  It is generally believed that downlink cell-free networks perform best under
centralized implementations where the local channel state information (CSI)
acquired by the access-points (AP) is forwarded to one or more central
processing units (CPU) for the computation of the joint precoders based on
global CSI. However, mostly due to limited fronthaul capabilities, this
procedure incurs some delay that may lead to partially outdated precoding
decisions and hence performance degradation. In some scenarios, this may even
lead to worse performance than distributed implementations where the precoders
are locally computed by the APs based on partial yet timely local CSI. To
address this issue, this study considers the problem of robust precoding design
merging the benefits of timely local CSI and delayed global CSI. As main
result, we provide a novel distributed precoding design based on the recently
proposed team minimum mean-square error method. As a byproduct, we also obtain
novel insights related to the AP-CPU functional split problem. Our main
conclusion, corroborated by simulations, is that the opportunity of performing
some local precoding computations at the APs should not be neglected, even in
centralized implementations.
