Mask-Compliant Clipping-Aware Precoding for Multi-User MIMO-OFDM Systems

Orthogonal frequency-division multiplexing (OFDM) is widely adopted in frequency-selective channels for its ability to simplify equalization, yet it also causes large signal peaks, out-of-band (OOB) emissions, and spectral leakage. We study downlink precoding/combining for multi-user multiple-input multiple-output (MU-MIMO)--OFDM systems by minimizing the sum of the users' mean-squared errors (MSEs) under per-subcarrier transmit-power limits, per-antenna OOB spectral-mask constraints, and per-antenna peak-amplitude (clipping) constraints, which confine the emitted spectrum and limit waveform peaks to reduce power-amplifier saturation, nonlinear distortion, and spectral regrowth. The resulting nonconvex problem is handled by a minimum mean-squared error (MMSE) based block coordinate descent (BCD), with a closed-form combiner update and an alternating direction method of multipliers (ADMM) algorithm with closed-form updates for the precoder subproblem. Simulations show clear gains over well-known benchmark schemes.