Power Angular Spectrum Research Articles

Analytical Performance Evaluation of Full-Dimensional MIMO Systems Using Realistic Spatial Correlation Models

In this paper, we compute the analytical spatial channel correlation matrix in a polarized uniform planar array multiple-input multiple-output (MIMO) system. The antennas are considered with three-dimensional gain patterns. A realistic multiclustered propagation environment is considered. Earlier works in this area assumed arbitrary spatial clustering parameters, which do not adhere to practical situations. On the other hand, practical channel models provide methods for generating channel coefficients through simulation only. In this paper, cluster parameters from standard models such as the 3rd Generation Partnership Project (3GPP) WINNER II MIMO channel model for long term evolution (LTE)-Advanced and other proposed models for future 5G systems for sub-6 GHz and mmWave frequencies have been used to arrive at an analytical correlation coefficient expression. The spatial correlation has been shown to depend on the parameters of the cluster power angular spectrum (PAS). The analytical performance metrics such as bit error rate (BER) and spectral efficiency (SE) arrived using the correlation matrices are found to match closely with those obtained from the Monte Carlo simulations using the 3GPP channel models. We also show the difference in SE results obtained using the proposed model and a model based on an existing hypothetical PAS assumption whereby the usefulness of the proposed model for designing future 5G systems is reflected. Also, the analytical method developed here results in significant computation time reduction for calculation of different metrics such as BER and SE.

Channel Estimation for TDD/FDD Massive MIMO Systems With Channel Covariance Computing

In this paper, we propose a new channel estimation scheme for TDD/FDD massive MIMO systems by reconstructing (sometimes also referred to as covariance computing or covariance fitting) uplink/downlink channel covariance matrices (CCMs) with the aid of array signal processing techniques. Specifically, the angle parameters and power angular spectrum (PAS) of channel are extracted from the instantaneous uplink channel state information (CSI). Then, the uplink CCM is reconstructed and can be used to improve the uplink channel estimation without any additional training cost. By virtue of angle reciprocity as well as PAS reciprocity between uplink and downlink channels, the downlink CCM could also be inferred with a similar approach even for the FDD massive MIMO systems. Then, the downlink instantaneous CSI can be obtained by training toward the dominant eigen-directions of each user. The proposed strategy is applicable to various PAS distributions. Numerical results are provided to demonstrate the superiority of the proposed methods over the existing ones.

Measurements and Analysis of Angular Characteristics and Spatial Correlation for High-Speed Railway Channels

Spatial characteristics of the propagation channel have a vital impact on the application of multi-antenna techniques. This paper analyzes angular characteristics and the spatial correlation for high-speed railway (HSR) channels, based on a novel moving virtual antenna array (MVAA) measurement scheme. The principle of the MVAA scheme is deeply investigated and is further verified by a theoretical geometry-based stochastic model. Using the MVAA scheme, virtual single-input multiple-output (SIMO) channel impulse response data are derived from single-antenna measurements in typical HSR scenarios, involving viaduct, cutting, and station. Based on the SIMO channel data, angle of arrival is extracted according to the unitary estimation of signal parameters by the rotational invariance techniques algorithm, and is compared with the theoretical result. Moreover, power angular spectrum and root mean square (rms) angular spread (AS) are provided, and the rms AS results are statistically modeled and comprehensively compared. In addition, spatial correlation is calculated and analyzed, and a rms AS-dependent spatial correlation model is newly proposed to describe the relationship between the angular dispersion and the spatial correlation. The presented results could be used in multi-antenna channel modeling and will facilitate the assessment of multi-antenna technologies for future HSR mobile communication systems.

Indoor Propagation Channel Simulations at 60 GHz Using Point Cloud Data

Deterministic field prediction has been widely used to provide channel data for coverage analysis. Among these prediction tools, point cloud-based methods have been developed for millimeter-wave frequencies in order to characterize the environment with higher precision, but they have not taken into account all the necessary propagation mechanisms. In this paper, we present the implementation for predicting both specular reflections and diffraction as well as the total channel, including the aforementioned mechanisms along with scattering and shadowing. Both line-of-sight (LOS) and non-LOS channels are predicted and validated against measurements in a cafeteria. The result shows excellent agreement between prediction and measurement in terms of power delay profiles, power angular spectra, path loss, mean delay, delay spread, and azimuth spread.

