The paper proposes a general framework for both time-domain (TD) and frequency-domain (FD) iterative blockwise equalization in single carrier (SC) wideband multiple-input multiple-output (MIMO) channels. First, a novel turbo blockwise operating equalizer structure is proposed by jointly optimizing the feed-forward and feedback filters at each iteration based on the minimum mean squared error (MMSE) criterion. Optimization of the filter coefficients, utilized for feed-forward equalization and decision feedback, is performed in both time and frequency domains, and the equivalence between them is established by unifying the iterative block equalization with the feed-forward and feedback filters in various domains. The corresponding filters are obtained analytically in a closed form as a solution of the constrained Wiener-Hopf equation with the use of average reliability information. Second, asymptotic performance and diversity analysis of the proposed single carrier frequency domain equalizer (SC-FDE) is carried out that leads to insights on the structures of the filters in the high SNR regime. Furthermore, we elaborate on the rate and diversity tradeoff of the space-time coded SC-FDE based on the proposed equalizer structure and the space-frequency coded OFDM systems. Performance comparison between the proposed SC-FDE scheme and OFDM is made. The proposed SC-FDE scheme performs very close to the genie-aided performance bounds and better than OFDM based transmission.