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Interleave division multiple access (IDMA) recently attracted many research activities because of its excellent performance despite its reasonable low complexity. The low complexity is usually realized by the multiuser detector that applies an approximation similar to the rake receiver for CDMA systems. So far, this type of detector has been most frequently considered in IDMA literature. In this paper we investigate the performance of IDMA based on linear minimum mean square error (MMSE) detection. The MMSE detector is more complex than the rake-like approximation. At the price of the complexity, however, it is shown that the MMSE detector brings several advantages over the rake-like approach such as the superior performance on channels with spectrally poor characteristics, effective iterative processing for lower SNR values, faster convergence and therefore shorter decoding delays, and better performance for short block length. We also confirm that the complexity can be drastically reduced by the low rank approximation of the MMSE filter by its multistage representation without compromising on the performance.