  We consider the uplink of a cloud radio access network (C-RAN), where massive
MIMO remote radio heads (RRHs) serve as relays between users and a centralized
baseband unit (BBU). Although employing massive MIMO at RRHs can improve the
spectral efficiency, it also significantly increases the amount of data
transported over the fronthaul links between RRHs and BBU, which becomes a
performance bottleneck. Existing fronthaul compression methods for conventional
C-RAN are not suitable for the massive MIMO regime because they require
fully-digital processing and/or real-time full channel state information (CSI),
incurring high implementation cost for massive MIMO RRHs. To overcome this
challenge, we propose to perform a two-timescale hybrid analog-and-digital
spatial filtering at each RRH to reduce the fronthaul consumption.
Specifically, the analog filter is adaptive to the channel statistics to
achieve massive MIMO array gain, and the digital filter is adaptive to the
instantaneous effective CSI to achieve spatial multiplexing gain. Such a design
can alleviate the performance bottleneck of limited fronthaul with reduced
hardware cost and power consumption, and is more robust to the CSI delay. We
propose an online algorithm for the two-timescale non-convex optimization of
analog and digital filters, and establish its convergence to stationary
solutions. Finally, simulations verify the advantages of the proposed scheme.
