On the connection between noncircularly-symmetric and noncentral fading models: univariate and multivariate analysis

• Autores: Laureano Moreno Pozas
• Directores de la Tesis: Eduardo Martos Naya (dir. tes.), Francisco Javier López Martínez (dir. tes.)
• Lectura: En la Universidad de Málaga ( España ) en 2017
• Idioma: español
• Tribunal Calificador de la Tesis: Marco Chiani (presid.), Juan Manuel Romero Jerez (secret.), Mohamed-Slim Alouini (voc.)
• Programa de doctorado: Programa de Doctorado en Ingeniería de Telecomunicación por la Universidad de Málaga
• Materias:
  • Matemáticas
    • Álgebra
      • Teoría de matrices
    • Probabilidad
      • Procesos estocásticos
• Enlaces
  • Tesis en acceso abierto en: RIUMA
• Resumen

  • This thesis provides new statistical connections between noncircularly-symmetric central and circularly-symmetric noncentral underlying complex Gaussian models. This is particularly interesting since it facilitates the analysis of noncircularly-symmetric models, which are often underused despite their practical interest, since their analysis is more challenging.

    Although these statistical connections have a wide range of applications in different areas of univariate and multivariate analysis, this thesis is framed in the context of wireless communications, to jointly analyze noncentral and noncircularly-symmetric fading models. We provide an unified framework for the five classical univariate fading models, i.e. the one-sided Gaussian, Rayleigh, Nakagami-m, Nakagami-q and Rician, and their most popular generalizations, i.e the Rician shadowed, η-µ, κ-µ and κ-µ shadowed. Moreover, we present new simple results regarding the ergodic capacity of single-input single-output systems subject to κ-µ shadowed, κ-µ and η-µ fadings.

    With applications to multiple-input multiple-output communications, we are interested in matrices of the form W=XX^H (or W=X^H X), where X is a complex Gaussian matrix with unequal variance in the real and imaginary parts of its entries, i.e., X belongs to the noncircularly-symmetric Gaussian subclass. By establishing a novel connection with the well-known complex Wishart ensemble, we facilitate the statistical analysis of W and give new insights on the effects of such asymmetric variance profile.