Multiplexing More Data Streams in the MU-MISO Downlink by Interference Exploitation Precoding

In this paper, we focus on the constructive interference (CI) precoding for the scenario when the number of streams simultaneously transmitted by the base station (BS) is larger than that of transmit antennas at the BS, and derive the optimal precoding structure by employing the pseudo inverse. We show that the optimal pre-scaling vector in IE precoding is equal to a linear combination of the right singular vectors that correspond to zero singular values of the coefficient matrix. By formulating the dual problem, we further show that the optimal precoding matrix can be expressed as a function of the dual variables in a closed form, and an equivalent quadratic programming (QP) formulation is derived for computational complexity reduction. Numerical results validate our analysis and demonstrate significant performance improvements for interference exploitation precoding in the considered scenario.