One of the major challenges for Cloud / Centralized Radio Access Network (C-RAN) lies in the limited bandwidth of the fronthaul (FH) network which connects a centralized baseband unit (BBU) to one or more remote radio units (RRU). In particular for massive multiple-input multiple-output (MIMO) uplink processing, the required FH capacity increases proportionally to the number of transceiver units (TXRUs) (and not the number of MIMO layers) for traditional receiver processing at the BBU. This can become a bottleneck for deploying large antenna arrays where MIMO detection is performed at the BBU. In [1] distributed minimum mean-squared error interference rejection combining (MMSE-IRC) processing for C-RAN architecture is proposed, where receive (Rx) beamforming at the RRU is performed to compress the received branches before transporting them to the BBU for MIMO detection. We find that the proposed processing is not practically robust due to high-dimension covariance matrix estimation from a limited number of interference samples. In this paper, we propose an advancement of the idea in [1] by considering distributed MMSE-IRC processing which is based on a structured covariance matrix estimation approach. It is shown that the proposed approach provides more robust uplink performance while guaranteeing moderate FH loads and low complexity RRU processing.