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In this paper, we propose a singular value decomposition (SVD) algorithm with superlinear-convergence rate, which is suitable for the beamforming mechanism in MIMO-OFDM channels with short coherent time, or short training sequence. The proposed superlinear-convergence SVD (SL-SVD) algorithm has the following features: 1) superlinear-convergence rate; 2) the ability of being extended smaller numbers of transmit and receive antennas; 3) being insensitive to dynamic range problems during the iterative process in hardware implementations; and 4) low computational cost. We verify the proposed design by using the VLSI implementation with CMOS 90 nm technology. The post-layout result of the design has the feature of 0.48 core area and 18 mW power consumption. Our design can achieve 7 M channel-matrices/s, and can be extended to deal with different transmit and receive antenna sets.