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The goal of this paper is to compare the performance of the linear minimum mean square error (MMSE) detector  for a class of code division multiple access (CDMA) systems in time and frequency selective channels. Specifically, we consider direct sequence (DS)-CDMA, multicarrier (MC)-CDMA, and the MC-DS-CDMA systems. Two key tools are used in our development. First, a general time-frequency framework that includes the different CDMA systems as special cases. Second, the duality between time and frequency domains that is used to derive equivalences between the different CDMA systems operating over purely frequency selective and purely time selective channels. We then combine the insights obtained from these special cases to assess the performance of CDMA systems over time and frequency selective channels. We provide sufficient conditions for the codes employed by the CDMA systems for the equivalences to hold. Numerical results are presented to illustrate the results

Equivalence of Linear MMSE Detection in DS-CDMA and MC-CDMA Systems over Time and Frequency Selective Channels