Using sound waves to track finger motion offers several advantages over cameras — which don’t work without line-of-sight or when the device is hidden by fabric or another obstructions — and other technologies like radar that require both custom sensor hardware and greater computing power, said senior author and UW assistant professor of computer science and engineering Shyam Gollakota.

But standard sonar echoes are weak and typically not accurate enough to track finger motion at high resolution. Errors of a few centimeters would make it impossible to differentiate between writing individual letters or subtle hand gestures.

So the UW researchers used “Orthogonal Frequency Division Multiplexing” (used in cellular telecommunications and WiFi), allowing for tracking phase changes in the echoes and correcting for any errors in the finger location.

Fans of beloved science fiction author Douglas Adams recall the gesture-based interface used in The Hitchhiker's Guide to the Galaxy from a generation earlier, and can't wait to use this idea on their smartphones:

A loud clatter of gunk music flooded through the Heart of Gold cabin as Zaphod searched the sub-etha radio wave bands for news of himself. The machine was rather difficult to operate. For years radios had been operated by means of pressing buttons and turning dials; then as the technology became more sophisticated the controls were made touch-sensitive--you merely had to brush the panels with your fingers; now all you had to do was wave your hand in the general direction of the components and hope. It saved a lot of muscular expenditure, of course, but meant that you had to sit infuriatingly still if you wanted to keep listening to the same program.

Zaphod waved a hand and the channel switched again.

Update 15-Jul-2016: Here's an earlier reference to the idea of a gesture interface from Samuel R. Delany's Babel-17 (1968):

Rydra shook her head. She passed her hand before the filing crystal. In the concaved screen at the base, words flashed. She stilled her fingers. "Navigator-Two. . . ." She turned her hand. "Navigator-One. . . ." She paused and ran her hand in a different direction.". . . male, male, male, female...

Rydra watched, her hand drifting through centimeters over the crystal's face. The names on the screen flashed back and forth.

Rydra's hand came down on the crystal face, and the name glowed on the screen.
(Read more about the filing crystal)

End update.