MIMO信道的GBDB模型及其信道容量分析

针对非频率选择性Rice衰落MIMO移动信道，建立GBDB模型，并推导出新的MIMO系统的GBDB模型的空时联合相关函数。新的GBDB模型统一现有的多种MIMO信道模型，新的空时联合相关函数综合考虑了无线衰落信道收发两端的多普勒扩展、非均匀角度扩展以及平均发射与到达方向，综合考虑了收发端天线阵的配置。最后基于新的空时联合相关函数，分析了非均匀散射参数以及Rice分布参数变化对MIMO信道统计容量的影响。     

Capacity Performance of Polarized Distributed MIMO System on Rician Channel

The analytical upper bound and lower bound on the ergodic capacity of polarized distributed antenna system and their relation with antenna polarization on Rician channel are deduced by applying properties of complex non-central Wishart matrices and matrix-variate non-central quadratic forms. Compared to the related studies, our analysis is extended to account for the polarized distributed system with Rician fading where a line-of-sight component exists and both ends are affected by spatial correlation. The antenna polarization has some impacts on the capacity bounds according to the expressions of capacity bounds. Both the transmitter and the receiver are equipped with multiple polarization antennas, and the transmitters are of linear layout. A power allocation scheme based on the path loss fading is presented by maximizing the capacity upper bound. The power allocation scheme is feedback efficient compared with those power allocation schemes based on statistical parameters of the channel which need a large amount of feedback. In the simulations, the ergodic capacity of polarized distributed MIMO is analyzed. Comparisons are taken on the effects of angle spread, Rician factor and power on the ergodic capacity. The proposed power allocation scheme is superior to the equal power allocation scheme and has very close performance to the optimal power allocation scheme.     

On the Ergodic Capacity and Energy Efficiency for Fading MIMO NOMA Systems

Non-orthogonal multiple access (NOMA) is expected to be a promising multiple access techniques for 5G networks due to its superior spectral efficiency (SE). Previous research mainly focus on the design to improve the SE performance with instantaneous channel state information (CSI). In this paper, we consider the fading MIMO channels with only statistical CSI at the transmitter, and explore the potential gains of MIMO NOMA scheme in terms of both ergodic capacity and energy efficiency (EE). The ergodic capacity maximization problem is first studied for the fading multiple-input multiple-output (MIMO) NOMA systems. We derive the optimal input covariance structure and propose both optimal and low complexity suboptimal power allocation schemes to maximize the ergodic capacity of MIMO NOMA system. For the EE maximization, the optimization problem is formulated to maximize the system EE (defined by ergodic capacity under unit power consumption) under the total transmit power constraint and the minimum rate constraint of the weak user. By transforming the EE maximization problem into an equivalent one-dimensional optimization problem, the optimal power allocation for EE design is proposed. To further reduce the computation complexity, a near-optimal solution based on golden section search and suboptimal closed form solution are proposed as well. Numerical results show that the proposed NOMA schemes significantly outperform the traditional orthogonal multiple access scheme with traditional orthogonal multiple access transmission in terms of both SE and EE.     

同信道干扰下相关多输入多输出信道容量分析

在Rayleigh衰落环境下,研究了具有同信道干扰的多输入多输出(MIMO)信道容量问题,分析了通信用户发送端带有空间相关性的情况。假设接收端完美地知道信道状态信息而发送端不知道,基于矩阵变量分布理论,推导出MIMO信道互信息之矩生成函数的精确闭式表达式。利用该表达式进一步推导出MIMO遍历信道容量的精确表达式。用数值结果验证了分析结果的正确性,并给出各种参数对遍历信道容量的影响。     

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.     

Ergodic capacity and outage probability optimization for secondary user in cognitive radio networks under interference outage constraint

This paper considers a cognitive radio network where a secondary user (SU) coexists with a primary user (PU). The interference outage constraint is applied to protect the primary transmission. The power allocation problem to jointly maximize the ergodic capacity and minimize the outage probability of the SU, subject to the average transmit power constraint and the interference outage constraint, is studied. Suppose that the perfect knowledge of the instantaneous channel state information (CSI) of the interference link between the SU transmitter and the PU receiver is available at the SU, the optimal power allocation strategy is then proposed. Additionally, to manage more practical situations, we further assume only the interference link channel distribution is known and derive the corresponding optimal power allocation strategy. Extensive simulation results are given to verify the effectiveness of the proposed strategies. It is shown that the proposed strategies achieve high ergodic capacity and low outage probability simultaneously, whereas optimizing the ergodic capacity (or outage probability) only leads to much higher outage probability (or lower ergodic capacity). It is also shown that the SU performance is not degraded due to partial knowledge of the interference link CSI if tight transmit power constraint is applied.     

