  For massive machine-type communications, centralized control may incur a
prohibitively high overhead. Grant-free non-orthogonal multiple access (NOMA)
provides possible solutions, yet poses new challenges for efficient receiver
design. In this paper, we develop a joint user identification, channel
estimation, and signal detection (JUICESD) algorithm. We divide the whole
detection scheme into two modules: slot-wise multi-user detection (SMD) and
combined signal and channel estimation (CSCE). SMD is designed to decouple the
transmissions of different users by leveraging the approximate message passing
(AMP) algorithms, and CSCE is designed to deal with the nonlinear coupling of
activity state, channel coefficient and transmit signal of each user
separately. To address the problem that the exact calculation of the messages
exchanged within CSCE and between the two modules is complicated due to phase
ambiguity issues, this paper proposes a rotationally invariant Gaussian mixture
(RIGM) model, and develops an efficient JUICESD-RIGM algorithm. JUICESD-RIGM
achieves a performance close to JUICESD with a much lower complexity.
Capitalizing on the feature of RIGM, we further analyze the performance of
JUICESD-RIGM with state evolution techniques. Numerical results demonstrate
that the proposed algorithms achieve a significant performance improvement over
the existing alternatives, and the derived state evolution method predicts the
system performance accurately.
