This paper investigates the fronthaul compression problem in a user-centric cloud radio access network, in which single-antenna users are served by a central processor (CP) cooperatively via a cluster of remote radio heads (RRHs). To satisfy the fronthaul capacity constraint, this paper proposes a transform-compress-forward scheme, which consists of well-designed transformation matrices and uniform quantizers. The transformation matrices perform dimension reduction in the uplink and dimension expansion in the downlink. To reduce the communication overhead for designing the transformation matrices, this paper further proposes a deep learning framework to first learn a suboptimal transformation matrix at each RRH based on the local channel state information (CSI), and then to refine it iteratively. To facilitate the refinement process, we propose an efficient signaling scheme that only requires the transmission of low-dimensional effective CSI and its gradient between the CP and RRH, and further, a meta-learning based gated recurrent unit network to reduce the number of signaling transmission rounds. For the sum-rate maximization problem, simulation results show that the proposed two-stage neural network can perform close to the fully cooperative global CSI based benchmark with significantly reduced communication overhead for both the uplink and the downlink. Moreover, using the first stage alone can already outperform the existing local CSI based benchmark.
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