After restoring without backup my iPhone is unable to activate

Please look at this --> If you can't activate your iPhone - Apple Support

If you are the owner or the owner has shared all information with you then to open Activation Lock:- If it is Activation locked, read here --> Turn off Activation Lock - Apple Support Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Learn how to remove a device from a previous owner's account.

If you are not the owner and do not have the Apple ID and Password then there is no way that you can get into this iPhone unless the original owner shares the Apple ID and password with you. If you are lucky you can get into this iPhone if they (owner) accidentally remove the device from their apple ID.

Carrier Update (Required): Released by your Cellular Service provider (Carrier Update), affects your Outgoing / Incoming calls, SMS, Data etc..

How to Update Carrier Settings

You can manually check for and install a carrier settings, update with these steps: Make sure your device is connected to a Wi-Fi or cellular network. Tap Settings > General > About. If an update is available, you'll see an option to update your carrier settings.

Update your carrier settings on your iPhone or iPad - Apple Support