Nexus 4 with no signal (sleep mode) I have a problem with my sister's Nexus4.
When I try to call her I have the reply that the phone is off while if I call the other phone (HTC Legend with the same operator) I can talk regularly.

It happened both at home or outside.

It is not a operator problem because I change the operator twice and with the same operator in the same places I can phone with no problem.

The strange is that when a try to call N4 I am not able to start the call and after that the N4 receive a sms with the "lost call" and return it on-line.

it seems it falls in a sleep mode when the creen is off
Try to call the phone with a landline. If the problem persists try a factory reset, if that don't fix the problem I'm afraid you have a hardware issue.