Copula-Based Modeling of RIS-Assisted Communications: Outage Probability Analysis

Statistical characterization of the signal-to-noise ratio (SNR) of reconfigurable intelligent surface (RIS)-assisted communications in the presence of phase noise is an important open issue. In this letter, we exploit the concept of copula modeling to capture the non-standard dependence features that appear due to the presence of discrete phase noise. In particular, we consider the outage probability of RIS systems in Rayleigh fading channels and provide joint distributions to characterize the dependencies due to the use of finite resolution phase shifters at the RIS. Numerical assessments confirm the validity of closedform expressions of the outage probability and motivate the use of bivariate copula for further RIS studies.

[1]  Xuanli Wu,et al.  STAR-RIS Aided NOMA in Multi-Cell Networks: A General Analytical Framework with Gamma Distributed Channel Modeling , 2021, ArXiv.

[2]  Fabrizio Durante,et al.  Copula Theory and Its Applications , 2010 .

[3]  Qingqing Wu,et al.  Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface With Discrete Phase Shifts , 2019, IEEE Transactions on Communications.

[4]  Wei-Ping Zhu,et al.  Performance Evaluation and Diversity Analysis of RIS-Assisted Communications Over Generalized Fading Channels in the Presence of Phase Noise , 2020, IEEE Open Journal of the Communications Society.

[5]  Kezhi Wang,et al.  Uplink Achievable Rate of Intelligent Reflecting Surface-Aided Millimeter-Wave Communications with Low-Resolution ADC and Phase Noise , 2020 .

[6]  A. M. Mathai,et al.  The H-Function: Theory and Applications , 2009 .

[7]  Thomas de Quincey.  [C] , 2000, The Works of Thomas De Quincey, Vol. 1: Writings, 1799–1820.

[8]  P. Alam.  ‘N’ , 2021, Composites Engineering: An A–Z Guide.

[9]  Mohamed-Slim Alouini,et al.  Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise , 2020, IEEE Wireless Communications Letters.

[10]  Ghosheh Abed Hodtani,et al.  Copula-Based Analysis of Physical Layer Security Performances Over Correlated Rayleigh Fading Channels , 2021, IEEE Transactions on Information Forensics and Security.

[11]  Qingqing Wu,et al.  Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming , 2018, IEEE Transactions on Wireless Communications.

[12]  Justin P. Coon,et al.  Communication Through a Large Reflecting Surface With Phase Errors , 2019, IEEE Wireless Communications Letters.

[13]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[14]  Mohamed-Slim Alouini,et al.  Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How it Works, State of Research, and Road Ahead , 2020, ArXiv.

[15]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[16]  Justin P. Coon,et al.  Study of Intelligent Reflective Surface Assisted Communications with One-bit Phase Adjustments , 2020, GLOBECOM 2020 - 2020 IEEE Global Communications Conference.

[17]  A. Kilbas.  H-Transforms: Theory and Applications , 2004 .

[18]  Zhijin Qin,et al.  Reconfigurable Intelligent Surfaces: Principles and Opportunities , 2020, IEEE Communications Surveys and Tutorials.

[19]  Satishs Iyengar,et al.  Multivariate Models and Dependence Concepts , 1998 .

[20]  Wessam Ajib,et al.  Bit Error Rate Analysis for Reconfigurable Intelligent Surfaces with Phase Errors , 2021, ArXiv.

[21]  M. Haugh,et al.  An Introduction to Copulas , 2016 .