Qurrat-Ul-Ain Nadeem

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

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 channels 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. 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 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 behavior 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.

3D Massive MIMO Systems: Modeling and Performance Analysis

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 channels 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 signal-to-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.

Design of 5G Full Dimension Massive MIMO Systems

This paper discusses full-dimension multiple-input-multiple-output (FD-MIMO) technology, which is currently an active area of research and standardization in wireless communications for evolution toward Fifth Generation (5G) cellular systems. FD-MIMO utilizes an active antenna system (AAS) with a 2-D planar array structure that not only allows a large number of antenna elements to be packed within feasible base station form factors, but also provides the ability of adaptive electronic beamforming in the 3-D space. However, the compact structure of large-scale planar arrays drastically increases the spatial correlation in FD-MIMO systems. In order to account for its effects, the generalized spatial correlation functions for channels constituted by individual elements and overall antenna ports in the AAS are derived. Exploiting the quasi-static channel covariance matrices of users, the problem of determining the optimal downtilt weight vector for antenna ports, which maximizes the minimum signal-to-interference ratio of a multi-user multiple-input-single-output system, is formulated as a fractional optimization problem. A quasi-optimal solution is obtained through the application of semi-definite relaxation and Dinkelbach’s method. Finally, the user-group specific elevation beamforming scenario is devised, which offers significant performance gains as confirmed through simulations. These results have direct application in the analysis of 5G FD-MIMO systems.

Performance Analysis of Compact FD-MIMO Antenna Arrays in a Correlated Environment

Full dimension multiple-input-multiple-output (FD-MIMO) is one of the key technologies proposed in the third Generation Partnership Project (3GPP) for the fifth generation communication systems. The reason can be attributed to its ability to yield significant performance gains through the deployment of active antenna elements at the base station in the vertical as well as the conventional horizontal directions, enabling several elevation beamforming strategies. The resulting improvement in spectral efficiency largely depends on the orthogonality of the sub-channels constituting the FD-MIMO system. Accommodating a large number of antenna elements with sufficient spacing poses several constraints for practical implementation, making it imperative to consider compact antenna arrangements that minimize the overall channel correlation. Two such configurations considered in this paper are the uniform linear array (ULA) and the uniform circular array (UCA) of antenna ports, where each port is mapped to a group of physical antenna elements arranged in the vertical direction. The generalized analytical expression for the spatial correlation function (SCF) for the UCA is derived, exploiting results on spherical harmonics and Legendre polynomials. The mutual coupling between antenna dipoles is accounted for and the resulting SCF is also presented. The second part of this paper compares the spatial correlation and mutual information (MI) performance of the ULA and UCA configurations in the 3GPP 3-D urban-macro and urban-micro cell scenarios, utilizing results from random matrix theory on the deterministic equivalent of the MI for the Kronecker channel model. Simulation results study the performance patterns of the two arrays as a function of several channel and array parameters and identify applications and environments suitable for the deployment of each array.

Spatial correlation characterization of a uniform circular array in 3D MIMO systems

In this paper, we consider a uniform circular array (UCA) of directional antennas at the base station (BS) and the mobile station (MS) and derive an exact closed-form expression for the spatial correlation present in the 3D multiple-input multiple-output (MIMO) channel constituted by these arrays. The underlying method leverages the mathematical convenience of the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials. In contrast to the existing results, this generalized closed-form expression is independent of the form of the underlying angular distributions and antenna patterns. Moreover, the incorporation of the elevation dimension into the antenna pattern and channel model renders the proposed expression extremely useful for the performance evaluation of 3D MIMO systems in the future. Verification is achieved with the help of simulation results, which highlight the dependence of the spatial correlation on channel and array parameters. An interesting interplay between the mean angle of departure (AoD), angular spread and the positioning of antennas in the array is demonstrated.

Spatial Correlation Characterization of a Full Dimension Massive MIMO System

Elevation beamforming and Full Dimension MIMO (FD-MIMO) are currently active areas of research and standardization in 3GPP LTE-Advanced. FD-MIMO utilizes an active antenna array system (AAS), that provides the ability of adaptive electronic beam control over the elevation dimension, resulting in a better system performance as compared to the conventional 2D MIMO systems. FD-MIMO is more advantageous when amalgamated with massive MIMO systems, in that it exploits the additional degrees of freedom offered by a large number of antennas in the elevation. To facilitate the evaluation of these systems, a large effort in 3D channel modeling is needed. This paper aims at providing a summary of the recent 3GPP activity around 3D channel modeling. The 3GPP proposed approach to model antenna radiation pattern is compared with the ITU approach. A closed-form expression is then worked out for the spatial correlation function (SCF) for channels constituted by individual antenna elements in the array by exploiting results on spherical harmonics and Legendre polynomials. The proposed expression can be used to obtain correlation coefficients for any arbitrary 3D propagation environment. Simulation results corroborate and study the derived spatial correlation expression. The results are directly applicable to the analysis of future 5G 3D massive MIMO systems.

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

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.

On the mutual information of 3D massive MIMO systems: An asymptotic approach

Motivated by the recent interest in 3D beamforming to enhance system performance, we present an information-theoretic channel model for multiple-input multiple-output (MIMO) systems, that can support the elevation dimension. The principle of maximum entropy is used to determine the distribution of the channel matrix consistent with the prior angular information. We provide an explicit expression for the cumulative density function (CDF) of the mutual information in the large number of transmit antennas and paths regime. The derived Gaussian approximation is quite accurate even for realistic system dimensions. The simulation results study the achievable performance through the meticulous selection of the transmit antenna downtilt angles. The results are directly applicable to the analysis of 5G 3D massive MIMO systems.