We consider the problem where an active DecisionMaker (DM) is tasked to identify the true hypothesis using as few as possible observations while maintaining accuracy. The DM collects observations according to its determined actions and knows the distributions under each hypothesis. We propose a deterministic and adaptive multi-stage hypothesis-elimination strategy where the DM selects an action, applies it repeatedly, and discards hypotheses in light of its obtained observations. The DM selects actions based on maximal separation expressed by the distance between the parameter vectors of each distribution under each hypothesis. Close distributions can be clustered, simplifying the search and significantly reducing the number of required observations. Our algorithms achieve vanishing Average Bayes Risk (ABR) as the error probability approaches zero, i.e., the algorithm is asymptotically optimal. Furthermore, we show that the ABR is bounded when the number of hypotheses grows. Simulations are carried out to evaluate the algorithm's performance compared to another multi-stage hypothesis-elimination algorithm, where an improvement of several orders of magnitude in the mean number of observations required is observed.

We consider the standard Multi-User Multiple-Input-Multiple-Output (MU-MIMO) system, where only$K$active users, unknown in advance, out of$N$, wish to convey their messages to a single receiver. We derive two necessary lower bounds on the number of antennas (degrees of freedom) on both the receiver and transmitter sides, where the first holds for any MU-MIMO system and the second holds for any energy detection-based MU-MIMO. Then, we revisit techniques with identical scaling laws, such as compressive sensing and group testing, and discuss when the optimal antenna scaling laws for the MU-MIMO problem can be obtained. We also numerically evaluate the presented bounds and compare them against recent achievability results from the last ISIT.

The number of wireless devices continues to grow, and more antennas per device are added, increasing the challenge of efficient resource allocation, especially for uplink streams. To address this, we propose a novel massive multiple-user multiple-input-multiple-output (MU-MIMO) scheme based on Group Testing (GT) with non-cooperative self-scheduling users, reducing the required overhead and complexity. Specifically, we show that out of a population ofNdevices withMmessages each, it is possible for the base station (BS) to jointly identify and decode up toKdevices, unknown in advance, simultaneously without the BS applying any scheduling algorithm or collecting channel state information. The BS efficiently decodes the transmissions with vanishing error probability using onlyO(KlogNM) antennas, which implies order–optimal number of antennas.

The number of wireless devices continues to grow, and more antennas per device are being added, increasing the challenge of efficient resource allocation, especially for uplink streams. To address this, we propose a novel massive multipleuser multiple-input-multiple-output (MU-MIMO) scheme based on Group Testing (GT) with non-cooperative self-scheduling users, reducing the required overhead and complexity. Specifically, we show that out of a population of N devices with $\mathcal{M}$ messages each, it is possible for the base station (BS) to jointly identify and decode up to K devices, unknown in advance, simultaneously and without any scheduling or channel state information. The BS efficiently decodes the transmissions with vanishing error probability using only $O(K\log N\mathcal{M})$ antennas, which implies order–optimal sum-rate.