  This paper studies reconfigurable intelligent surface (RIS) assisted device
activity detection for grant-free (GF) uplink transmission in wireless
communication networks. In particular, we consider mobile devices located in an
area where the direct link to an access point (AP) is blocked. Thus, the
devices try to connect to the AP via a reflected link provided by an RIS.
Therefore, a RIS phase-shift design is desired that covers the entire blocked
area with a wide reflection beam because the exact locations and times of
activity of the devices are unknown in GF transmission. In order to study the
impact of the phase-shift design on the device activity detection, we derive a
generalized likelihood ratio test (GLRT) based detector and present an
analytical expression for the probability of detection. Assuming knowledge of
statistical CSI, we formulate an optimization problem for the phase-shift
design for maximization of the guaranteed probability of detection for all
locations within a given coverage area. To tackle the non-convexity of the
problem, we propose two different approximations of the objective function. The
first approximation leads to a design that aims to reduce the variations of the
end-to-end channel while taking system parameters such as transmit power, noise
power, and probability of false alarm into account. The second approximation
can be adopted for versatile RIS deployments because it only depends on the
line-of-sight component of the end-to-end channel and is not affected by system
parameters. For comparison, we also consider a phase-shift design maximizing
the average channel gain and a baseline analytical phase-shift design for large
blocked areas. Our performance evaluation shows that the proposed
approximations result in phase-shift designs that guarantee high probability of
detection across the coverage area and outperform the baseline designs.
