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In direct sequence-code division multiple access (DS-CDMA) systems over frequency-selective channels, blind joint equalisation and multiuser detection has been the focus subject of research by many researchers. In this scheme, only the desired user's spreading code and timing information are available to the receiver. The two-stage constant modulus algorithm (CMA)-based receiver proposed, implements an adaptive blind joint equalisation and multiuser detection without explicit channel estimation. The first stage of the algorithm can be seen as a linear combination of blind adaptive minimum output energy (MOE) detectors based on total data correlation matrix. In this study, the authors adopt a MOE detector based on interference correlation matrix instead of total data correlation matrix to improve the performance of the first-stage detector, thus achieving an improved two-stage CMA-based blind joint equalisation and multiuser detection algorithm. In addition, the convergence of the proposed adaptive algorithm is analysed. Both the analysis and computer simulation verify the performance improvement of our proposed algorithm.