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To provide new and/or higher rate wireless services with limited spectrum resources, frequency overlay has been naturally proposed to accommodate the new and legacy systems in a common band. We address the multiuser detection problem for overlaid code-division multiple-access (CDMA) scenarios. However, in contrast to the well-studied conventional single-rate CDMA, miscellaneous systems overlay almost always indicates the presence of multirate traffic that introduces an additional degree of freedom in receiver design-i.e., differences in the symbol rates. We concentrate on receiver design for multirate traffic, while assuming a lack of information exchange between the constituent (new and legacy) systems, as is commonplace in practice. We propose a receiver architecture based on linear parallel interference cancellation where the out-of-rate intersystem interference is estimated and subtracted by means of its characteristic subspace, thereby avoiding the need for the exact knowledge of signature waveforms of the interfering system. Simulation results validate our solution and show that the proposed receiver has better performance in various aspects than several other solutions for the same purpose.