  The performance of cloud radio access network (C-RAN) is limited by the
finite capacities of the backhaul links connecting the centralized processor
(CP) with the base-stations (BSs), especially when the backhaul is implemented
in a wireless medium. This paper proposes the use of wireless multicast
together with BS caching, where the BSs pre-store contents of popular files, to
augment the backhaul of C-RAN. For a downlink C-RAN consisting of a single
cluster of BSs and wireless backhaul, this paper studies the optimal cache size
allocation strategy among the BSs and the optimal multicast beamforming
transmission strategy at the CP such that the user's requested messages are
delivered from the CP to the BSs in the most efficient way. We first state a
multicast backhaul rate expression based on a joint cache-channel coding
scheme, which implies that larger cache sizes should be allocated to the BSs
with weaker channels. We then formulate a two-timescale joint cache size
allocation and beamforming design problem, where the cache is optimized offline
based on the long-term channel statistical information, while the beamformer is
designed during the file delivery phase based on the instantaneous channel
state information. By leveraging the sample approximation method and the
alternating direction method of multipliers (ADMM), we develop efficient
algorithms for optimizing cache size allocation among the BSs, and quantify how
much more cache should be allocated to the weaker BSs. We further consider the
case with multiple files having different popularities and show that it is in
general not optimal to entirely cache the most popular files first. Numerical
results show considerable performance improvement of the optimized cache size
allocation scheme over the uniform allocation and other heuristic schemes.
