Symbol-Level Precoding for PAPR Reduction in Multi-User MISO-OFDM Systems

In this paper, we study symbol-level precoding (SLP) design for time-domain peak-to-average power ratio (PAPR) reduction in a multi-user MISO-OFDM transmission through the idea of constructive interference (CI). Specifically, we design the precoded transmit signals that minimize the symbol-level transmit power subject to per-antenna time-domain PAPR constraint and CI condition, using the knowledge of both data information and channel state information (CSI), based on which a non-convex problem is established. This non-convex problem is transformed into a convex one by the vectorization and relaxation method. For the relaxed problem, we employ Lagrangian method and Karush-Kuhn-Tucker (KKT) conditions to obtain a closed-form expression on the precoded signals as a function of the Lagrangian multipliers. Subsequently, we study the dual problem and obtain the optimal Lagrangian multipliers via the proposed alternating iterative algorithm. We further consider the practical communication scenario with imperfect CSI, where the original CI constraint is transformed into a probabilistic constraint in order to achieve robustness against statistically CSI errors. Numerical results validate that the proposed low-complexity algorithm achieves an enhanced performance over existing methods in terms of transmit power, PAPR and computation complexity, both in ideal perfect CSI and practical imperfect CSI cases.