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Blind symbol detection for mobile communications systems has been widely studied and can be implemented by using either adaptive or iterative techniques. However, adaptive blind algorithms require data of sufficient length to converge. Therefore, in a rapidly changing environment, they are likely to be unable to track the changing channels. In such a situation, one possible solution is to use iterative blind algorithms. Iterative blind source separation algorithms based on the least-squares constant modulus algorithm (LSCMA) for instantaneous multiple-input multiple-output (MIMO) systems are proposed. Since the LSCMA cannot guarantee correct separation, and hence cannot be used directly for MIMO channels, two extensions are considered: cancellation techniques (successive and parallel), and using an orthogonality constraint to ensure independence among different outputs. In common with many block iterative algorithms, it is found that for small block sizes there can be a BER flare-up effect at high SNR, although this can be removed for a sufficiently large block size. Of the proposed algorithms, simulation results show that the orthogonality-based algorithm has the best performance, and is comparable to the iterative least-squares with projection (ILSP) algorithm, but offers cheaper computational complexity.