  The number of wireless devices is drastically increasing, resulting in many
devices contending for radio resources. In this work, we present an algorithm
to detect active devices for unsourced random access, i.e., the devices are
uncoordinated. The devices use a unique, but non-orthogonal preamble, known to
the network, prior to sending the payload data. They do not employ any carrier
sensing technique and blindly transmit the preamble and data. To detect the
active users, we exploit partial channel state information (CSI), which could
have been obtained through a previous channel estimate. For static devices,
e.g., Internet of Things nodes, it is shown that CSI is less time-variant than
assumed in many theoretical works. The presented iterative algorithm uses a
maximum likelihood approach to estimate both the activity and a potential phase
offset of each known device. The convergence of the proposed algorithm is
evaluated. The performance in terms of probability of miss detection and false
alarm is assessed for different qualities of partial CSI and different
signal-to-noise ratio.
