An Improved Simulator for the Correlation-Based MIMO Channel in Multiple Cluster Scattering Environments

An improved MIMO radio channel simulator is proposed, based on the most popular correlation-based MIMO channel model called Kronecker model and the sum-of-sinusoids (SoS) method which is widely used to generate Rayleigh fading waveforms with temporal correlation. Firstly, a simplified simulation model for generating multiple independent Rayleigh fading waveforms is presented, which employs only one random variable to set all Doppler frequency components in all waveforms. Next, a fast spatial correlation calculation technique, in a closed-form expression implemented by the Fourier Transform both for outdoor and indoor multiple cluster scattering environments, is introduced, which accurately reproduces the desired spatial correlation properties and indicates a direct dependence between spatial correlation and channel physical parameters. The ergodic and outage capacity of the simulated channel are also evaluated with respect to different azimuth of arrival and azimuth of departure (AoA/AoD) under the condition of 3GPP SCM (3rd Generation Partnership Project Spatial channel model) [23]. The presented simulator is therefore suitable for the theoretical analysis of MIMO radio systems, including dynamic system simulation.     

互耦效应对四元方阵天线阵列信道容量的影响

针对目前广泛研究的直线型排布阵列在来波平均到达角较大时信道容量会急剧下降的事实,提出并重点研究一种具空域对称结构的正方形排列四元天线阵列模型。在首先基于天线理论导出阵元耦合阻抗表达式的基础上,详细分析了引入阵列互耦效应后,阵元接收信号空域相关性及多输入多输出（MIMO）信道容量可能会受到的影响,并在来波角谱均匀分布情形下与传统四元直线阵的容量性能作仿真对比。理论分析和计算机数值仿真皆表明：由于空间对称的阵列排布结构导致四元方阵阵元间具有良好的互补性,因此,这种方阵阵列模型具有非常稳定的信道容量,更适合在实际通信环境中使用。     

Diversity‐multiplexing tradeoff over correlated Rayleigh fading channels: a non‐asymptotic analysis

In this paper, we present a finite‐signal‐to‐noise ratio (finite‐SNR) framework to establish tight bounds on the diversity‐multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity‐multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite‐SNR estimates of the diversity‐multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity‐multiplexing tradeoff at finite‐SNR. As expected, the diversity‐multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency of R bps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gain r is greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation. Copyright © 2009 John Wiley & Sons, Ltd.     

Transmit signal design for optimal estimation of correlated MIMO channels

We address optimal estimation of correlated multiple-input multiple-output (MIMO) channels using pilot signals, assuming knowledge of the second-order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the recently proposed virtual channel representation, which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in the correlated channel. However, our design framework is applicable to more general channel models, which include known channel models, such as the transmit and receive correlated model, as special cases. We show that optimal signaling is in a block form, where the block length depends on the signal-to-noise ratio (SNR) as well as the channel correlation matrix. The block signal corresponds to transmitting beams in successive symbol intervals along fixed virtual transmit angles, whose powers are determined by (nonidentical) water filling solutions based on the optimization criteria. Our analysis shows that these water filling solutions identify exactly which virtual transmit angles are important for channel estimation. In particular, at low SNR, the block length reduces to one, and all the power is transmitted on the beam corresponding to the strongest transmit angle, whereas at high SNR, the block length has a maximum length equal to the number of active virtual transmit angles, and the power is assigned equally to all active transmit angles. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

Adaptive MIMO Transmission for Exploiting the Capacity of Spatially Correlated Channels

We consider a novel low-complexity adaptive multiple-input multiple-output (MIMO) transmission technique. The approach is based on switching between low-complexity transmission schemes, including statistical beamforming, double space-time transmit diversity, and spatial multiplexing, depending on the changing channel statistics, as a practical means of approaching the spatially correlated MIMO channel capacity. We first derive new ergodic capacity expressions for each MIMO transmission scheme in spatially correlated channels. Based on these results, we demonstrate that adaptive switching between MIMO schemes yields significant capacity gains over fixed transmission schemes. We also derive accurate analytical approximations for the optimal signal-to-noise-ratio switching thresholds, which correspond to the crossing-points of the capacity curves. These thresholds are shown to vary, depending on the spatial correlation, and are used to identify key switching parameters. Finally, we propose a practical switching algorithm that is shown to yield significant spectral efficiency improvements over nonadaptive schemes for typical channel scenarios     

