Networking – Direction of WiFi antenna

There are other, simpler, less elegant solutions, but in order to set this up the way you want it, where moving between access points is completely seamless, you will need routers which support wireless distribution system. Essentially the way WDS works is that each router is configured with the same radio channel, encryption scheme, and (for usability's sake, though not technically required) SSID. One or more base stations is connected by ethernet, and then repeater stations rebroadcast that signal. Clients can move back and forth between access points transparently; you will automatically connect to whichever is closest. You will need routers which are compatible and support WDS for this to work.

This isn't going to work.

For microwave devices, signal loss in the cable is enormous, so unless your antenna is within several meters of the device, there won't be any signal for it to emit.

Your best bet would be to install powerful antennas in the basement, next to the device or to get a repeater. There are some interesting directional antennas which you could use. If the device is going to be in the basement, you could just point the antenna to emit up.

Also, make sure that the antenna supports frequencies you are going to use. This could be a problem if your router has 5GHz mode.