not 100% sure if the ways to achieve that behavior only are possible through that permission, or even if there's some workaround of that behavior, but I'm almost sure so I'm posting.
Going to the particular case, I'd need for my Android app to check what's the signal strength with which the device is connected to the telephony network, and it looks like that's impossible to do without having enabled the permission for accessing user's location.
Problem is that app doesn't look like it has anything to do with needing user's location, indeed, if it's only possible through that permission, I consider that a fail in Android design from user experience point of view, so my guess is that it could make some users suspicious about that, specially considering that from Android API 23 you need to explicitly confirm a dialog to allow the permission.
I guess I'd need some very good words not to make the user suspicious, or well, maybe I'm also overlooking the users that would feel suspicious about my app.
Which would be a good way to handle this in terms of user experience if on last instance that permission is needed to achieve that behavior?