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     

Closed-form capacity expressions of orthogonalized correlated MIMO channels

Space-time block codes are known to orthogonalize the multiple-input multiple-output (MIMO) wireless channel, thus reducing the space-time vector detection to a simpler scalar detection problem. The capacity over orthogonalized ergodic correlated Rayleigh and Ricean flat-fading MIMO channels has so far only been given in integral form. This letter derives a closed form capacity expression over such channels, hence avoiding numerical integrations or Monte Carlo simulations.     

Characterizing the statistical properties of mutual information in MIMO channels

We consider Gaussian multiple-input multiple-output (MIMO) frequency-selective spatially correlated fading channels, assuming that the channel is unknown at the transmitter and perfectly known at the receiver. For Gaussian codebooks, using results from multivariate statistics, we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal-to-noise ratio (SNR). We show that our bound is tighter than previously reported analytical lower bounds, and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity. Based on a closed-form approximation of the variance of mutual information in correlated flat-fading MIMO channels, we provide insights into the multiplexing-diversity tradeoff for Gaussian code books. Furthermore, for a given total number of antennas, we consider the problem of finding the optimal (ergodic capacity maximizing) number of transmit and receive antennas, and we reveal the SNR-dependent nature of the maximization strategy. Finally, we present numerical results and comparisons between our capacity bounds and previously reported bounds.     

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 of distributed PHY-layer sensor networks

Sensor networks are comprised of nodes with minimal baseband and RF functionalities. In such networks, it is assumed that a source sensor communicates with a target sensor over a number of relaying sensors by utilizing distributed low-complexity space-time encoding techniques, hence the resulting communication scenario is a generalized form of orthogonalized multiple-input multiple-output (MIMO) channels. The contributions of this paper are the derivation of the Shannon capacity in terms of natural units per second per Hertz for such space-time encoded distributed communication scenarios. Closed-form capacity expressions are derived for ergodic flat-fading Rayleigh and Nakagami channels, as well as the communication-rate outage probabilities for aforementioned channels. It is shown that the distributed Alamouti scheme yields the best performance over ergodic channels. In the case of nonergodic channels, the 3/4-rate sporadic space-time block code (STBC) is shown to give optimum performance. Finally, Monte Carlo simulations are used to assess the performance of distributed multistage sensor networks. It is shown that notable power savings can be achieved, compared to the traditional single-link sensor networks.     

Optimal power allocation for cognitive radio under interference outage constraint

Cognitive radio is able to share the spectrum with primary licensed user, which greatly improves the spectrum efficiency. We study the optimal power allocation for cognitive radio to maximize its ergodic capacity under interference outage constraint. An optimal power allocation scheme for the secondary user with complete channel state information is proposed and its approximation is presented in closed form in Rayleigh fading channels. When the complete channel state information is not available, a more practical transmitter-side joint access ratio and transmit power constraint is proposed. The new constraint guarantees the same impact on interference outage probability at primary user receiver. Both the optimal power allocation and transmit rate under the new constraint are presented in closed form. Simulation results evaluate the performance of proposed power allocation schemes and verify our analysis.     

