An SDP Approach for PAPR Reduction in OFDM Systems using Partial Transmit Sequences

The partial transmit sequences (PTS) algorithm has been extensively used in the literature to reduce the high levels of peak-to-average power ratio (PAPR) in OFDM systems. A key step in the PTS approach is the use of a finite set of phase factors b_nu to rotate the data before transmission in order to reduce the PAPR. The choice of these factors is however heuristic in nature and an exhaustive search to find the optimum combination of phase factors exhibits exponential complexity. In this paper, we propose a novel semi definite programming (SDP) approach that finds the optimal set of phase rotation factors used in the PTS technique at a polynomial cost. In particular, by reformulating the general non-convex optimization problem into a generic convex one using an SDP relaxation approach, the optimal set of phase rotation coefficients can be found efficiently using an interior-point optimization method. A fundamental result of this paper is that the SDP formulation provides also a lower bound for the performance of the PTS technique. Using the complementary cumulative distribution function (CCDF) measure, we show that the novel method performs better than the conventional OFDM-PTS system for different transmission parameters and modulation schemes.