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it probably won't work. You are only 3 mi from transmitters but the ground will block ALL transmissions. putting it in the joists may work, but with such heavy construction in floors i don't guarentee anything.
Not to mention all sorts of random distortion and diffraction everytime someone walks by upstairs.
Assuming that you only want the big-name transmitters from your 3 mi towers a small directional antenna (upstairs a set-top would be more than enough) sounds like the best bet to me. You can always mount it higher in your house (if possible). You'll need one with UHF/high-VHF capabilities, if you want NBC and CBS.
P.S don't buy too big of an antenna, you're pretty close to your transmitter(s) and you could overload something with a huge antenna.
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