Abstract: The problem of linear spatial precoding design is investigated for multipleantenna systems in frequency selective channels. For block transmission systems using cyclic prefix, it is shown that the linear spatial precoding design problem is equivalent to design one common spatial precoding for multiple adjacent frequency points, which can be numerically solved by convex optimization. Then a low-complexity suboptimal precoding aimed at maximizing the upper bound of channel capacity is proposed, which degenerates to the existing eigen-beamforming (EBF) when the equal power allocation is used. For non-block transmission systems, the drawbacks of EBF are analyzed. Then a novel algorithm based on successive searching, called successive EBF (SS-EBF), is proposed, which has a significant performance gain over EBF for high signal-to-noise ratio (SNR).