A Generalized Spatial Correlation Model for 3D MIMO Channels based on the Fourier Coefficients of Power Spectrums

Handle URI:
http://hdl.handle.net/10754/552782
Title:
A Generalized Spatial Correlation Model for 3D MIMO Channels based on the Fourier Coefficients of Power Spectrums
Authors:
Nadeem, Qurrat-Ul-Ain ( 0000-0001-8423-3482 ) ; Kammoun, Abla ( 0000-0002-0195-3159 ) ; Debbah, Merouane; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 )
Abstract:
Previous studies have confirmed the adverse impact of fading correlation on the mutual information (MI) of two-dimensional (2D) multiple-input multiple-output (MIMO) systems. More recently, the trend is to enhance the system performance by exploiting the channel’s degrees of freedom in the elevation, which necessitates the derivation and characterization of three-dimensional (3D) channels in the presence of spatial correlation. In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for 3D MIMO channels. This novel SCF is developed for a uniform linear array of antennas with nonisotropic antenna patterns. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials. The resulting expression depends on the underlying arbitrary angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty of the proposed method lies in the SCF being valid for any 3D propagation environment. The developed SCF determines the covariance matrices at the transmitter and the receiver that form the Kronecker channel model. In order to quantify the effects of correlation on the system performance, the information-theoretic deterministic equivalents of the MI for the Kronecker model are utilized in both mono-user and multi-user cases. Numerical results validate the proposed analytical expressions and elucidate the dependence of the system performance on azimuth and elevation angular spreads and antenna patterns. Some useful insights into the behaviour of MI as a function of downtilt angles are provided. The derived model will help evaluate the performance of correlated 3D MIMO channels in the future.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
A Generalized Spatial Correlation Model for 3D MIMO Channels based on the Fourier Coefficients of Power Spectrums 2015:1 IEEE Transactions on Signal Processing
Journal:
IEEE Transactions on Signal Processing
Issue Date:
7-May-2015
DOI:
10.1109/TSP.2015.2430841
Type:
Article
ISSN:
1053-587X; 1941-0476
Additional Links:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7103347
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorNadeem, Qurrat-Ul-Ainen
dc.contributor.authorKammoun, Ablaen
dc.contributor.authorDebbah, Merouaneen
dc.contributor.authorAlouini, Mohamed-Slimen
dc.date.accessioned2015-05-14T07:14:36Zen
dc.date.available2015-05-14T07:14:36Zen
dc.date.issued2015-05-07en
dc.identifier.citationA Generalized Spatial Correlation Model for 3D MIMO Channels based on the Fourier Coefficients of Power Spectrums 2015:1 IEEE Transactions on Signal Processingen
dc.identifier.issn1053-587Xen
dc.identifier.issn1941-0476en
dc.identifier.doi10.1109/TSP.2015.2430841en
dc.identifier.urihttp://hdl.handle.net/10754/552782en
dc.description.abstractPrevious studies have confirmed the adverse impact of fading correlation on the mutual information (MI) of two-dimensional (2D) multiple-input multiple-output (MIMO) systems. More recently, the trend is to enhance the system performance by exploiting the channel’s degrees of freedom in the elevation, which necessitates the derivation and characterization of three-dimensional (3D) channels in the presence of spatial correlation. In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for 3D MIMO channels. This novel SCF is developed for a uniform linear array of antennas with nonisotropic antenna patterns. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials. The resulting expression depends on the underlying arbitrary angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty of the proposed method lies in the SCF being valid for any 3D propagation environment. The developed SCF determines the covariance matrices at the transmitter and the receiver that form the Kronecker channel model. In order to quantify the effects of correlation on the system performance, the information-theoretic deterministic equivalents of the MI for the Kronecker model are utilized in both mono-user and multi-user cases. Numerical results validate the proposed analytical expressions and elucidate the dependence of the system performance on azimuth and elevation angular spreads and antenna patterns. Some useful insights into the behaviour of MI as a function of downtilt angles are provided. The derived model will help evaluate the performance of correlated 3D MIMO channels in the future.en
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7103347en
dc.rights(c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.en
dc.subject3D multiple-input multiple-output (MIMO) systemsen
dc.subjectelevation beamformingen
dc.subjectmutual informationen
dc.subjectpower azimuth spectrumen
dc.subjectpower elevation spectrumen
dc.subjectspatial correlationen
dc.titleA Generalized Spatial Correlation Model for 3D MIMO Channels based on the Fourier Coefficients of Power Spectrumsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalIEEE Transactions on Signal Processingen
dc.eprint.versionPost-printen
dc.contributor.institutionSupélec, Gif-sur-Yvette, France and Mathematical and Algorithmic Sciences Lab, Huawei France R&D, Paris, Franceen
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