Abstract: A new low complexity Turbo frequency equalization (TFDE) scheme with compandingbased transformation is proposed for cyclic prefix (CP) single carrier (SC) spatial multiplexing multiple-input multiple-output (MIMO) systems based on the variational inference method. Compared to the traditional TFDE method for MIMO systems, the proposed scheme has two distinct features. First, the a priori mean and variance matrix of the transmitted data symbols are computed with the companding a posteriori information from the decoder within the soft-in soft-out (SISO) frequency domain equalizer (FDE). Second, the a priori information for decoding is calculated by the extrinsic mean and variance of data symbols gleaned from the SISO FDE and the companding extrinsic information coming from the decoder. Analysis and simulation results demonstrate that the proposed scheme outperforms the traditional MIMO TFDE algorithm in terms of bit error rate (BER) performance, convergence speed of iteration and the global computational complexity.