Signal Constellations with Algebraic Properties and their Application in Spatial Modulation Transmission Schemes (Schriftenreihe der Institute für Systemdynamik (ISD) und optische Systeme (IOS))

Nowadays, most digital modulation schemes are based on conventional signal constellations that have no algebraic group, ring, or field properties, e.g. square quadrature-amplitude modulation constellations. Signal constellations with algebraic structure can enhance the system performance. For instance, multidimensional signal constellations based on dense lattices can achieve performance gains due to the dense packing. The algebraic structure enables low-complexity decoding and detection schemes. In this work, signal constellations with algebraic properties and their application in spatial modulation transmission schemes are investigated. Several design approaches of two- and four-dimensional signal constellations based on Gaussian, Eisenstein, and Hurwitz integers are shown. Detection algorithms with reduced complexity are proposed. It is shown, that the proposed Eisenstein and Hurwitz constellations combined with the proposed suboptimal detection can outperform conventional two-dimensional constellations with ML detection. Acknowledgments 6 Abstract 7 Contents 8 Notation 10 Abbreviations 10 System Parameters 11 Number Sets and Symbols 11 Math Operators and Operations 12 1 Introduction 14 2 Channel Models and Transmission Scenarios 18 2.1 Channel Models 18 2.1.1 AWGN Channel 18 2.1.2 Rayleigh Fading Channel 20 2.2 The Fundamental Concept of Spatial Modulation 21 2.2.1 Spatial Modulation 22 2.2.2 Generalized Spatial Modulation 23 2.2.3 Generalized Multistream Spatial Modulation 24 2.2.4 Spatial Permutation Modulation 26 3 Signal Constellations with Algebraic Properties 30 3.1 Two-Dimensional Signal Constellations 31 3.1.1 Codes over Gaussian and Eisenstein Integers 31 3.1.2 Decoding of OMEC Codes for the AWGN Channel 35 3.1.3 Product Codes Based on OMEC Codes 39 3.1.4 LDPC Codes based on OMEC Codes 41 3.2 Four-Dimensional Signal Constellations 45 3.2.1 Quaternions and the Subset of Lipschitz and Hurwitz Integers 47 3.2.2 Construction of Finite Sets 51 3.2.3 CFM Comparison and ML Performance 53 3.2.4 Suboptimal Signal Detection 59 3.2.5 Set Partitioning 64 3.2.6 Multilevel Coding 67 3.3 Discussion 71 4 Spatial Modulation with Two-Dimensional Signal Constellations 73 4.1 Spatial Modulation 74 4.1.1 Known Detection Methods 74 4.1.2 Modified Gaussian Approximation Method 77 4.1.3 Computational Complexity Analysis 78 4.1.4 Signal Constellation Design 80 4.1.5 Simulation Results 81 4.2 Space-Time Block-Coded Spatial Permutation Modulation 82 4.2.1 Space-Time Block-Code Construction 84 4.2.2 ML Detection 86 4.2.3 Simulation Results 87 4.3 Discussion 89 5 Spatial Modulation with Multidimensional Signal Constellations 91 5.1 Generalized Suboptimal Detection 91 5.1.1 MGAM for GMSM 92 5.1.2 Detection of the Signal Points 93 5.1.3 Computational Complexity Analysis 95 5.1.4 Simulation Results 96 5.2 Hurwitz-Integer Signal Constellations for GMSM 98 5.2.1 Construction of Finite Sets 99 5.2.2 Suboptimal Symbol Detection with Hurwitz-Based Signal Sets 101 5.2.3 Computational Complexity Analysis 103 5.2.4 Simulation Results 106 5.3 OMEC Code Based GMSM Transmission 107 5.3.1 Decoding and Detection 107 5.3.2 Simulation Results 109 5.4 Discussion 110 6 Conclusions 113 A Bibliography 115