MIMO系统在空时二维相关莱斯快衰落信道下的性能

与准静态独立的瑞利衰落信道模型相比较,在MIMO(Multi-Input Multi-Output)系统中,实际信道更趋向于空时相关莱斯快衰落。考虑到MIMO系统的收发分集优势以及收发两端天线阵列的空时相关性,在简单论述了MIMO系统和信道模型的基础上,该文利用多变量统计学理论,推导出MIMO系统在空时相关莱斯快衰落信道下平均成对差错概率上界的闭合表达式,并探讨了信道特性对系统性能的影响,然后给出相应仿真结果。     

Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole

The capacity of multiple-input multiple-output (MIMO) wireless channels is limited by both the spatial fading correlation and rank deficiency of the channel. While spatial fading correlation reduces the diversity gains, rank deficiency due to double scattering or keyhole effects decreases the spatial multiplexing gains of multiple-antenna channels. In this paper, taking into account realistic propagation environments in the presence of spatial fading correlation, double scattering, and keyhole effects, we analyze the ergodic (or mean) MIMO capacity for an arbitrary finite number of transmit and receive antennas. We assume that the channel is unknown at the transmitter and perfectly known at the receiver so that equal power is allocated to each of the transmit antennas. Using some statistical properties of complex random matrices such as Gaussian matrices, Wishart (1928) matrices, and quadratic forms in the Gaussian matrix, we present a closed-form expression for the ergodic capacity of independent Rayleigh-fading MIMO channels and a tight upper bound for spatially correlated/double scattering MIMO channels. We also derive a closed-form capacity formula for keyhole MIMO channels. This analytic formula explicitly shows that the use of multiple antennas in keyhole channels only offers the diversity advantage, but provides no spatial multiplexing gains. Numerical results demonstrate the accuracy of our analytical expressions and the tightness of upper bounds.     

A Generalized Model for the Spatial Characteristics of the Cellular Mobile Channel

In this paper, we present an intensive study of the spatial characteristics of the cellular mobile channel for picocell, microcell, and macrocell environments. We review the previous physical channel models and make appropriate comments/corrections wherever needed. We find that almost all physical channel models proposed so far are specific to particular cellular environments and that no general model exists in the literature. Thus, we propose a generalized physical channel model, referred to as the eccentro-scattering model, and derive the expressions for the probability density function (pdf) in an angle of arrival (AoA) of the multipath signals at a base station (BS) for the picocell, microcell, and macrocell environments using the two most commonly used scatterers' distributions, i.e., uniform and Gaussian. The derived formulas, in closed form, can be further used in designing beamwidth and channel tracking algorithms and assessing the performance of smart antennas. We discuss the relations between the results obtained for different cellular environments in the uniform and the Gaussian scattering and investigate the effects of the standard deviation of the scatter density and size of the scattering disc on the pdf of AoA at the BS. Previous work on the AoA statistics considering either the shape of the scattering regions or the distribution of scatterers within that region can more easily be reproduced using the provided general formula. We prove that assuming the scatterers to be either uniformly or Gaussian distributed in sparsely populated areas gives almost the same distribution of AoA of multipaths at the BS.     

On the cooperative MIMO communication for energy-efficient cluster-to-cluster transmission at wireless sensor network

Energy-efficient data transmission is one of the key factors for energy-efficient wireless sensor networks (WSN). Cooperative multiple input multiple output (MIMO) explores the wireless communication schemes between multiple sensors emphasizing the MIMO structure. In this paper, an energy-efficient cooperative technique is proposed for a WSN where selected numbers of sensors at the transmitting end are used to form a MIMO structure wirelessly connected with a selected number of sensors at the receiving end. The selection of nodes in the transmitting end is based on a selection function, which is a combination of channel condition, residual energy, inter-sensor distance in a cluster, and geographical location, whereas the selection in the receiving side is performed on the basis of channel condition. Data are sent by the sensors in a cluster to a data-gathering node (DGN) using a multihop transmission. We are concentrating our design on the intermediate hop, where sensors in a cluster transmit their data to the sensors in another cluster with MIMO communication. Energy models are evaluated for both correlated and uncorrelated scenarios. The delay model of the proposed cooperative MIMO is also derived. Experimental results show that the selected MIMO structure outperforms the unselected MIMO in terms of total energy consumption. They also show energy-efficient performance by around 20% over unselected MIMO when they are compared with single-input-single-output structure. Also, the proposed approach takes around 50 more rounds than the geographically selected approach before dying at distance d?>?20 m.     

