There are two methods can wake up the client device from S3/S4 by server side device: ( client and server in same LAN )
1. Use the "Wake on LAN" which is enabling the option "Allow the device to wake the computer" ( In my client device , it supports PCIE WAKE# technology )
2. Use the Intel AMT technology which providing WebUI to control the remotely wake up the client device from S3/S4.
In my experiments: