  Channel matrix sparsification is considered as a promising approach to reduce
the progressing complexity in large-scale cloud-radio access networks (C-RANs)
based on ideal channel condition assumption. In this paper, the research of
channel sparsification is extend to practical scenarios, in which the perfect
channel state information (CSI) is not available. First, a tractable lower
bound of signal-to-interferenceplus-noise ratio (SINR) fidelity, which is
defined as a ratio of SINRs with and without channel sparsification, is derived
to evaluate the impact of channel estimation error. Based on the theoretical
results, a Dinkelbach-based algorithm is proposed to achieve the global optimal
performance of channel matrix sparsification based on the criterion of
distance. Finally, all these results are extended to a more challenging
scenario with pilot contamination. Finally, simulation results are shown to
evaluate the performance of channel matrix sparsification with imperfect CSIs
and verify our analytical results.
