  The use of a large excess of service antennas brings a variety of performance
benefits to distributed MIMO C-RAN, but the corresponding high fronthaul data
loads can be problematic in practical systems with limited fronthaul capacity.
In this work we propose the use of lossy dimension reduction, applied locally
at each remote radio head (RRH), to reduce this fronthaul traffic. We first
consider the uplink, and the case where each RRH applies a linear dimension
reduction filter to its multi-antenna received signal vector. It is shown that
under a joint mutual information criteria, the optimal dimension reduction
filters are given by a variant of the conditional Karhunen-Loeve transform,
with a stationary point found using block co-ordinate ascent. These filters are
then modified such that each RRH can calculate its own dimension reduction
filter in a decentralised manner, using knowledge only of its own instantaneous
channel and network slow fading coefficients. We then show that in TDD systems
these dimension reduction filters can be re-used as part of a two-stage reduced
dimension downlink precoding scheme. Analysis and numerical results demonstrate
that the proposed approach can significantly reduce both uplink and downlink
fronthaul traffic whilst incurring very little loss in MIMO performance.
