Capacity of MRC on Correlated Rician Fading Channels

A new exact explicit expression is derived for the ergodic capacity of maximal ratio combining (MRC) schemes over arbitrarily correlated Rician fading channels. This is used to study the effects of channel correlation on the ergodic capacity. Numerical results reveal that both the phase and the magnitude of correlation have an impact on the ergodic capacity of Rician fading channels. This is in contrast to correlated Rayleigh fading, where the phase of the correlation has no effect on the ergodic capacity. It is also observed that negatively correlated branches in Rician fading may lead to an increase in ergodic capacity beyond that obtained by uncorrelated branches.     

具有功率分配因子的不可信中继系统的中断性能和遍历保密容量

基于不存在直接链路的具有不可信中继的三节点系统,本文在协作干扰模型中引入功率分配因子,对两种放大转发因子下系统的中断概率和遍历保密容量进行了计算及对比分析。首先,系统采用平均放大因子,推导出其保密中断概率;然后,在引入同样功率分配因子的基础上,系统改用自适应瞬时放大因子,得出保密中断概率的下界;为了对比,本文接着给出了系统两种情况下的遍历保密容量;最后,仿真验证了中断概率和遍历保密容量计算的准确性,数值仿真表明引入功率分配因子可减小系统的中断概率和提高系统的遍历保密容量,瞬时放大因子下系统性能较平均放大因子下更好。      

On the bounds of frequency-selective channel capacity with doubly correlated geometrical MIMO channel model

The multi-input multi-output (MIMO) technology plays an important role in link transmissions. This article considers the general case for the ergodic capacity in doubly correlated frequency-selective MIMO channel. In the study, the geometrical MIMO channel model is presented. Based on the formula of MIMO ergodic capacity, the capacity limits are studied with arbitrary finite number of antennas in the frequency-selective MIMO channel. It first derives the exact expressions for the upper bound and lower bound in doubly correlated MIMO channel. The results for the single-ended correlation and independent identically distributed (i.i.d.) MIMO channel are also obtained as special cases. Then the simple expressions of the capacity bounds are attained at high SNR. Finally, results are provided by Monte Carlo simulations to verify the tightness of the derived bounds.     

Space-Frequency Precoding with Space–Tap Correlation Information at the Transmitter

In closed-loop methods for obtaining exact channel state information at the transmitter (CSI-Tx), the overhead associated with the feedback can be excessive for fast mobiles. Channel statistics-based CSI-Tx requires a much smaller overhead and is, therefore, attractive for use with fast mobiles. We study ways to exploit correlation-based CSI-Tx in a multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) system. We focus on a channel environment in which spatial and tap correlations are present. We propose a channel model for the case that spatial and tap correlations can be separated and show that in this case channel correlation decreases the ergodic capacity of an MIMO-OFDM system when no CSI-Tx is available. However, this decrease can be mitigated when correlation-based CSI-Tx is exploited. We introduce an optimal precoding approach to maximize capacity with spatial and tap correlation-based CSI-Tx. We also propose a statistical waterfilling scheme, which leads to almost optimal capacity performance without requiring computationally intensive numerical optimization. Based on these approaches, the impact of spatial and tap correlations is investigated.     

基于双端莱斯相关几何信道模型的MIMO系统容量界研究

MIMO system can provide higher capacity in independent conditions. When the spatial-temporal fading correlation exists, the capacity may decrease. In this paper, the geometrical MIMO channel model is presented with Rician factor. Based on the MIMO ergodic capacity, the capacity bounds are derived with arbitrary finite number of antennas.The bounds are derived in the exact expressions in doubly correlated MIMO Rician channel. Then a simple expression for the capacity bounds is attained for the high SNR. Finally, the tightness of derived bounds is verified by Monte Carlo simulation.     