Diversity analysis for frequency-selective MIMO-OFDM systems with general spatial and temporal correlation model

In this paper, the effect of a general spatial and temporal fading correlation structure on the performance of coded multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems is studied. The analysis handles an arbitrary joint transmit-receive spatial correlation model, including the non-Kronecker model. An upper bound on the maximum achievable diversity order for frequency-selective MIMO-OFDM systems with general temporal and spatial correlation is derived. Furthermore, a space-time-frequency code design that can achieve the upper bound for any arbitrarily correlated channel scenario is provided. The general framework of the analysis includes space-frequency (SF)-coded systems as a special case. For the SF-coded MIMO-OFDM system, it is shown that any SF code designed to achieve full diversity in the independent fading channel can achieve full diversity in an arbitrary spatially correlated channel. The derived analytical results are consistent with those in the existing literature for special correlation structures. Extensive simulation results are provided to confirm the theoretical analysis.     

Directional Estimation of Block-Fading MIMO Channels Using Spherical Harmonics Expansion and Tensor Analysis

The well-known benefits of multiple input multiple output (MIMO) wireless communication systems suppose an efficient use of spatial diversity at both the transmitter and receiver. An important and not well-explored path toward improving MIMO system performance using spatial diversity takes into account the interactions among the antennas and the (physical) propagation medium. In this work, spherical harmonics and tensor analysis are originally combined into the problem of MIMO channel modeling and estimation. The use of spherical harmonics allows to represent the antenna radiation patterns in terms of coefficients of an expansion of spatially orthogonal functions, thus decoupling the transmit and receive antenna array responses from the physical propagation medium. Assuming a single-scattering propagation scenario driven by a finite number of specular multipaths, the parallel factor model is used to decompose the spherical modes of the MIMO channel into a sum of rank-one spherical mode tensors, whose dimensions are transmit modes, receive modes, and time. Then, we extend the tensor modeling framework to double scattering channels by resorting to the PARATUCK model that captures the interactions between multiple-scattering clusters. Capitalizing on the structure of these tensor models, we derive tensor-based alternating least squares algorithms for estimating directional MIMO channels in the spherical harmonics domain, from which the directions of arrival and directions of departure are extracted by means of a MUSIC-based method. Simulation results are provided to assess the performance of the proposed algorithms in selected system configurations. Our results also show the impact of the spherical expansion order on the accuracy of DoD/DoA estimates using the proposed algorithms.     

Geometrical Modeling of Scattering Environment for Highways in Umbrella Cell Based MIMO Communication Systems

In this paper, we develop a three-dimensional (3D) eccentricity-based cylindrical geometrical channel model for nonisotropic multiple-input-multiple-output (MIMO) communication systems under umbrella macrocellular environment. We use elliptic cylindrical geometry to model the scattering phenomenon in streets, canyons and highways. The scattering objects like, high-rise building, trees and vegetation that lie along the roadside premises are modeled by the height of an elliptical cylinder. The proposed channel model targets fast moving vehicles on the highways in an umbrella-cell of cellular communication networks. We assume that both ends of the communication link are equipped with multiple antenna arrays, where, mobile-station antenna height is lower than base-station antenna. Utilizing the proposed MIMO communication channel model, we obtain closed-form expressions for the space–time correlation function among the MIMO antenna elements. The obtained theoretical expressions are plotted and analyzed for different values of channel parameters. Finally, we compare the proposed model with the existing models in the literature and prove that our model can be deduced to the existing two-dimensional and 3D channel models.     

Simulation Models for Investigation of Multiuser Scheduling in MIMO Broadcast Channels

Spatial correlation is a result of insufficient antenna spacing among multiple antenna elements, while temporal correlation is caused by Doppler spread. This paper compares the effect of spatial and temporal correlation in order to investigate the performance of multiuser scheduling algorithms in multiple‐input multiple‐output (MIMO) broadcast channels. This comparison includes the effect on the ergodic capacity, on fairness among users, and on the sum‐rate capacity of a multiuser scheduling algorithm utilizing statistical channel state information in spatio‐temporally correlated MIMO broadcast channels. Numerical results demonstrate that temporal correlation is more meaningful than spatial correlation in view of the multiuser scheduling algorithm in MIMO broadcast channels. Indeed, the multiuser scheduling algorithm can reduce the effect of the Doppler spread if it exploits the information of temporal correlation appropriately. However, the effect of spatial correlation can be minimized if the antenna spacing is sufficient in rich scattering MIMO channels regardless of the multiuser scheduling algorithm used.     

Exact BER analysis of OSTBCs in spatially correlated MIMO channels

The bit-error rate (BER) performance of orthogonal space-time block codes (STBCs) in correlated multiple-input multiple-output (MIMO) channels is studied. We first derive closed-form exact BER equations for pulse amplitude modulation, quadrature amplitude modulation, and phase-shift keying constellations in a correlated Rayleigh MIMO channel. The BER expressions can be easily evaluated without any numerical methods. Then we consider correlated MIMO channels where the line of sight components exist and they suffer from shadowing, namely, correlated shadowed Rician MIMO channels. For three practical channel scenarios, the BER is analyzed, and closed-form BER equations are presented.     

