  We consider training-based channel estimation for a cloud radio access
network (CRAN), in which a large amount of remote radio heads (RRHs) and users
are randomly scattered over the service area. In this model, assigning
orthogonal training sequences to all users will incur a substantial overhead to
the overall network, and is even impossible when the number of users is large.
Therefore, in this paper, we introduce the notion of local orthogonality, under
which the training sequence of a user is orthogonal to those of the other users
in its neighborhood. We model the design of locally orthogonal training
sequences as a graph coloring problem. Then, based on the theory of random
geometric graph, we show that the minimum training length scales in the order
of $\ln K$, where $K$ is the number of users covered by a CRAN. This indicates
that the proposed training design yields a scalable solution to sustain the
need of large-scale cooperation in CRANs. Numerical results show that the
proposed scheme outperforms other reference schemes.
