Massive MIMO requires a large number of antennas and the same amount of power amplifiers (PAs), one per antenna. As opposed to 4G base stations, which could afford highly linear PAs, next-generation base stations will need to use inexpensive PAs, which have a limited region of linear amplification. One of the research challenges is effectively handling signals which have high peak-to-average power ratios (PAPRs), such as orthogonal frequency division multiplexing (OFDM). This paper introduces a PAPR-aware precoding scheme that exploits the excessive spatial degrees-of-freedom of large scale multiple-input multipleoutput (MIMO) antenna systems. This typically requires finding a solution to a nonconvex optimization problem. Instead of relaxing the problem to minimize the peak power, we introduce a practical semidefinite relaxation (SDR) framework that enables accurately and efficiently approximating the theoretical PAPR-aware precoding performance for OFDM-based massive MIMO systems. The framework allows incorporating channel uncertainties and intercell coordination. Numerical results show that several orders of magnitude improvements can be achieved w.r.t. state of the art techniques, such as instantaneous power consumption reduction and multiuser interference cancellation. The proposed PAPRaware precoding can be effectively handled along with the multicell signal processing by the centralized baseband processing platforms of next-generation radio access networks. Performance can be traded for the computing efficiency for other platforms