Multiple Access Channel in Massive Multi-User MIMO Using Group Testing

The number of wireless devices (e.g., cellular phones, IoT, laptops) connected to Wireless Local Area Networks (WLAN) grows each year exponentially. The orchestration of the connected devices becomes infeasible, especially when the number of resources available at the single access point (e.g., Base Station, Wireless Access Points) is limited. On the other hand, the number of antennas at each device grows too. We leverage the large number of antennas to suggest a massive multiple-user multiple-input-multiple-output (MU-MIMO) scheme using sparse coding based on Group Testing (GT) principles, which reduces overhead and complexity. We show that it is possible to jointly identify and decode up to $K$ messages simultaneously out of $N\cdot C$ messages (where $N$ is the number of users and $C$ is the number of messages per user) without any scheduling overhead or prior knowledge of the identity of the transmitting devices. Our scheme is order-optimal in the number of users and messages, utilizing minimal knowledge of channel state and an efficient (in both run-time and space) decoding algorithm requiring $O(K\log NC)$ antennas. We derive sufficient conditions for vanishing error probability and bound the minimal number of antennas necessary for our scheme.