  We consider the problem of ESPRIT-oriented precoder design for beamspace
angle-of-departure (AoD) estimation in downlink mmWave multiple-input
single-output communications. Standard precoders (i.e., directional/sum beams)
yield poor performance in AoD estimation, while Cramer-Rao bound-optimized
precoders undermine the so-called shift invariance property (SIP) of ESPRIT. To
tackle this issue, the problem of designing ESPRIT-oriented precoders is
formulated to jointly optimize over the precoding matrix and the SIP-restoring
matrix of ESPRIT. We develop an alternating optimization approach that updates
these two matrices under unit-modulus constraints for analog beamforming
architectures. Simulation results demonstrate the validity of the proposed
approach while providing valuable insights on the beampatterns of the
ESPRIT-oriented precoders.
