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Recently, the space-time coded code division multiple access (ST-coded CDMA) has been widely investigated for the great demand of capacities and transmission rates in the future wireless communication systems. The blind Capon multiuser receiver had been designed to achieve the goal, which is implemented by the linearly constrained minimum variance (LCMV) filter. However, due to the lengthy spreading codes, the receiver has the drawbacks of large computational complexity and slow convergence speed in computing the filter weightts. To alleviate the detrimen of large filter weights, the parallel PA-GSC filter structure is proposed to take the place of LCMV filter. Based on the subspace techniques, a transformation scheme is designed to choose the effective degrees of freedom in the PA-GSC filter. Besides, a simplified PA-GSC receiver with lower complexity is also proposed. Computer simulations are given to demonstrate the effectiveness of the PA-GSC filter for the ST-coded CDMA systems.