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In this paper, we present a group of subspace code-timing estimation algorithms for asynchronous code-division multiple-access (CDMA) systems with bandlimited chip waveforms. The proposed schemes are frequency-domain based techniques that exploit a unique structure of the received signal in the frequency domain. They can be implemented either blindly or in a training-assisted manner. The proposed blind code-timing estimators require only the spreading code of the desired user, whereas the training-assisted schemes assume the additional knowledge of the transmitted symbols of the desired user. Through a design parameter of user choice, the proposed schemes offer flexible tradeoffs between performance, user capacity, and complexity. They can deal with both time- and frequency-selective fading channels. Numerical simulations show that the proposed schemes are near-far resistant, and compare favorably to an earlier subspace code-timing estimation scheme that is implemented in the time domain.