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In this paper, we investigate a pilot-based channel estimation scheme for the uplink of CDMA systems. Assuming the linear minimum mean squared error (MMSE) estimator, we aim to minimize the "worst-case" MSE of all users by optimizing their channel-input sequences (pilot signals). We derive a lower bound on the "worst-case" MSE and show that the bound can be either met by constructing optimal sets or not depending on certain system parameters. In the latter case we construct sequences that we think have good properties.