  In this paper, we consider the problem of activity detection in grant-free
code-domain non-orthogonal multiple access (NOMA). We focus on performing
activity detection via subspace methods under a setup where the data and pilot
spreading signatures are of different lengths, and consider a realistic
frame-structure similar to existing mobile networks. We investigate the impact
of channel correlation on the activity detection performance; first, we
consider the case where the channel exhibits high correlation in time and
frequency and show how it can heavily deteriorate the performance. To tackle
that, we propose to apply user-specific masking sequences overlaid on top of
the pilot signatures. Second, we consider the other extreme with the channel
being highly selective, and show that it can also negatively impact the
performance. We investigate possible pilots' reallocation strategies that can
help reduce its impact.
