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The intercarrier interference (ICI) due to the Doppler frequency shift, sampling clock offset, time-varying multipath fading and local oscillator frequency offset becomes the major difficulty for the data transmission via the wireless orthogonal frequency division multiplexing (OFDM) systems. The existing ICI mitigation schemes involve the frequency-domain channel estimation/equalization or the additional coding and therefore require the pilot symbols which reduce the throughput. The frequency-domain channel estimation/equalization relies on the huge matrix inversion with high computational complexity especially for the OFDM technologies possessing many subcarriers such as digital video broadcasting (DVB) systems and wireless metropolitan-area networks (WMAN). In our previous work, we proposed a semi-blind ICI equalization scheme using the joint multiple matrix diagonalization (JMMD) algorithm and empirically showed that the proposed method significantly improved the symbol error rates for QPSK- and 16QAM-OFDM systems. In this paper, we discuss the sufficient condition for the theoretical ICI equalizability and also propose an alternative semi-blind ICI equalization method based on the joint approximate diagonalization of eigen-matrices (JADE) algorithm, which is much more computationally efficient than our previous method.