  A vast population of low-cost low-power transmitters sporadically sending
small amounts of data over a common wireless medium is one of the main
scenarios for Internet of things (IoT) data communications. At the medium
access, the use of grant-free solutions may be preferred to reduce overhead
even at the cost of multiple-access interference. Unsourced multiple access
(UMA) has been recently established as relevant framework for energy efficient
grant-free protocols. The use of a compressed sensing (CS) transmission phase
is key in one of the two main classes of UMA protocols, yet little attention
has been posed to sparse greedy algorithms as orthogonal matching pursuit (OMP)
and its variants. We analyze their performance and provide relevant guidance on
how to optimally setup the CS phase. Minimum average transmission power and
minimum number of channel uses are investigated together with the performance
in terms of receiver operating characteristic (ROC). Interestingly, we show how
the basic OMP and generalized OMP (gOMP) are the most competitive algorithms in
their class.
