  In this paper, we explore the low-complexity optimal bilinear equalizer (OBE)
combining scheme design for cell-free massive multiple-input multiple-output
networks with spatially correlated Rician fading channels. We provide a
spectral efficiency (SE) performance analysis framework for both the
centralized and distributed processing schemes with bilinear equalizer
(BE)-structure combining schemes applied. The BE-structured combining is a set
of schemes that are constructed by the multiplications of channel
statistics-based BE matrices and instantaneous channel estimates. Notably, we
derive closed-form achievable SE expressions for centralized and distributed
BE-structured combining schemes. We propose one centralized and two distributed
OBE schemes: Centralized OBE (C-OBE), Distributed OBE based on Global channel
statistics (DG-OBE), and Distributed OBE based on Local channel statistics
(DL-OBE), which maximize their respective SE expressions. OBE matrices in these
schemes are tailored based on varying levels of channel statistics. Notably, we
obtain new and insightful closed-form results for the C-OBE, DG-OBE, and DL-OBE
combining schemes. Numerical results demonstrate that the proposed OBE schemes
can achieve excellent SE, even in scenarios with severe pilot contamination.
