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 paper 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 paper 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.
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