  In fog-aided cellular systems, content delivery latency can be minimized by
jointly optimizing edge caching and transmission strategies. In order to
account for the cache capacity limitations at the Edge Nodes (ENs),
transmission generally involves both fronthaul transfer from a cloud processor
with access to the content library to the ENs, as well as wireless delivery
from the ENs to the users. In this paper, the resulting problem is studied from
an information-theoretic viewpoint by making the following practically relevant
assumptions: 1) the ENs have multiple antennas; 2) only uncoded fractional
caching is allowed; 3) the fronthaul links are used to send fractions of
contents; and 4) the ENs are constrained to use one-shot linear precoding on
the wireless channel. Assuming offline proactive caching and focusing on a high
signal-to-noise ratio (SNR) latency metric, the optimal information-theoretic
performance is investigated under both serial and pipelined fronthaul-edge
transmission modes. The analysis characterizes the minimum high-SNR latency in
terms of Normalized Delivery Time (NDT) for worst-case users' demands. The
characterization is exact for a subset of system parameters, and is generally
optimal within a multiplicative factor of 3/2 for the serial case and of 2 for
the pipelined case. The results bring insights into the optimal interplay
between edge and cloud processing in fog-aided wireless networks as a function
of system resources, including the number of antennas at the ENs, the ENs'
cache capacity and the fronthaul capacity.
