MAP Estimation-Based Device Activity Detection for Massive Grant-Free Access with Unknown Device Activity Probabilities

For massive grant-free access, maximum a posterior (MAP) estimation-based device activity detection is known to achieve superior detection accuracy in the scenario of known activity probabilities. Unfortunately, no comparable Bayesian statistical estimation method exists in the scenario of unknown activity probabilities. This paper investigates MAP estimation-based device activity detection in this scenario. First, we formulate the hierarchical MAP estimation problem for device activities, which is a very challenging non-convex problem. For tractability, we obtain its approximate non-convex problem and prove its equivalence to the MAP estimation problem of device activities and activity probabilities. Next, we propose a block coordinate descent (BCD)-based algorithm to obtain the approximate MAP estimation problem's stationary points. Finally, we numerically show that the proposed algorithm achieves a superior detection accuracy and short computation time tradeoff compared with the state-of-the-art device activity detection methods.