Blind multi-user detection is of special interest for multiple access interference (MAI) mitigation in code-division multiple-access (CDMA) systems since it is impractical to assume perfect knowledge of parameters such as spreading codes, time delays and amplitudes of all the users in a rapidly changing mobile environment. In [1], the blind decorrelating detector and the minimum mean square error (MMSE) detector were developed based on subspace estimation and derived in closed forms of the signal subspace components. To combat frequency-selective fading, the subspace approach to blind multi-user detection was extended to multi-carrier CDMA (MCCDMA) systems, e.g. in [2]. In this Letter, we develop further the algorithm presented in [1, 2], and show how the condition of the signal subspace can be improved by using not only the autocorrelation, but also the pseudo-autocorrelation of the received observations, leading to improved performance in blind multi-user detection.