arXiv:2510.17445v4 Announce Type: replace-cross Abstract: In existing literature, a two-stage architecture comprising of large-scale fading decoding (LSFD) at the central processing unit (CPU) and local combining at the access points (APs) is commonly deployed for uplink processing in scalable cell-free massive multiple-input multiple-output (CF-mMIMO) systems. However, centralized LSFD (c-LSFD) requires cross-AP channel statistics at the CPU and local combining uses schemes that either do not suppress interference optimally or result in analytically intractable solutions. We provide novel schemes to address both concerns. First, we propose the decentralized LSFD (d-LSFD) scheme that maximizes a surrogate signal-to-interference-plus-noise ratio built only from local interference covariance statistics and identify covariance-action regime where it is equivalent to c-LSFD. Second, based on the fact that the antennas at each AP provide spatial degrees of freedom (DoFs) for both interference suppression and coherent array gain, we interpret every combining scheme as solving the optimal DoF allocation problem over available DoFs. Selective zero-forcing (ZF) schemes solve this problem over both the dimension and composition of the local ZF subspace. We then provide the DoF-adaptive ZF-subspace (DAZS) combining scheme, which lets each AP select the optimal directions in the ZF subspace by maximizing its local sum spectral efficiency. Our numerical results establish the efficacy and efficiency of the proposed schemes compared to the corresponding existing schemes.