Universidade Estadual de Campinas Faculdade de Engenharia El etrica - - PowerPoint PPT Presentation
Universidade Estadual de Campinas Faculdade de Engenharia El etrica e de Computac ao Departamento de Telem atica A New Mathematical Approach for the Design of Digital Communication Systems a Rodrigo G. Cavalcante, Henrique Lazari,
aAcknowledgement: To FAPESP, CAPES and CNPq, Brazilian agencies, for supporting this research.
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Topological Invariants Topology Topology Properties Riemannian Geometry Geometric Invariants in Homogeneous Spaces Genus Sectional Curvature Graph Channel DMC Existence of GU Signal Sets Realization Abstract Approach
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a a Sphere g=0 a b a b Torus g=1 M−QAM M−PSK Space Model Plane Model Topological Space Metric Space Pe(QAM) < Pe(PSK)
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1 2 3 4 5 6 7 1 2 3 4 5 1 2 3 4 5 6 7 1 2 3 4 5 Catenoid Trinoid
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Plane Model Space Model Edges identification
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ρ
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−6 −4 −2 2 4 6 8 10 12 10
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10 Pe S/N (dB) K=1 K=0 K=−1 K=−2
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10 Pe S/N (dB) 8−PSK K=0 16−PSK K=0 8−PSK K=−1 16−PSK K=−1
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2 4 6 8 10 12 14 16 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 M−PSK dK/d0 K=1 K=0 K=−1 K=−3
K1 K2 K3 x2 x1
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K
xm
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−5 −4 −3 −2 −1 1 10
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10 Pe 4−PSK 8−PSK Curvature (K)
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