  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 P_i*R_r*Q_i^H. An advantage of GMUD is that multiple pairs of unitary
matrices P_i and Q_i can be obtained with one single R_r. Since the column of
Q_i can be used as the transmission beam of a particular user, multiple
solutions of Q_i 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.
