  This paper considers a downlink cloud radio access network (C-RAN) in which
all the base-stations (BSs) are connected to a central computing cloud via
digital backhaul links with finite capacities. Each user is associated with a
user-centric cluster of BSs; the central processor shares the user's data with
the BSs in the cluster, which then cooperatively serve the user through joint
beamforming. Under this setup, this paper investigates the user scheduling, BS
clustering and beamforming design problem from a network utility maximization
perspective. Differing from previous works, this paper explicitly considers the
per-BS backhaul capacity constraints. We formulate the network utility
maximization problem for the downlink C-RAN under two different models
depending on whether the BS clustering for each user is dynamic or static over
different user scheduling time slots. In the former case, the user-centric BS
cluster is dynamically optimized for each scheduled user along with the
beamforming vector in each time-frequency slot, while in the latter case the
user-centric BS cluster is fixed for each user and we jointly optimize the user
scheduling and the beamforming vector to account for the backhaul constraints.
In both cases, the nonconvex per-BS backhaul constraints are approximated using
the reweighted l1-norm technique. This approximation allows us to reformulate
the per-BS backhaul constraints into weighted per-BS power constraints and
solve the weighted sum rate maximization problem through a generalized weighted
minimum mean square error approach. This paper shows that the proposed dynamic
clustering algorithm can achieve significant performance gain over existing
naive clustering schemes. This paper also proposes two heuristic static
clustering schemes that can already achieve a substantial portion of the gain.
