Towards reducing the training signaling overhead in large scale and dense
cloud radio access networks (CRAN), various approaches have been proposed based
on the channel sparsification assumption, namely, only a small subset of the
deployed remote radio heads (RRHs) are of significance to any user in the
system. Motivated by the potential of compressive sensing (CS) techniques in
this setting, this paper provides a rigorous description of the performance
limits of many practical CS algorithms by considering the performance of the,
so called, oracle estimator, which knows a priori which RRHs are of
significance but not their corresponding channel values. By using tools from
stochastic geometry, a closed form analytical expression of the oracle
estimator performance is obtained, averaged over distribution of RRH positions
and channel statistics. Apart from a bound on practical CS algorithms, the
analysis provides important design insights, e.g., on how the training sequence
length affects performance, and identifies the operational conditions where the
channel sparsification assumption is valid. It is shown that the latter is true
only in operational conditions with sufficiently large path loss exponents.Comment: 6 pages, two-column format; ICC 201