Efficient Multi-Frame Activity Detection for Temporally Correlated Grant-Free Massive Access

Device activity detection is critical for grant-free random access in massive machine-type communications (mMTC). Its performance can be improved by exploiting the temporal correlation of activity status over consecutive frames. To this end, we first characterize the joint distribution of device activities using the multivariate Bernoulli (MVB) model, thereby formulating the multi-frame activity detection as a maximum a posteriori (MAP) problem. Then, by leveraging the coordinate descent (CD) framework, we design an efficient algorithm named MVB-MAP-CD, which decomposes the non-convex MAP problem into a sequence of tractable, small-scale sub-problems. Numerical results and comparisons with benchmark schemes validate the superior detection performance of the proposed algorithm, even in scenarios with low temporal correlation and short pilot sequences.