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Constellation Design With Hypercube Graphs
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DOI：10.1109/LSP.2023.3308813.png)
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Abstract
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A high peak-to-average power ratio (PAPR) is a major disadvantage of orthogonal frequency division multiplexing (OFDM) communications systems. In this letter, 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.
Keywords:
Birkhoff's theorem
Gray codes
hypercube graphs
integer linear programming
OFDM PAPR
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