Fast millimeter-wave beam training with receive beamforming

This paper proposes fast millimeter-wave (mm-wave) beam training protocols with receive beamforming. Both IEEE standards and the academic literature have generally considered beam training protocols involving exhaustive search over all possible beam directions for both the beamforming initiator and responded However, this operation requires a long time (and thus overhead) when the beamwidth is quite narrow such as for mm-wave beams (1° in the worst case). To alleviate this problem, we propose two types of adaptive beam training protocols for fixed and adaptive modulation, respectively, which take into account the unique propagation characteristics of millimeter waves. For fixed modulation, the proposed protocol allows for interactive beam training, stopping the search when a local maximum of the power angular spectrum is found that is sufficient to support the chosen modulation/coding scheme. We furthermore suggest approaches to prioritize certain directions determined from the propagation geometry, long-term statistics, etc. For adaptive modulation, the proposed protocol uses iterative multi-level beam training concepts for fast link configuration that provide an exhaustive search with significantly lower complexity. Our simulation results verify that the proposed protocol performs better than traditional exhaustive search in terms of the link configuration speed for mobile wireless service applications.

On the Covariance Matrix and Capacity Evaluation of Reconfigurable Antenna Array Systems

In this paper, we derive analytical expressions to compute the covariance matrix of the signals impinging on a reconfigurable antenna array. We consider a receiver equipped with a linear antenna array where each antenna element can be independently configured to create a directive radiation pattern toward a selected direction. In our derivation, we assume a multimodal truncated Laplacian distribution to model the power angular spectrum (PAS) of the signals arriving at the array. Using the derived expressions, we are able to evaluate the correlation between the received signals as a function of the signal spatial distribution, the antenna array topology, and the radiation pattern characteristics of each element in the array. We also study the capacity of a reconfigurable multiple-input multiple-output (RE-MIMO) system and illustrate its relation to radiation pattern configurations and characteristics. We demonstrate how the derived expressions can be used to efficiently choose the configuration for each reconfigurable antenna element in the array that leads to an optimal compromise between low receive correlation and high receive power in order to maximize the link capacity. Simulation results are provided to validate our analytical expressions.

Rician Channel Modeling for Multiprobe Anechoic Chamber Setups

This letter discusses over-the-air (OTA) testing for multiple-input–multiple-output (MIMO)-capable terminals, with emphasis on modeling Rician channel models in the multiprobe anechoic chamber setups. A technique to model Rician channels is proposed. The line-of-sight (LOS) component, within arbitrary polarization and an arbitrary impinging direction, and non-LOS (NLOS) component, with any impinging power angular spectrum (PAS), can be created. Simulation results show that the emulated Rician channels approximate the target models accurately in terms of field envelope distribution, $K$ -factor, Doppler spectrum, and spatial correlation at the receiver (Rx) side.

Estimating Discrete Power Angular Spectra in Multiprobe OTA Setups

The letter discusses over-the-air (OTA) testing for multiple-input-multiple-output (MIMO) capable terminals with emphasis on estimating discrete power angular spectrum modeled at the receiver (Rx) side in the test zone. Two techniques based on a uniform circular array (UCA) are proposed to obtain accurate direction-of-arrival estimates as well as power estimates of the impinging signals in the test zone. Simulation results match well with the target, as expected. Measurement results based on a virtual UCA in a practical 3-D multiprobe setup further support the simulation results. Possible reasons for the deviations between simulations and measurements are also investigated.

Closed-Form Evaluation of the MIMO Channel Spatial Covariance

The full spatial covariance matrix of the multiple-input multiple-output channel is an important quantity that is used in channel modeling, communication system signal processing, and performance analysis. This paper formulates a closed-form expression for this covariance matrix based on the average multipath propagation characteristics and the radiation patterns of the antennas in the transmit and receive arrays. Simplifications to the formulation are established for cases where the propagation can be represented using discrete plane waves or where the power angular spectrum can be modeled using clusters that satisfy uniform, truncated Gaussian, or truncated Laplacian distributions. Numerical studies demonstrate application of the formulation as well as its accuracy under different scenarios.

A Two-Dimensional Geometry-Based Stochastic Model

In this paper, the problem of deriving the power angular scattering response (PASR) resulting from a Gaussian scatterer distribution is undertaken. The scatter cluster can be located arbitrarily in the vicinity of the mobile unit. Furthermore, for the considered scatter geometry we derive both the angular and distance statistics at the observation point, allowing a theoretical characterization of the PASR. A major byproduct of this analysis is that the Gaussian scatterer hypothesis is formally shown to produce a Gaussian power angular spectrum in a macrocell environment, which is in accordance with existing measurements.

