Multi-User SISO Precoding based on Generalized Multi-Unitary Decomposition for Single-carrier Transmission in Frequency Selective Channel

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In this paper, we propose to exploit the richly scattered multi-path nature of a frequency selective channel to provide additional degrees of freedom for desigining effective precoding schemes for multi-user communications. We design the precoding matrix for multi-user communications based on the Generalized Multi-Unitary Decomposition (GMUD), where the channel matrix H is transformed into Pᵢ*Rᵣ*Qᵢʰ. An advantage of GMUD is that multiple pairs of unitary matrices Pᵢ and Qᵢ can be obtained with one single Rᵣ. Since the column of Qᵢ can be used as the transmission beam of a particular user, multiple solutions of Qᵢ provide a large selection of transmission beams, which can be exploited to achieve high degrees of orthogonality between the multipaths, as well as between the interfering users. Hence the proposed precoding technique based on GMUD achieves better performance than precoding based on singular value decomposition.