Hi Staticswitch,
Thank you for using the Apple Support Communities! I understand you may be seeing a spinning wheel icon in your status bar, as if something is actively communicating with the network on your iPhone. I'd like to help.
Check your data usage to see if you can identify any increases with specific applications. This can help isolate if the network activity pertains to a certain application on your device. Also, check which applications are able to access and use your cellular data, and adjust their access to your preference. This article will walk you through both of these options: Check the cellular data usage on your iPhone and iPad - Apple Support.
Please also take a look at this article, under the section, 'Use Background App Refresh', to see if there are any applications you wish to turn off, as this could be causing the spinning wheel: Switch apps on your iPhone, iPad, or iPod touch - Apple Support.
If you are able to identify the usage to a specific app, you can try forcing the app to quit by following these steps:How to force an app to close on your iPhone, iPad, or iPod touch - Apple Support.
Keep me posted. Regards.