  Hybrid beamforming is known to be a cost-effective and wide-spread solution
for a system with large-scale antenna arrays. This work studies the
optimization of the analog and digital components of the hybrid beamforming
solution for remote radio heads (RRHs) in a downlink cloud radio access network
(C-RAN) architecture. Digital processing is carried out at a baseband
processing unit (BBU) in the "cloud" and the precoded baseband signals are
quantized prior to transmission to the RRHs via finite-capacity fronthaul
links. In this system, we consider two different channel state information
(CSI) scenarios: 1) ideal CSI at the BBU 2) imperfect effective CSI.
Optimization of digital beamforming and fronthaul quantization strategies at
the BBU as well as analog radio frequency (RF) beamforming at the RRHs is a
coupled problem, since the effect of the quantization noise at the receiver
depends on the precoding matrices. The resulting joint optimization problem is
examined with the goal of maximizing the weighted downlink sum-rate and the
network energy efficiency. Fronthaul capacity and per-RRH power constraints are
enforced along with constant modulus constraint on the RF beamforming matrices.
For the case of perfect CSI, a block coordinate descent scheme is proposed
based on the weighted minimum-mean-square-error approach by relaxing the
constant modulus constraint of the analog beamformer. Also, we present the
impact of imperfect CSI on the weighted sum-rate and network energy efficiency
performance, and the algorithm is extended by applying the sample average
approximation. Numerical results confirm the effectiveness of the proposed
scheme and show that the proposed algorithm is robust to estimation errors.
