In this paper, we propose a noncoherent space-frequency (SF) code for multiple-input-multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) systems for broadband wireless communications. The proposed noncoherent SF code matrix is constructed as a combination of a noncoherent SF code matrix and a differential modulation matrix. Comparing to noncoherent SF codes and differential SF codes in the literature, the advantages of our proposed code are higher spectrum efficiency, no error floor and more suitable for broadband communication systems. Taking advantage of the codeword structure of the proposed SF code, we devise a two-stage decoding scheme, in which the decoding process is implemented in two steps by decoding the component noncoherent codeword matrix and the component differential codeword matrix sequentially. Accordingly, the decoding scheme efficiently reduces decoding complexity. Simulation results show that our proposed scheme with two-stage decoding yields better performance than the noncoherent SF codes and frequency-domain differential codes proposed in the literature.
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