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 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.Comment: Accepted in IEEE Transactions on signal processin

Radiation pattern analysis of antenna systems for MIMO and diversity configurations

Multiple-input multiple-output (MIMO) antenna systems and antenna configurations for wideband multimode diversity rank among the emerging key technologies in next generation wireless communication systems. The analysis of such transmission systems usually neglects the influences of real antenna radiation characteristics as well as the influences of mutual coupling in a multielement antenna arrangement. Nevertheless, to achieve a detailed description of diversity gain and channel capacity by using several transmit-and receive antennas in a wireless link, it is essential to take all those effects into account. The expansion of the radiation fields in terms of spherical eigenmodes allows an analytical description of the antenna radiation characteristics and accounts for all the coupling effects in multielement antenna configurations. Therefore the radiation pattern analysis by spherical eigenmode expansion provides an efficient alternative to establish an analytical approach in the calculation of envelope correlation or channel capacity. © 2005 Copernicus GmbH

Computation of antenna pattern correlation and MIMO performance by means of surface current distribution and spherical wave theory

In order to satisfy the stringent demand for an accurate prediction of MIMO channel capacity and diversity performance in wireless communications, more effective and suitable models that account for real antenna radiation behavior have to be taken into account. One of the main challenges is the accurate modeling of antenna correlation that is directly related to the amount of channel capacity or diversity gain which might be achieved in multi element antenna configurations. Therefore spherical wave theory in electromagnetics is a well known technique to express antenna far fields by means of a compact field expansion with a reduced number of unknowns that was recently applied to derive an analytical approach in the computation of antenna pattern correlation. In this paper we present a novel and efficient computational technique to determine antenna pattern correlation based on the evaluation of the surface current distribution by means of a spherical mode expansion

Spherical mode analysis of planar frequency-independent multi-arm antennas based on its surface current distribution

Deployment in the design of mobile radio terminals focuses on the implementation of multiradio transmission systems, using a multiplicity of different radio standards combined with high-speed data communication over multiple-input multiple-output (MIMO) and multimode diversity techniques. Hence, planar log.-per. four-arm antennas are predistined to meet the requirements of future mobile multiradio RF-frontends and will be introduced and analysed in terms of an efficient spherical mode analysis by means of surface current distribution in order to derive an analytic access to MIMO- and polarisation-diversity performance computation. A remarkable parameter reduction and a faster numerical analysis with respect to conventional techniques may be achieved. The sources in the near-field antenna region are based on the numerical computation of surface currents involving the finite element method (FEM). Relations between the variations of the geometrical antenna parameters and the excitation of discrete spherical modes are presented and will be analysed in detail

Maximum Gain, Effective Area, and Directivity

Fundamental bounds on antenna gain are found via convex optimization of the current density in a prescribed region. Various constraints are considered, including self-resonance and only partial control of the current distribution. Derived formulas are valid for arbitrarily shaped radiators of a given conductivity. All the optimization tasks are reduced to eigenvalue problems, which are solved efficiently. The second part of the paper deals with superdirectivity and its associated minimal costs in efficiency and Q-factor. The paper is accompanied with a series of examples practically demonstrating the relevance of the theoretical framework and entirely spanning wide range of material parameters and electrical sizes used in antenna technology. Presented results are analyzed from a perspective of effectively radiating modes. In contrast to a common approach utilizing spherical modes, the radiating modes of a given body are directly evaluated and analyzed here. All crucial mathematical steps are reviewed in the appendices, including a series of important subroutines to be considered making it possible to reduce the computational burden associated with the evaluation of electrically large structures and structures of high conductivity.Comment: 12 pages, 15 figures, submitted to TA

3D spatial fading correlation for uniform angle of arrival distribution

We derive a closed-form expression for the spatial fading correlation (SFC) between two arbitrary points in 3D-space for the uniform limited azimuth-elevation angle of arrival probability density function (pdf). This expression simplifies the computatio

Spatially-Stationary Model for Holographic MIMO Small-Scale Fading

Imagine an array with a massive (possibly uncountably infinite) number of antennas in a compact space. We refer to a system of this sort as Holographic MIMO. Given the impressive properties of Massive MIMO, one might expect a holographic array to realize extreme spatial resolution, incredible energy efficiency, and unprecedented spectral efficiency. At present, however, its fundamental limits have not been conclusively established. A major challenge for the analysis and understanding of such a paradigm shift is the lack of mathematically tractable and numerically reproducible channel models that retain some semblance to the physical reality. Detailed physical models are, in general, too complex for tractable analysis. This paper aims to take a closer look at this interdisciplinary challenge. Particularly, we consider the small-scale fading in the far-field, and we model it as a zero-mean, spatially-stationary, and correlated Gaussian scalar random field. A physically-meaningful correlation is obtained by requiring that the random field be consistent with the scalar Helmholtz equation. This formulation leads directly to a rather simple and exact description of the three-dimensional small-scale fading as a Fourier plane-wave spectral representation. Suitably discretized, this yields a discrete representation for the field as a Fourier plane-wave series expansion, from which a computationally efficient way to generate samples of the small-scale fading over spatially-constrained compact spaces is developed. The connections with the conventional tools of linear systems theory and Fourier transform are thoroughly discussed

Integral Identities for Passive Systems and Spherical Waves in Scattering and Antenna Problems

Sum rules and physical limitations within electromagnetic theory and antenna theory have received significant attention in the last few years. However, the derivations are often relying on application specific and sometimes unsupported assumptions, and therefore a mathematically rigorous and generally applicable approach seems timely. Such an approach is presented in this thesis, along with examples and all the necessary proofs. The approach is also applied in the thesis to derive sum rules and physical limitations on electromagnetic spherical wave scattering. This has not been done before, despite the widespread use of spherical wave decompositions. For example, spherical waves and the antenna scattering matrix provide a complete and compact description of all the important properties of an antenna, are crucial parts in spherical near-field antenna measurements, and have been used recently to model antenna-channel interaction and multiple-input multiple-output (MIMO) communication systems. This thesis is also the first to present a method to estimate spherical wave coefficients from propagation channel measurements. The results of this thesis can roughly be divided into three categories: Firstly, a general approach to derive sum rules and physical limitations on input-output systems based on the assumptions of causality and passivity is presented (Paper I). Secondly, sum rules and physical limitations on the scattering and matching of electromagnetic spherical waves are derived, and the implications for antennas are explored (Papers II-IV). Thirdly, a method to estimate spherical wave coefficients from channel measurements, and the results of a measurement campaign, are presented and analysed (Paper V). The thesis consists of a General Introduction and five appended papers