Impact of Spatial Correlation on Statistical Precoding

Abstract — Multiple antennas at the transmitter and the receiver can be used to achieve diversity or multiplexing gain or a combination of the two gains. Most works to date study schemes that achieve either of the two extremes in this diversity-multiplexing trade-off. In this work, we assume communication with a fixed number (M) of independent data-streams and a linear receiver architecture. Motivated by a limited feedback paradigm, we focus on precoding with a semi-unitary matrix. We first provide evidence that the optimal semi-unitary pre-coder consists of the M dominant right singular vectors of the channel. Then, we study the average relative enhancement in error probability and relative loss in mutual information with statistical precoding and show that these quantities vanish in the receive antenna asymptotics. For a given transmit and receive antenna dimension, Nt and Nr, we also show that these quantities are minimized if the eigenvalues of the transmit covariance matrix can be partitioned into two components: a dominant component of M eigenvalues that is well-conditioned and a sub-dominant component of Nt −M eigenvalues that is ill-conditioned away from the dominant component. I