Spatially and temporally correlated MIMO channels: modeling and capacity analysis

Wireless communication systems employing multiple antennas at both the transmitter and receiver have been shown to offer significant gains over single-antenna systems. Recent studies on the capacity of multiple-input-multiple-output (MIMO) channels have focused on the effect of spatial correlation. The joint effect of spatial and temporal correlation has not been well studied. In this paper, a geometric MIMO channel model is presented, which considers motion of the receiver and nonisotropic scattering at both ends of the radio link. A joint space-time cross-correlation function is derived from this model and variates with this joint correlation are generated by using the vector autoregressive stochastic model. The outage capacity of this channel is considered where the effects of antenna spacing, antenna array angle, degree of nonisotropic scattering, and receiver motion are investigated. When n transmit and n receive antennas are employed, it is shown that the outage capacity still increases linearly with respect to n, despite the presence of spatial and temporal correlation. Furthermore, analytical expressions are derived for the ergodic capacity of a MIMO channel for the cases of spatial correlation at one end and at both ends of the radio link. The latter case does not lend itself to numerical evaluation, but the former case is shown to be accurate by comparison with simulation results. The proposed analysis is very general, as it is based on the transmit and receive antenna correlations matrices.     

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.     

相关信道下MIMO信道容量优化算法的研究

该文研究MIMO系统收发端天线采用均匀线阵且放置空间有限,存在相关衰落时信道容量的优化方法。采用规范化信道模型,分析了信道相关性对平均信道容量和最优信号协方差矩阵的影响,推导了最优协方差矩阵的一阶条件;利用Jensen's不等式确定了信道容量的上界,给出了闭式解,并对相关信道下信号的传输模式进行了讨论。仿真结果表明,采用该优化方法,在各种SNR下,其平均容量接近Jensen's上界;得出信道相关程度对信道平均容量的影响依赖于信噪比的结论。     

OCDMA系统中新型正交码的设计及性能研究

为了得到性能较为良好的正交码,采用没有重复数字的全间隔集,进行了地址码的设计和系统仿真验证,设计出的正交码具有理想的相关性和灵活的码字容量。分析整个系统,在考虑各种噪声和多址干扰的影响下,推导出正交码的误比特率公式。自行设计并搭建了采用光纤延时线作为编解码器的异步光码多分址系统。结果表明,该正交码能够适应更多用户的需求,通过误比特率公式计算和系统仿真得到的结果都较为理想,此研究对需要大容量的光码多分址系统的进一步发展具有一定的帮助。     

Beneficial impact of channel correlations on MIMO capacity

The potential beneficial impact of channel correlations on the capacity of MIMO systems is investigated. In contrast to most previous work, the present analysis is based on a comprehensive model of the channel correlation structure. It is therefore illustrated that fading cross-correlations may increase the ergodic capacity, sometimes even beyond the supposedly ideal case of independent channels. Starting from considerations on an analytical upper bound of the capacity, the study is then supported by simulation results of the actual ergodic capacity in arbitrary MIMO channels using a simple geometry-based stochastic model.     

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。     

Space–Time Power Schedule for Distributed MIMO Links Without Instantaneous Channel State Information at the Transmitting Nodes

A space-time optimal power schedule for multiple distributed multiple-input multiple-output (MIMO) links without the knowledge of the instantaneous channel state information (CSI) at the transmitting nodes is proposed. A readily computable expression for the ergodic sum capacity of the MIMO links is derived. Based on this expression, which is a non-convex function of power allocation vectors, a projected gradient algorithm is developed to optimize the power allocation. For a symmetric set of MIMO links with independent identically distributed channels, it is observed that the space-time optimal power schedule reduces to a uniform isotropic power schedule when nominal interference is low, or to an orthogonal isotropic power schedule when nominal interference is high. Furthermore, the transition region between the latter two schedules is seen to be very sharp in terms of nominal interference-to-noise ratio (INR). For MIMO links with correlated channels, the corresponding space-time optimal power schedule is developed based on the knowledge of the channel correlation matrices. It is shown that the channel correlation has a great impact on the ergodic capacity and the optimality of different power scheduling approaches.     

Introducing Space into MIMO Capacity Calculations

The large spectral efficiencies promised for multiple-input multiple-output (MIMO) wireless fading channels are derived under certain conditions which do not fully take into account the spatial aspects of the channel. Spatial correlation, due to limited angular spread or insufficient antenna spacing, significantly reduces the performance of MIMO systems. In this paper we explore the effects of spatially selective channels on the capacity of MIMO systems via a new capacity expression which is more general and realistic than previous expressions. By including spatial information we derive a closed-form expression for ergodic capacity which uses the physics of signal propagation combined with the statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and leads to valuable insights into the factors determining capacity for a wide range of scattering models.     

Statistical Eigenmode Transmission Over Jointly Correlated MIMO Channels

We investigate multiple-input multiple-output (MIMO) eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.     

