  In this paper, we introduce a novel approach to user-centric association and
feedback bit allocation for the downlink of a cell-free massive MIMO (CF-mMIMO)
system, operating under limited feedback constraints. In CF-mMIMO systems
employing frequency division duplexing, each access point (AP) relies on
channel information provided by its associated user equipments (UEs) for
beamforming design. Since the uplink control channel is typically shared among
UEs, we take account of each AP's total feedback budget, which is distributed
among its associated UEs. By employing the Saleh-Valenzuela multi-resolvable
path channel model with different average path gains, we first identify
necessary feedback information for each UE, along with an appropriate codebook
structure. This structure facilitates adaptive quantization of multiple paths
based on their dominance. We then formulate a joint optimization problem
addressing user-centric UE-AP association and feedback bit allocation. To
address this challenge, we analyze the impact of feedback bit allocation and
derive our proposed scheme from the solution of an alternative optimization
problem aimed at devising long-term policies, explicitly considering the
effects of feedback bit allocation. Numerical results show that our proposed
scheme effectively enhances the performance of conventional approaches in
CF-mMIMO systems.
