Radar uses electromagnetic waves (like Wifi but higher frequency) so it can go through walls, and even typical range for gesture recognition is less than meter, It probably can go at least 10 times as far by boosting the gain of the amplifier, it is not constrained like a theremin would be because it is already working in the far field region of the antenna.

Because it work at such high frequency (but not so high that it can still go through walls), it has many very small antennas arrays, and sense sub millimeter movements even from far away. It also has beam-forming capabilities, meaning it can focus the direction in which to sense. Because it is radar, things which moves are of interests and are filtered easily from the background.

Typically this piece of technology already can or will soon be able to : sense how many humans are around it, where they are, how fast they breath, how fast the heart is pulsating, who they are by computing some heart-base ID.

It is low-power and always-on, 360° with focus-able attention. It is cheap because it can be made on a chip. (Edit: fixing typos)