  Channel state information (CSI) is of vital importance in wireless
communication systems. Existing CSI acquisition methods usually rely on pilot
transmissions, and geographically separated base stations (BSs) with
non-correlated CSI need to be assigned with orthogonal pilots which occupy
excessive system resources. Our previous work adopts a data-driven deep
learning based approach which leverages the CSI at a local BS to infer the CSI
remotely, however the relevance of CSI between separated BSs is not specified
explicitly. In this paper, we exploit a model-based methodology to derive the
Cram\'er-Rao lower bound (CRLB) of remote CSI inference given the local CSI.
Although the model is simplified, the derived CRLB explicitly illustrates the
relationship between the inference performance and several key system
parameters, e.g., terminal distance and antenna array size. In particular, it
shows that by leveraging multiple local BSs, the inference error exhibits a
larger power-law decay rate (w.r.t. number of antennas), compared with a single
local BS; this explains and validates our findings in evaluating the
deep-neural-network-based (DNN-based) CSI inference. We further improve on the
DNN-based method by employing dropout and deeper networks, and show an
inference performance of approximately $90\%$ accuracy in a realistic scenario
with CSI generated by a ray-tracing simulator.
