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In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced, and system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) equalizer. Unfortunately, the direct ZF method requires the inversion of an N times N ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. In this paper, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O (N3) to O (N log2 N). Another feature of the proposed algorithm is that it can converge very fast, typically in one or two iterations. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-plus-noise ratio (SINR). For a multiple-input-multiple-output (MIMO) OFDM system, the complexity of the ZF method becomes more intractable. We then extend the method proposed for SISO-OFDM systems to MIMO-OFDM systems. It can be shown that the computational complexity can be reduced even more significantly. Simulations show that the proposed methods perform almost as well as the direct ZF method, while the required computational complexity is reduced dramatically.