  This article studies a novel distributed precoding design, coined team
minimum mean-square error (TMMSE) precoding, which rigorously generalizes
classical centralized MMSE precoding to distributed operations based on
transmitter-specific channel state information (CSIT). Building on the
so-called theory of teams, we derive a set of necessary and sufficient
conditions for optimal TMMSE precoding, in the form of an infinite dimensional
linear system of equations. These optimality conditions are further specialized
to cell-free massive MIMO networks, and explicitly solved for two important
examples, i.e., the classical case of local CSIT and the case of unidirectional
CSIT sharing along a serial fronthaul. The latter case is relevant, e.g., for
the recently proposed radio stripe concept and the related advances on
sequential processing exploiting serial connections. In both cases, our optimal
design outperforms the heuristic methods that are known from the previous
literature. Duality arguments and numerical simulations validate the
effectiveness of the proposed team theoretical approach in terms of ergodic
achievable rates under a sum-power constraint.
