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This contribution investigates semi-blind adaptive spatial filtering or equalisation for multiple-input multiple-output (MIMO) systems that employ high-throughput quadrature amplitude modulation (QAM) signalling. A minimum number of training symbols, equal to the number of receivers (we assume that the number of transmitters is no more than that of receivers), are first utilized to provide a rough least squares channel estimate of the system is MIMO channel matrix for the initialization of the spatial equalizer is weight vectors. A constant modulus algorithm aided soft decision-directed blind algorithm, originally derived for blind equalization of single-input single-output and single-input multiple-output systems employing high-order QAM signalling, is then extended to adapt the spatial equalizers for MIMO systems. This semi-blind scheme has a low computational complexity, and our simulation results demonstrate that it converges fast to the minimum mean-square-error spatial equalization solution.