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

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    Type
    Article
    Authors
    Nadeem, Qurrat-Ul-Ain cc
    Kammoun, Abla cc
    Debbah, Merouane
    Alouini, Mohamed-Slim cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2015-05-07
    Online Publication Date
    2015-05-07
    Print Publication Date
    2015-07
    Permanent link to this record
    http://hdl.handle.net/10754/552782
    
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    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.
    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
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Signal Processing
    DOI
    10.1109/TSP.2015.2430841
    arXiv
    1504.05455
    Additional Links
    http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7103347
    ae974a485f413a2113503eed53cd6c53
    10.1109/TSP.2015.2430841
    Scopus Count
    Collections
    Articles; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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