Today’s mmWave WLANs can realize simultaneous multi-user multi-stream transmission solely on the downlink. In this paper, we present <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</b> plink <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</b> ulti-user <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> eamforming on single <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</b> F chain <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> P (UMBRA), a novel framework for supporting multi-stream multi-user uplink transmissions via a single RF chain. We design multi-user overlayed constellations and multi-user receiver mechanisms to enable concurrent time-triggered uplink multi-user transmissions received on a single RF chain AP. We devise exemplary beam selection policies to jointly adapt beams at users and the AP for targeting aggregate rate maximization without increasing training requirements compared to single-user systems. We implement the key components of using a programmable WLAN testbed using software-defined radios and commercial 60-GHz transceivers and collect over-the-air measurements using phased-array antennas and horn antennas with varying beamwidth. We find that in comparison to single-user transmissions, achieves more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.45 \times $</tex-math> </inline-formula> improvement in aggregate rate regardless of the choice of the user group, geometric separation, receiver beamwidth, and also under LOS blockage.