  Massive Machine-Type Communications (mMTC) is a key service category in the
current generation of wireless networks featuring an extremely high density of
energy and resource-limited devices with sparse and sporadic activity patterns.
In order to enable random access in such mMTC networks, base station needs to
identify the active devices while operating within stringent access delay
constraints. In this paper, an energy efficient active device identification
protocol is proposed in which active devices transmit On-Off Keying (OOK)
modulated preambles jointly and base station employs non-coherent energy
detection avoiding channel estimation overheads. The minimum number of
channel-uses required by the active user identification protocol is
characterized in the asymptotic regime of total number of devices $\ell$ when
the number of active devices $k$ scales as $k=\Theta(1)$ along with an
achievability scheme relying on the equivalence of activity detection to a
group testing problem. Several practical schemes based on Belief Propagation
(BP) and Combinatorial Orthogonal Matching Pursuit (COMP) are also proposed.
Simulation results show that BP strategies outperform COMP significantly and
can operate close to the theoretical achievability bounds. In a
partial-recovery setting where few misdetections are allowed, BP continues to
perform well.
