  Cell-free massive multiple-input multiple-output (MIMO) is an emerging
technology that will reshape the architecture of next-generation networks. This
paper considers the sequential fronthaul, whereby the access points (APs) are
connected in a daisy chain topology with multiple sequential processing stages.
With this sequential processing in the uplink, each AP refines users' signal
estimates received from the previous AP based on its own local received signal
vector. While this processing architecture has been shown to achieve the same
performance as centralized processing, the impact of the limited memory
capacity at the APs on the store and forward processing architecture is yet to
be analyzed. Thus, we model the received signal vector compression using
rate-distortion theory to demonstrate the effect of limited memory capacity on
the optimal number of APs in the daisy chain fronthaul. Without this memory
constraint, more geographically distributed antennas alleviate the adverse
effect of large-scale fading on the signal-to-interference-plus-noise-ratio
(SINR). However, we show that in case of limited memory capacity at each AP,
the memory capacity to store the received signal vectors at the final AP of
this fronthaul becomes a limiting factor. In other words, we show that when
deciding on the number of APs to distribute the antennas, there is an inherent
trade-off between more macro-diversity and compression noise power on the
stored signal vectors at the APs. Hence, the available memory capacity at the
APs significantly influences the optimal number of APs in the fronthaul.
