Constellation Design with Hypercube Graphs

A high peak-to-average power ratio (PAPR) is a major disadvantage of orthogonal frequency division multiplexing (OFDM) communications systems. In this paper, we present a graph-theoretic heuristic to mitigate high PAPR. In particular, we focus on searching for an optimal Gray-coded mapping to encode user messages such that minimum PAPR is obtained for a given message sequence in an M-ary quadrature amplitude modulation (QAM). We exploit the bijection between vertex-weighted lattice constellations and hypercube graphs to formulate the OFDM PAPR optimization as a computationally efficient integer linear program (ILP) through the application of Birkhoff's theorem to doubly stochastic matrices . Our numerical experiments show an average PAPR reduction of 9-10 dB using the hypercube-graph-based constellation map over the worst map while still within 0.5 dB of the brute-force method.