  Cell-free massive multiple-input multiple-output (CFmMIMO) is a paradigm that
can improve users' spectral efficiency (SE) far beyond traditional cellular
networks. Increased spatial diversity in CFmMIMO is achieved by spreading the
antennas into small access points (APs), which cooperate to serve the users.
Sequential fronthaul topologies in CFmMIMO, such as the daisy chain and
multi-branch tree topology, have gained considerable attention recently. In
such a processing architecture, each AP must store its received signal vector
in the memory until it receives the relevant information from the previous AP
in the sequence to refine the estimate of the users' signal vector in the
uplink. In this paper, we adopt vector-wise and element-wise compression on the
raw or pre-processed received signal vectors to store them in the memory. We
investigate the impact of the limited memory capacity in the APs on the optimal
number of APs. We show that with no memory constraint, having single-antenna
APs is optimal, especially as the number of users grows. However, a limited
memory at the APs restricts the depth of the sequential processing pipeline.
Furthermore, we investigate the relation between the memory capacity at the APs
and the rate of the fronthaul link.
