  Although signal distortion-based peak-to-average power ratio (PAPR) reduction
is a feasible candidate for orthogonal frequency division multiplexing (OFDM)
to meet standard/regulatory requirements, the error vector magnitude (EVM)
stemming from the PAPR reduction has a deleterious impact on the performance of
high data-rate achieving multiple-input multiple-output (MIMO) systems.
Moreover, these systems must constrain the adjacent channel leakage ratio
(ACLR) to comply with regulatory requirements. Several recent works have
investigated the mitigation of the EVM seen at the receivers by capitalizing on
the excess spatial dimensions inherent in the large-scale MIMO that assume the
availability of perfect channel state information (CSI) with spatially
uncorrelated wireless channels. Unfortunately, practical systems operate with
erroneous CSI and spatially correlated channels. Additionally, most standards
support user-specific/CSI-aware beamformed and cell-specific/non-CSI-aware
broadcasting channels. Hence, we formulate a robust EVM mitigation problem
under channel uncertainty with nonconvex PAPR and ACLR constraints catering to
beamforming/broadcasting. To solve this formidable problem, we develop an
efficient scheme using our recently proposed three-operator alternating
direction method of multipliers (TOP-ADMM) algorithm and benchmark it against
two three-operator algorithms previously presented for machine learning
purposes. Numerical results show the efficacy of the proposed algorithm under
imperfect CSI and spatially correlated channels.
