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Although signal distortion-based peak-to-average power ratio (PAPR) reductionis 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 ofhigh 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 haveinvestigated the mitigation of the EVM seen at the receivers by capitalizing onthe excess spatial dimensions inherent in the large-scale MIMO that assume theavailability of perfect channel state information (CSI) with spatiallyuncorrelated wireless channels. Unfortunately, practical systems operate witherroneous CSI and spatially correlated channels. Additionally, most standardssupport user-specific/CSI-aware beamformed and cell-specific/non-CSI-awarebroadcasting channels. Hence, we formulate a robust EVM mitigation problemunder channel uncertainty with nonconvex PAPR and ACLR constraints catering tobeamforming/broadcasting. To solve this formidable problem, we develop anefficient scheme using our recently proposed three-operator alternatingdirection method of multipliers (TOP-ADMM) algorithm and benchmark it againsttwo three-operator algorithms previously presented for machine learningpurposes. Numerical results show the efficacy of the proposed algorithm underimperfect CSI and spatially correlated channels.

EVM Mitigation with PAPR and ACLR Constraints in Large-Scale MIMO-OFDM Using TOP-ADMM