Single carrier (SC) code division multiple access (CDMA) with block transmission has been shown to be more effective while utilising a low-complexity equaliser to combat frequency-selective fading channels, when compared with conventional direct sequence CDMA technology. It also has lower peak-to-average power ratio and lower frequency sensitivity compared with multicarrier CDMA. The authors propose two blind channel estimation methods for uplink multiple input multiple output SC-CDMA systems with block transmisssion-one is the subspace-based method and the other is the so-called autocorrelation contribution method (ACM). Both the methods provide close performance to the case with perfect channel knowledge at high signal-to- noise ratio (SNR) without any training data required. It is shown that ACM yields a better performance than the subspace method at a lower SNR, and a similar performance at a high SNR, with the advantages of avoiding rank determination and noise power estimation as in the subspace method. In addition, the authors integrate layered space frequency equalisation with blind channel estimation, which provides improved performance over the conventional linear equalisation, by employing successive interference cancellation.