  Cloud Radio Access Network (C-RAN) is a promising architecture for
unprecedented capacity enhancement in next-generation wireless networks thanks
to the centralization and virtualization of base station processing. However,
centralized signal processing in C-RANs involves high computational complexity
that quickly becomes unaffordable when the network grows to a huge size. Among
the first, this paper endeavours to design a scalable uplink signal detection
algorithm, in the sense that both the complexity per unit network area and the
total computation time remain constant when the network size grows. To this
end, we formulate the signal detection in C-RAN as an inference problem over a
bipartite random geometric graph. By passing messages among neighboring nodes,
message passing (a.k.a. belief propagation) provides an efficient way to solve
the inference problem over a sparse graph. However, the traditional
message-passing algorithm is not guaranteed to converge, because the
corresponding bipartite random geometric graph is locally dense and contains
many short loops. As a major contribution of this paper, we propose a
randomized Gaussian message passing (RGMP) algorithm to improve the
convergence. Instead of exchanging messages simultaneously or in a fixed order,
we propose to exchange messages asynchronously in a random order. The proposed
RGMP algorithm demonstrates significantly better convergence performance than
conventional message passing. The randomness of the message update schedule
also simplifies the analysis, and allows the derivation of the convergence
conditions for the RGMP algorithm. In addition, we propose a blockwise RGMP
(B-RGMP) algorithm for practical implementation. The average computation time
of B-RGMP remains constant when the network size increases.