MIMO Precoder Designs for Frequency-Selective Fading Channels Using Spatial and Path Correlation

Multiple-input–multiple-output (MIMO) precoder design for frequency-selective fading channels using partial channel information based on the spatial and path correlation matrices is presented. By representing a frequency-selective fading channel as a multipath model with $L$ effective paths, a general precoding structure is proposed and used to derive optimum precoding designs that maximize Jensen's upper bound on the channel ergodic capacity under the transmitted power constraint for two cases, i.e., uncorrelated and correlated channel paths. Analytical results show that, in the uncorrelated case, the precoder structure consists of a number of parallel precoders for frequency-flat fading channels. The power assignment to each precoder and the power allocation over the eigenmodes of each precoder are calculated based on the power of channel paths and the eigenvalues of the transmit correlation matrix. In the correlated case, the precoder structure is an eigenbeamformer with the beams referred to a function of eigenvectors of the Kronecker product of path and transmit correlation matrices. Furthermore, the power allocated to each eigenmode can be obtained from a statistical water-pouring policy that is specified by the product of eigenvalues of the transmit antenna and path correlation matrices. Simulation results for different scenarios indicate that the proposed precoder can increase the ergodic capacity of MIMO systems in a frequency-selective fading environment with spatial and path correlations, and its offered capacity gain is increased with the level of correlation and numbers of antennas and channel paths.      

Capacity scaling and spectral efficiency in wide-band correlated MIMO channels

The dramatic linear increase in ergodic capacity with the number of antennas promised by multiple-input multiple-output (MIMO) wireless communication systems is based on idealized channel models representing a rich scattering environment. Is such scaling sustainable in realistic scattering scenarios? Existing physical models, although realistic, are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters, such as the angles of arrival and delays. In this paper, we leverage a recently introduced virtual representation of physical models that is essentially a Fourier series representation of wide-band MIMO channels in terms of fixed virtual angles and delays. Motivated by physical considerations, we propose a D-connected model for correlated channels defined by a virtual spatial channel matrix consisting of D nonvanishing diagonals with independent and identically distributed (i.i.d.) Gaussian entries. The parameter D provides a meaningful and tractable measure of the richness of scattering. We derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth. In the large antenna regime, we show that linear capacity scaling is possible if D scales linearly with the number of antennas. This, in turn, is possible if the number of resolvable paths grows quadratically with the number of antennas. The capacity saturates for linear growth in the number of paths (fixed D). The ergodic capacity does not depend on frequency selectivity of the channel in the wide-band case. Increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior. For large bandwidth, the capacity scales linearly with the signal-to-noise ratio (SNR) as well. We also provide an explicit characterization of the wide-band slope recently proposed by Verdu. Numerical results are presented to illustrate the key theoretical results.     

Benefit of pattern diversity via two-element array of circular patch antennas in indoor clustered MIMO channels

In this paper, we analyze a multiple-input multiple-output (MIMO) array consisting of two circular microstrip antennas, designed to exploit pattern diversity. We analytically derive the spatial correlation coefficients of this array as a function of the mode excited, for realistic clustered MIMO channel models. We compare the performance of the circular patch array (CPA) against an array of two spaced dipoles. In particular, we compute a theoretical tradeoff to predict when the pattern diversity provided by the CPA is more effective than space diversity from the uniform linear array (ULA), based on the eigenvalues of the spatial correlation matrix. Through simulations, we show that CPAs yield better performance or satisfy more restrictive size constraints than ULAs in clustered MIMO channels, depending on the element spacing of the ULA. These results make the CPA an attractive solution for miniaturized MIMO arrays for portable devices or access points.     

General Capacity Bounds for Spatially Correlated Rician MIMO Channels

This paper considers the capacity of spatially correlated Rician multiple-input multiple-output (MIMO) channels. We consider the general case with double-sided correlation and arbitrary rank channel means. We derive tight upper and lower bounds on the ergodic capacity. In the particular cases when the numbers of transmit and receive antennas are equal, or when the correlation is single sided, we derive more specific bounds which are computationally efficient. The bounds are shown to reduce to known results in cases of independent and identically distributed (i.i.d.) and correlated Rayleigh MIMO channels. We also analyze the outage characteristics of the correlated Rician MIMO channels at high signal-to-noise ratio (SNR). We derive the mean and variance of the mutual information and show that it is well approximated by a Gaussian distribution. Finally, we present numerical results which show the effect of the antenna configuration, correlation level (angle spreads), Rician$K$-factor, and the geometry of the dominant Rician paths.