Update:

Because I supposed, the usb-wifi adapter supplied by avalon may be defective: today I bought this USB-Wifi adapter (Cudy WU650 AC650 USB WiFi Adapter) new, tried it with this Wifi-USB-Device, but no success: Miner display says: "No USB Devices Inserted", even though I had the usb wifi adapter plugged in.

Last attempt, plug in USB Ethernet adapter that I bought separately and LAN cable into the Avalon miner.
 IP address is shown in the miner display. Enter this IP address in the browser on my PC. Must scan QR code from Avalon. Only now can I configure the miner with the Avalon Family App, set the pool and let it work.

Read the description at canaan.io for this Avalon Nano 3S Miner, it is said to work with Wifi. I don't want to use LAN cables all the time. There is no LAN cable laid where the miner is located and would have to be installed first. I would like to use WLAN. How can the problem be solved? Canaan Support no answer since 10 days.