The FCC regulations are very long, hard to understand, and occasionally contradictory - I know, I work in the industry. The closest section of the law that comes to mind is for very low power (typically under 1mW) devices that do not require the user to have a licence. These are so called "part 15" devices, which refers to the Code of Federal Regulations (CFR) Title 47, Part 15.

While the user of these sorts of devices doesn't require a licence, the device itself needs to be certified, so that, among other things, it doesn't spew noise all over the RF spectrum. This device wouldn't pass.

There are also experimental licences that can be held by businesses such as RF equipment manufacturers that allow for using equipment that hasn't yet received FCC approval. They are usually band restricted, geographically restricted and power restricted, and you must take care to not have high levels of spurious emissions.

edit: Here's a PDF explainer on Part 15 devices: https://transition.fcc.gov/Bureaus/Engineering_Technology/Do...

See https://www.fcc.gov/media/radio/low-power-radio-general-info...

I don't live in the United States, and I don't give a damn about the FCC.