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In this paper, a novel time domain upsampling linear receiver is proposed for an asynchronous multicarrier code division multiple access system in frequency-selective Rayleigh fading channels. After anti-aliasing filtering, the received discrete-time upsampled signal is processed by a finite-impulse-response (FIR) filter at the receiver without any pre-processing. For the FIR filter, the observation window is extended to two-symbol duration in order to capture a complete desired symbol and eliminate the knowledge of signature waveform and timing acquisition requirement, and the tap coefficients are optimised according to the minimum mean square error (MMSE) criterion by employing a normalised least-mean-square algorithm. The proposed time domain upsampling MMSE (TDU-MMSE) receiver works in a decision-directed mode after training by a pre-defined sequence. The theoretical bit error rate (BER) is derived for the proposed receiver and agrees very well with the simulation results. Moreover, it has been shown that the TDU-MMSE receiver is able to achieve better BER performance than the conventional linear MMSE (LMMSE) and partial sampling MMSE (PS-MMSE) with lower computation complexity.