  This paper proposes a dimension reduction-based signal compression scheme for
uplink distributed MIMO cloud radio access networks (C-RAN) with an overall
excess of receive antennas, in which users are jointly served by distributed
multi-antenna receivers connected to a central processor via individual
finite-capacity fronthaul links. We first show that, under quantization
noise-limited operation, applying linear dimension reduction at each receiver
before compressing locally with a uniform quantization noise level results in a
sum capacity that scales approximately linearly with fronthaul capacity, and
can come within a fixed gap of the cut-set bound. The dimension reduction
filters that maximize joint mutual information are then shown to be truncated
forms of the conditional Karhunen-Loeve transform, with a block coordinate
ascent algorithm for finding a stationary point given. Analysis and numerical
results indicate that the signal dimension can be reduced without significant
loss of information, particularly at high signal-to-noise ratio, preserving the
benefits of using excess antennas. The method is then adapted for the case of
imperfect channel state information at the receivers. The scheme significantly
outperforms conventional local signal compression at all fronthaul rates, and
with complexity linear in network size represents a scalable solution for
distributed MIMO C-RAN systems.
