  This paper studies the uplink of a cloud radio access network (C-RAN) where
the cell sites are connected to a cloud-computing-based central processor (CP)
with noiseless backhaul links with finite capacities. We employ a simple
compress-and-forward scheme in which the base-stations(BSs) quantize the
received signals and send the quantized signals to the CP using either
distributed Wyner-Ziv coding or single-user compression. The CP decodes the
quantization codewords first, then decodes the user messages as if the remote
users and the cloud center form a virtual multiple-access channel (VMAC). This
paper formulates the problem of optimizing the quantization noise levels for
weighted sum rate maximization under a sum backhaul capacity constraint. We
propose an alternating convex optimization approach to find a local optimum
solution to the problem efficiently, and more importantly, establish that
setting the quantization noise levels to be proportional to the background
noise levels is near optimal for sum-rate maximization when the
signal-to-quantization-noise ratio (SQNR) is high. In addition, with Wyner-Ziv
coding, the approximate quantization noise level is shown to achieve the
sum-capacity of the uplink C-RAN model to within a constant gap. With
single-user compression, a similar constant-gap result is obtained under a
diagonal dominant channel condition. These results lead to an efficient
algorithm for allocating the backhaul capacities in C-RAN. The performance of
the proposed scheme is evaluated for practical multicell and heterogeneous
networks. It is shown that multicell processing with optimized quantization
noise levels across the BSs can significantly improve the performance of
wireless cellular networks.
