A linear decentralized receiver capable of suppressing multiple-access interference (MAI) for asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems with aperiodic random signature sequences is proposed. Performance bounds on this receiver are also obtained. Using them as performance measures, the problem of chip waveform selection in DS-CDMA systems with the proposed receiver under the near-far scenario is investigated. In particular, the performance of several practical chip waveforms is compared. An LMS-type adaptive algorithm is developed to obtain the parameters needed in the receiver, which only requires the signature sequence and coarse timing information of the desired user.