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...

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Bibliographic Details
Published inIEEE signal processing letters Vol. 30; pp. 1 - 5
Main Authors Mishra, Kumar Vijay, Krishnan, Sunder Ram, Sadler, Brian M.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Birkhoff's theorem
Constellation diagram
Encoding
Graph theory
Graphs
Gray codes
hypercube graphs
Hypercubes
integer linear programming
Integer programming
Lattices
Messages
OFDM PAPR
Optimization
Orthogonal Frequency Division Multiplexing
Peak to average power ratio
Quadrature amplitude modulation
Reflective binary codes
Symbols
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Summary: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 <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula>-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.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2023.3308813