There are several ways.. Some re-broadcast in the TV band and you simply pick it up downstairs.
I have a pair of DVR's with additional stuff.. Now you can not do LIVE TV this way but.....
One can record then over the lan (Which can be wired or wireless) send to the other. or it can be streamed to a computer. or downloaded to a computer. or..
Well you ever see those ads "only our overpriced very expensive Cable or Satellit service lets you do all these things".. (Paraphrased a bit).. NOT TRUE. I do it all the time 25/year for the program guide.
The catch is the TUNER will always be UPSTAIRS. not downstairs so you have to go up to change channels unlless you have an RF Remote (And they make those too).
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times