  The Internet of Things paradigm heavily relies on a network of a massive
number of machine-type devices (MTDs) that monitor changes in various
phenomena. Consequently, MTDs are randomly activated at different times
whenever a change occurs. This essentially results in relatively few MTDs being
active simultaneously compared to the entire network, resembling targeted
sampling in compressed sensing. Therefore, signal recovery in machine-type
communications is addressed through joint user activity detection and channel
estimation algorithms built using compressed sensing theory. However, most of
these algorithms follow a two-stage procedure in which a channel is first
estimated and later mapped to find active users. This approach is inefficient
because the estimated channel information is subsequently discarded. To
overcome this limitation, we introduce a novel covariance-learning matching
pursuit algorithm that bypasses explicit channel estimation. Instead, it
focuses on estimating the indices of the active users greedily. Simulation
results presented in terms of probability of miss detection, exact recovery
rate, and computational complexity validate the proposed technique's superior
performance and efficiency.
