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Abstract Precoding techniques can be used in multiple input multiple output (MIMO) system to assign resources such as power and information optimally. This paper is concerned with limited feedback in precoded orthogonal space time block code (OSTBC) systems, which is a precoding technique for incomplete channel information response. The conventional approach to design the precoding codebook is based on the discrete Fourier transform (DFT) matrix, which has high computational complexity. In this paper, a new approach to design the precoding codebook for the limited feedback precoded OSTBC systems is proposed, which is based on the discrete fractional sine transform (DFRST) matrix. The proposed DFRST-based precoding codebook design approach has lower computational complexity comparing to that of the DFT-based design with very similar bit error rate (BER) performance.