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The combination of code-division multiple-access and multicarrier (MC) modulation has been proposed to develop high data-rate wireless communication systems. Due to the longer symbol duration in comparison with single-carrier systems, MC systems are more sensitive to various imperfections, including phase noise and frequency offsets due to local oscillators and Doppler spreading due to motion that results in temporal channel variations. The performance of current systems is significantly limited by these imperfections because they disperse the transmitted power in a particular subcarrier into adjacent subcarriers, thereby causing interference between the subcarriers at the receiver. We consider a single-user communication system and use a canonical model for the received signal that efficiently captures the effects of all impairments. The model uses Fourier basis functions that are fixed for all imperfections while the expansion coefficients depend on imperfections. Using the model, we introduce a receiver structure that implements the matched filter (MF), and hence, optimal. The MF is implemented through a Rake receiver in the frequency domain. The receiver fully compensates for frequency offsets as well as phase noise, thereby eliminating the performance loss due to these factors. Furthermore, in contrast to existing designs, it delivers improved performance under fast fading by exploiting Doppler diversity. Finally, the same integrated receiver structure works for all imperfections eliminating the need for devising a separate correction technique for each.