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 space-time correlation model for multielement antenna systems inmobile fading channels

Analysis and design of multielement antenna systems in mobile fading channels require a model for the space-time cross correlation among the links of the underlying multiple-input multiple-output (MIMO) channel. In this paper, we propose a general space-time cross-correlation function for mobile frequency nonselective Rice fading MIMO channels, in which various parameters of interest such as the angle spreads at the base station and the user, the distance between the base station and the user, mean directions of the signal arrivals, array configurations, and Doppler spread are all taken into account. The new space-time cross-correlation function includes all the relevant parameters of the MIMO fading channel in a clean compact form, suitable for both mathematical analysis and numerical calculations/simulations. It also covers many known correlation models as special cases. We demonstrate the utility of the new space-time correlation model by clarifying the limitations of a widely accepted correlation model for MIMO fading channels. As another application, we quantify the impact of nonisotropic scattering around the user, on the capacity of a MIMO fading channel     

Some remarkable properties of diagonally correlated MIMO channels

This paper investigates so-called diagonally correlated multiple input-multiple output (MIMO) channels, which provide higher ergodic capacity than independent and identically distributed (i.i.d.) fading channels. The presented analysis details physical scenarios leading to such channels, some properties of the channel matrix, and an analytical expression for its ergodic capacity.     

Simplified transmitter design for MIMO systems with channel uncertainty

This article investigates transmitter design in Rayleigh fading multiple input multiple output (MIMO) channels with spatial correlation when there are channel uncertainties caused by a combined effect of channel estimation error and limited feedback. To overcome the high computational complexity of the optimal transmit power allocation, a simple and suboptimal allocation is proposed by exploiting the transmission constraint and differentiating a bound based on Jensen inequality on the channel capacity. The simulation results show that the mutual information corresponding to the proposed power allocation closely approaches the channel capacity corresponding to the optimal one and meanwhile the computational complexity is greatly reduced.     

Dynamics of spatial correlation and implications on MIMO systems

The use of multiple antennas has found various applications in the area of wireless communications. One such application has recently become very popular and is referred to as the multiple-input multiple-output (MIMO) antenna system. The main idea behind MIMO is to establish independent parallel channels between multiple transmit and receive antennas. Each channel uses the same frequency, and the transmissions occur simultaneously. In such a configuration, the amount of data transmitted increases linearly with the number of parallel channels, which is what makes MIMO so popular in the wireless world. The enormous capacity offered by MIMO systems is not realizable when the parallel channels are highly correlated. The goal of this article is to highlight the correlation concept and its impact on MIMO systems. Although correlation can be defined in many dimensions, here we focus on spatial correlation, and specifically consider antenna correlations in mobile units. We provide an overview of spatial correlation and present its underlying parameters in detail. Special attention is given to mutual coupling since it has signal decorrelation and antenna gain reduction effects. We then present how correlation in a MIMO system affects the amount of data that can be transmitted (MIMO capacity) and briefly review how power should be distributed with the knowledge of correlation. Analyses indicate that in real propagation environments, the high capacity gain of MIMO systems can be realized with improved antenna selection algorithms and power allocation strategies.     

分布式发射天线MIMO信号的最优线性检测

 在分布式发射天线多输入多输出(MIMO)系统中,信道传播时延使各个发射天线的符号异步到达接收天线.接收信号符号间干扰的特殊性使分布式发射天线MIMO信号的线性检测算法更加复杂,最优线性检测算法也不能直接由最小均方误差(MMSE)准则得到.针对这一问题,提出了基于MMSE准则的分布式发射天线MIMO信号的最优线性检测算法:先最大比合并,再最小均方误差检测.并且,通过界定误码率上下限,得到其分集阶数.仿真结果验证了最优线性检测接收端信号处理方式的正确性.     

Power allocation over time‐varying multiple‐access interference channels

In this paper, power allocation over time‐varying multiple‐access interference channels is studied. Particularly, stochastic network sum‐rate maximizing and max‐min rate power allocation, and total power minimization problems are formulated, capturing the random nature of communication channels. Typically, a centralized controller must have perfect knowledge of global instantaneous channel state information for dynamic optimal power allocation; however, this may not be possible, because of the computational complexity and communication overheads/delays involved. Based on the second‐order statistics of the channel state information, the stochastic problem formulations are transformed into their optimal deterministic representations in terms of ergodic capacity, while ensuring satisfactory quality of service via target outage probability. However, such deterministic reformulations happen to be non‐convex and thus are computationally expensive. In turn, sub‐optimal reformulations are derived and solved via iterative low‐complexity algorithms. Simulation results demonstrate that the proposed deterministic sub‐optimal power allocation reformulations closely coincide with their optimal deterministic and dynamic counterparts, with the proposed algorithms converging in a finite number of iterations. Copyright © 2016 John Wiley & Sons, Ltd.