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Synchronous-CDMA techniques possess intrinsic protection against co-channel interference due to orthogonal codes employed. In the presence of multipath, however, each signal is subject to frequency-selective fading and the code orthogonality condition does not hold leading to increased cross correlations. To implement multiuser (adaptive) detection techniques in a fast changing environment, explicit knowledge of the (nonorthogonal) signature waveforms of all users may be required. Here, we propose a blind estimation scheme that provides closed-form signature waveform estimates by exploiting the underlying data structure of the outputs. In particular, we show that the subspace of the data matrix contains sufficient information of the signature waveforms. Based on this observation, a MUSIC-like algorithm that can accomplish blind estimation using a minimum number of data samples is derived.