This paper investigates a blind space–time equaliser (STE) designed for single-input multiple-output (SIMO) systems that employ high-throughput quadrature amplitude modulation schemes. A constant modulus algorithm (CMA) aided soft decision-directed (SDD) scheme, originally derived for low-complexity blind equalisation of single-input single-output channels, is extended to the SIMO scenario. Simulations are conducted to compare the performance of this blind adaptive scheme with another low-complexity blind STE referred to as the CMA aided decision directed (DD) scheme. The results obtained demonstrate that for SIMO systems the CMA aided SDD scheme exhibits advantages over the CMA aided DD arrangement, in terms of its faster convergence speed and lower computational complexity.