  In this paper, we consider an uplink heterogeneous cloud radio access network
(H-CRAN), where a macro base station (BS) coexists with many remote radio heads
(RRHs). For cost-savings, only the BS is connected to the baseband unit (BBU)
pool via fiber links. The RRHs, however, are associated with the BBU pool
through wireless fronthaul links, which share the spectrum resource with radio
access networks. Due to the limited capacity of fronthaul, the
compress-and-forward scheme is employed, such as point-to-point compression or
Wyner-Ziv coding. Different decoding strategies are also considered. This work
aims to maximize the uplink ergodic sum-rate (SR) by jointly optimizing
quantization noise matrix and bandwidth allocation between radio access
networks and fronthaul links, which is a mixed time-scale issue. To reduce
computational complexity and communication overhead, we introduce an
approximation problem of the joint optimization problem based on
large-dimensional random matrix theory, which is a slow time-scale issue
because it only depends on statistical channel information. Finally, an
algorithm based on Dinkelbach's algorithm is proposed to find the optimal
solution to the approximate problem. In summary, this work provides an economic
solution to the challenge of constrained fronthaul capacity, and also provides
a framework with less computational complexity to study how bandwidth
allocation and fronthaul compression can affect the SR maximization problem.
