  In future wireless networks, one fundamental challenge for massive
machine-type communications (mMTC) lies in the reliable support of massive
connectivity with low latency. Against this background, this paper proposes a
compressive sensing (CS)-based massive random access scheme for mMTC by
leveraging the inherent sporadic traffic, where both the active devices and
their channels can be jointly estimated with low overhead. Specifically, we
consider devices in the uplink massive random access adopt pseudo random
pilots, which are designed under the framework of CS theory. Meanwhile, the
massive random access at the base stations (BS) can be formulated as the sparse
signal recovery problem by leveraging the sparse nature of active devices.
Moreover, by exploiting the structured sparsity among different receiver
antennas and subcarriers, we develop a distributed multiple measurement vector
approximate message passing (DMMV-AMP) algorithm for further improved
performance. Additionally, the state evolution (SE) of the proposed DMMV-AMP
algorithm is derived to predict the performance. Simulation results demonstrate
the superiority of the proposed scheme, which exhibits a good tightness with
the theoretical SE.
