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The performance of MC-CDMA is limited by multiple access interference (MAI). To mitigate this problem, equal BER power control (PC) was proposed for MMSE-SIC receiver, which provides a powerful solution for MAI suppression (M. Tan and Y. Bar-Ness, IEEE Commun. Lett., vol. 8, pp. 348-350, 2004), wherein the power distribution on different users was derived under the assumption of perfect channel state information (CSI) at the receiver. In practice, CSI is obtained from channel estimation, in which errors are inevitable. Therefore, the analysis of the robustness of the MMSE-SIC with the equal BER PC to channel estimation errors (CEE) is of great importance. In this paper, a method of second-order approximation is applied to estimate the mean excess MSE (MEMSE) of different users in a given decision order. The accuracy of the approximation is confirmed by simulation results. Furthermore, it is interesting to find out that the MMSE-SIC receiver with the equal BER PC presents significant robustness to CEE.