Spatial correlation in 3D MIMO channels using fourier coefficients of power spectrums

Qurrat-Ul-Ain Nadeem (1) , Abla Kammoun (1) , Mérouane Debbah (2, 3) , Mohamed-Slim Alouini (1)

1 KAUST - King Abdullah University of Science and Technology [Saudi Arabia]
2 LANEAS - Large Networks and Systems Group
3 Mathematical and Algorithmic Sciences Lab [Paris]

In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for the standardized three-dimensional (3D) multiple-input multiple-output (MIMO) channel. This novel SCF is developed for a uniform linear array of antennas with non-isotropic 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 to obtain a closed-form expression for the SCF for arbitrary angular distributions and antenna patterns. The resulting expression depends on the underlying 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. Numerical results validate the proposed analytical expression and study the impact of angular spreads on the correlation. The derived SCF will help evaluate the performance of correlated 3D MIMO channels in the future.

Domaines: Mathématiques [math]; Statistiques [stat]; Sciences de l'ingénieur [physics]

Qurrat-Ul-Ain Nadeem, Abla Kammoun, Mérouane Debbah, Mohamed-Slim Alouini. Spatial correlation in 3D MIMO channels using fourier coefficients of power spectrums. IEEE wireless communications and networking conference (WCNC), Mar 2015, New Orleans, United States. ⟨10.1109/WCNC.2015.7127463⟩. ⟨hal-01242490⟩