  This paper proposes a multi-level cooperative architecture to balance the
spectral efficiency and scalability of cell-free massive multiple-input
multiple-output (MIMO) systems. In the proposed architecture, spatial expansion
units (SEUs) are introduced to avoid a large amount of computation at the
access points (APs) and increase the degree of cooperation among APs. We first
derive the closed-form expressions of the uplink user achievable rates under
multi-level cooperative architecture with maximal ratio combination (MRC) and
zero-forcing (ZF) receivers. The accuracy of the closed-form expressions is
verified. Moreover, numerical results have demonstrated that the proposed
multi-level cooperative architecture achieves a better trade-off between
spectral efficiency and scalability than other forms of cell-free massive MIMO
architectures.