3D Polarized Channel Modeling and Performance Comparison of MIMO Antenna Configurations With Different Polarizations

We propose a three-dimensional (3D) polarized MIMO channel model, which takes into account 3D power angular spectrum and comprehensive propagation characteristics of electromagnetic waves excited by polarized antennas. Based on the model, we derive a close form expression of the spatial correlation as a function of the physical parameters representing both characteristics of arbitrary antennas and propagation environment in 3D space. The spatial correlation expression allows to use the Von Mises Fisher (VMF) distribution, resulting in a more accurate and general channel model. Through simulation, we evaluate and compare performance, in terms of the spatial correlation and capacity, of 2 × 2 MIMO configurations with different polarizations, i.e., V/V, V/H, and slanted ±45° polarizations, as a function of critical input parameters including elevation angle, antenna orientation, antenna spacing, cross-polarization discrimination (XPD), and signal-to-noise ratio (SNR). The effect of the parameters on the performance is analyzed, and verified in certain cases through the literature.

Near-Optimal Radiation Patterns for Antenna Diversity

A recent method has been proposed for determining the optimal radiation characteristics of antennas that maximize the diversity gain for a given antenna aperture and power angular spectrum of the incident field. However, because this approach results in antennas whose current distributions overlap in the aperture, it is difficult to achieve the radiation characteristics using practical designs. This paper proposes several methods that construct the near-optimal radiation characteristics assuming the apertures representing distinct antennas are disjoint. Computational results show that the average diversity performance achieved for these approximate radiation characteristics is roughly 1.3 dB below that achieved using the optimal patterns.

Physical modelling of multiple-input multiple-output antennas and channels by means of the spherical vector wave expansion

The authors propose a new physically motivated model that allows the study of the interaction between the antennas and the propagation channel for multiple-input multiple-output (MIMO) systems. The key tools employed in the model are the expansion coefficients of the electromagnetic field in spherical vector waves and the scattering matrix representation of the properties of the antenna. The authors derive the expansion of the MIMO channel matrix, H, in spherical vector wave modes of the electromagnetic field of the antennas as well as the propagation channel. The authors also introduce the channel scattering dyadic, , with a corresponding correlation model for co-polarised and cross-polarised elements and introduce the concept of mode-to-mode channel mapping, the M-matrix, between the receive and transmit antenna modes. The M-matrix maps the modes excited by the transmitting antenna to the modes exciting the receive antennas and vice versa. The covariance statistics of this M-matrix are expressed as a function of the double-directional power-angular spectrum (PAS) of co-polarised and cross-polarised components of the electromagnetic field. Their approach aims at gaining insights into the physics governing the interaction between antennas and channels and it is useful for studying the performance of different antenna designs in a specified propagation channel as well as for modelling the propagation channel. It can furthermore be used to quantify the optimal properties of antennas in a given propagation channel. The authors illustrate the developed methodology by analysing the interaction of a 2×2 system of slant polarised half-wavelength dipole antennas with some basic propagation channel models.

Optimal Antenna Radiation Characteristics for Diversity and MIMO Systems

This paper proposes a method for determining the antenna element radiation characteristics that maximize diversity gain given a specific power angular spectrum of the propagation environment. The method numerically constructs the eigenfunctions of the covariance operator for the scenario subject to constraints on the radiated power and allowable level of supergain. The discussion also focuses on how the resulting radiation characteristics approximately optimize average capacity for multiple-input multiple-output communications. Computational results reveal that optimal antenna characteristics can provide significantly more diversity gain than that offered by the characteristics of a simple design. An example computation using genetic algorithm optimization demonstrates that a numerically optimized practical design can be designed whose performance is relatively close to that of the optimal array.

Measurement-based statistical model and simulation of mobile station anisotropic power angular spectrum

A statistical channel model of mobile station (MS) anisotropic power azimuth spectrum (PAS) is presented. This model is based on extensive outdoor urban/suburban channel measurements, and it uses the Von Mises (VM) function. We propose a method to generate the VM model parameters from the direction spread (DS) knowledge. Combined with a random generation of DS, we obtain a statistical PAS simulation.

Double characterisations of power angular spectrum in macro-cell environment

A propagation experiment using a uniform linear array at the base station in rural and suburban areas is presented. Wideband parameters, cluster behaviour and angular parameters at the base and mobile stations are analysed. Statistical results are provided and typical situations presented.