Spatial Correlation for DoA Characterization Using Von Mises, Cosine, and Gaussian Distributions

IEEE Trans. Signal Process.

et al. 2015

International audiencePrevious 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 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 MI for the Kronecker model are utilized in both mono-user and multiuser cases. Numerical results validate the proposed analytical expressions and elucidate the dependence of 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

Section: Introductionmentioning

confidence: 99%

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

IEEE Trans. Signal Process.

et al. 2015

“…where θ 0 is the mean AoD/AoA and σ is the angular spread in the elevation [40]. The characteristics of the azimuth angles are well captured by Wrapped Gaussian (WG) density spectrum [30], [41] which can be approximated quite accurately by the Von Mises (VM) distribution [42], [43] given by,…”

Section: Numerical Resultsmentioning

confidence: 99%

3D Massive MIMO Systems: Modeling and Performance Analysis

IEEE Trans. Wireless Commun.

et al. 2015

Multiple-input-multiple-output (MIMO) systems of current LTE releases are capable of adaptation in the azimuth only. Recently, the trend is to enhance system performance by exploiting the channel's degrees of freedom in the elevation, which necessitates the characterization of 3D channels. We present an information-theoretic channel model for MIMO systems that supports the elevation dimension. The model is based on the principle of maximum entropy, which enables us to determine the distribution of the channel matrix consistent with the prior information on the angles. Based on this model, we provide analytical expression for the cumulative density function (CDF) of the mutual information (MI) for systems with a single receive and finite number of transmit antennas in the general signalto-interference-plus-noise-ratio (SINR) regime. The result is extended to systems with finite receive antennas in the low SINR regime. A Gaussian approximation to the asymptotic behavior of MI distribution is derived for the large number of transmit antennas and paths regime. We corroborate our analysis with simulations that study the performance gains realizable through meticulous selection of the transmit antenna downtilt angles, confirming the potential of elevation beamforming to enhance system performance. The results are directly applicable to the analysis of 5G 3D-Massive MIMO-systems.

“…In the standards, elevation AoD and AoA are drawn from Laplacian density spectrum with parameters, mean θ 0 and spread σ [10], [18]. Also azimuth AoD and AOA are drawn from the Wrapped Gaussian (WG) density spectrum [11], [10], that can be approximated by Von Mises (VM) distribution [19], [6] as follows,…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The proposed method makes small angle spread approximation and offers significant gains in terms of computational cost. In [6], the authors derived exact closed-form expressions for the spatial correlation between receive antenna elements for cosine, Gaussian and Von Mises azimuth AoA distributions. The use of Von Mises was shown to simplify the expressions and the impact of mutual coupling on correlation was studied.…”

Section: Introductionmentioning

confidence: 99%

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

2015 IEEE Wireless Communications and Networking Conference (WCNC)

et al. 2015

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.