  Tailor-made for massive connectivity and sporadic access, grant-free random
access has become a promising candidate access protocol for massive
machine-type communications (mMTC). Compared with conventional grant-based
protocols, grant-free random access skips the exchange of scheduling
information to reduce the signaling overhead, and facilitates sharing of access
resources to enhance access efficiency. However, some challenges remain to be
addressed in the receiver design, such as unknown identity of active users and
multi-user interference (MUI) on shared access resources. In this work, we deal
with the problem of joint user activity and data detection for grant-free
random access. Specifically, the approximate message passing (AMP) algorithm is
first employed to mitigate MUI and decouple the signals of different users.
Then, we extend the data symbol alphabet to incorporate the null symbols from
inactive users. In this way, the joint user activity and data detection problem
is formulated as a clustering problem under the Gaussian mixture model.
Furthermore, in conjunction with the AMP algorithm, a variational Bayesian
inference based clustering (VBIC) algorithm is developed to solve this
clustering problem. Simulation results show that, compared with state-of-art
solutions, the proposed AMP-combined VBIC (AMP-VBIC) algorithm achieves a
significant performance gain in detection accuracy.
