  This paper presents a comprehensive communication theoretic model for the
physical layer of a cell-free user-centric network, formed by user equipments
(UEs), radio units (RUs), and decentralized units (DUs), uniformly spatially
distributed over a given coverage area. We consider RUs equipped with multiple
antennas, and focus on the regime where the UE, RU, and DU densities are
constant and therefore the number of such nodes grows with the coverage area. A
system is said scalable if the computing load and information rate at any node
in the network converges to a constant as the network size (coverage area)
grows to infinity. This imposes that each UE must be processed by a
(user-centric) finite-size cluster of RUs, and that such cluster processors are
dynamically allocated to the DUs (e.g., as software defined virtual network
functions) in order to achieve a balanced computation load. We also assume that
the RUs are connected to the DUs through a packet switching network, in order
to achieve adaptive routing and load balance. For this model, we define in
details the dynamic cluster formation and uplink pilot allocation. As a
consequence of the pilot allocation and the scalability constraint, each
cluster processor has a partial view of the network channel state information.
We define the condition of ``ideal partial CSI'' when the channel vectors that
can be estimated are perfectly known (while the ones that cannot be estimated
are not know at all). We develop two attractive cluster-based linear receiver
schemes for the uplink, and an uplink-downlink duality that allows to reuse
such vectors as precoders for the downlink.
