The little I know...
Wake On LAN is wired only - because the ethernet NIC card/chip is left partially powered on when the PC is off/hibernating. A WOL 802.3 packet arrives, the NIC sees it, and uses some control lines on the data bus of the PC to signal power supply to turn on DC that the CPU needs, to run the startup.
This page
https://en.wikipedia.org/wiki/Wake-on-LAN
and
http://revolutionwifi.blogspot.com/2010/11/wake-on-wireless-lan.html
has a section on a WiFi Wakeup "standard". See the section:
Configuration of the workstation's wireless adapter is required in order to allow the adapter to wake the system from a standby or low-power state. This is accomplished on Windows machines through the adapter properties dialog:
...
I suspect this presumes use of a PCI bus WiFi card rather than USB, or the more modern/common, post-PCI serial bus.