On the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without CSI at the transmitter

In this letter, the impact of correlation of the transmit antennas of a multiple-input single-output (MISO) system, with no channel state information (CSI) at the transmitter and perfect CSI at the receiver is analyzed. We show that the ergodic capacity for the single-user MISO system is Schur-concave with respect to the vector with eigenvalues of the channel covariance matrix, i.e., the more correlation that exists between the transmit antennas, the less is the achievable capacity. Furthermore, the capacity loss for fully correlated transmit antennas in comparison with the uncorrelated case is derived. The results for the ergodic capacity are compared with the impact of correlation on the outage probability. The relationship between correlation properties and outage probability is more complicated than the relationship between the correlation properties and the ergodic capacity. It is shown that the outage probability is Schur-convex in the high signal-to-noise ratio (SNR) regime, and Schur-concave in the low SNR regime.     

Performance analyses of subcarrier BPSK modulation over M turbulence channels with pointing errors

An aggregated channel model is achieved by fitting the Weibull distribution, which includes the effects of atmospheric attenuation, M distributed atmospheric turbulence and nonzero boresight pointing errors. With this approximate channel model, the bit error rate (BER) and the ergodic capacity of free-space optical (FSO) communication systems utilizing subcarrier binary phase-shift keying (BPSK) modulation are analyzed, respectively. A closed-form expression of BER is derived by using the generalized Gauss-Lagueree quadrature rule, and the bounds of ergodic capacity are discussed. Monte Carlo simulation is provided to confirm the validity of the BER expressions and the bounds of ergodic capacity.     

Capacity and optimal resource allocation for fading broadcastchannels .I. Ergodic capacity

In multiuser wireless systems, dynamic resource allocation between users and over time significantly improves efficiency and performance. In this two-part paper, we study three types of capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the outage capacity region with nonzero outage. We derive the ergodic capacity region of an M-user fading broadcast channel for code division (CD), time division (TD), and frequency division (FD), assuming that both the transmitter and the receivers have perfect channel side information (CSI). It is shown that by allowing dynamic resource allocation, TD, FD, and CD without successive decoding have the same ergodic capacity region, while optimal CD has a larger region. Optimal resource allocation policies are obtained for these different spectrum-sharing techniques. A simple suboptimal policy is also proposed for TD and CD without successive decoding that results in a rate region quite close to the ergodic capacity region. Numerical results are provided for different fading broadcast channels     

On the Ergodic Capacity of Rank-1 Ricean-Fading MIMO Channels

This paper investigates the ergodic capacity of Ricean-fading multiple-input-multiple-output (MIMO) channels with rank-1 mean matrices under the assumption that the channel is unknown at the transmitter and perfectly known at the receiver. After introducing the system model and the concept of ergodic capacity of MIMO channels, we derive the explicit expressions for the expected values of the determinant and log-determinant of complex noncentral Wishart matrices. Subsequently, we obtain new upper and lower bounds on the ergodic capacity of rank-1 Ricean-fading MIMO channels at any signal-to-noise ratio (SNR). We show that our bounds are tighter than previously reported analytical bounds, and discuss the impact of spatial fading correlation and Ricean K-factor with the help of these bounds. Furthermore, we extend the analysis of ergodic capacity to frequency selective spatially correlated Ricean-fading MIMO channels. We demonstrate that the calculation of ergodic capacity of frequency selective fading MIMO channels can be converted to the calculation of the one of equivalent frequency flat-fading MIMO channels. Finally, we present numerical results that confirm the theoretical analysis     

Performance Analysis of MC-CDMA Systems Under Nakagami Hoyt Fading

Based on an alternative expression for Q-function, a simple bit error rate expression is derived in this paper for multicarrier code division multiple access systems with maximal ratio combining in correlated Nakagami-q channels. Furthermore, in this paper, we derive bounds on the probability of error and ergodic capacity of spatially multiplexed MC-CDM systems with zero forcing unified successive interference cancellation technique. Closed-form expressions for Capacities per unit bandwidth and Outage probability using optimal power and rate adaptation policy are derived and plotted. Asymptotic approximations and upper bounds on spectrum efficiency are also derived and plotted. Numerical results for Symbol Error Rate are also derived and plotted using MATLAB.     

Capacity of MIMO channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high E/sub b//N/sub 0/.