  We study the problem of unsourced random access (URA) over Rayleigh
block-fading channels with a receiver equipped with multiple antennas. We
propose a slotted structure with multiple stages of orthogonal pilots, each of
which is randomly picked from a codebook. In the proposed signaling structure,
each user encodes its message using a polar code and appends it to the selected
pilot sequences to construct its transmitted signal. Accordingly, the
transmitted signal is composed of multiple orthogonal pilot parts and a
polar-coded part, which is sent through a randomly selected slot. The
performance of the proposed scheme is further improved by randomly dividing
users into different groups each having a unique interleaver-power pair. We
also apply the idea of multiple stages of orthogonal pilots to the case of a
single receive antenna. In all the set-ups, we use an iterative approach for
decoding the transmitted messages along with a suitable successive interference
cancellation technique. The use of orthogonal pilots and the slotted structure
lead to improved accuracy and reduced computational complexity in the proposed
set-ups, and make the implementation with short blocklengths more viable.
Performance of the proposed set-ups is illustrated via extensive simulation
results which show that the proposed set-ups with multiple antennas perform
better than the existing MIMO URA solutions for both short and large
blocklengths, and that the proposed single-antenna set-ups are superior to the
existing single-antenna URA schemes.
