Minimizing the peak-to-average power ratio of OFDM signals using convex optimization

The main disadvantage of orthogonal frequency-division multiplexing (OFDM) is the high time-domain peak-to-average power ratio (PAR) that limits transmitter power efficiency. Assuming no changes in receiver structure, the transmitter can only reduce PAR by distorting the data carriers or by adding power to the free carriers. This paper shows that the OFDM signal with globally minimum PAR, subject to constraints on the allowed constellation error and the free carrier power, can be efficiently computed using convex optimization. Simulation results are presented for the 802.11a/g wireless local-area network standard. The globally minimum PAR, subject to the constellation error constraint, ranges from 0.7 dB for 6-Mbps binary phase-shift keying to 4.1 dB for 54-Mbps 64-QAM. Tradeoff analysis shows that the free carrier power can be drastically reduced by backing off from this globally minimum PAR by less than 1 dB. A customized interior-point method (IPM) is derived for solving the OFDM optimization problem. The IPM reaches the desired tradeoff between PAR and free carrier power within two iterations, where the main computational complexity per iteration is four fast Fourier transforms plus the solution of a linear system of equations. The customized IPM is about 100 times faster than a general-purpose optimization algorithm.