Capacity Bounds for MIMO Nakagami- $m$ Fading Channels

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami- $m$ fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter $m$ on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-$m$ and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.      

On the capacity of log-normal fading channels

In this letter we provide an analytical expression for the moments of the capacity for the log-normal fading channel. Since the developed expression involves infinite series, we show that the error that results from the truncation of these series is insignificant. We also analyze in more details the ergodic capacity by giving a simpler expression for the remainder of the truncated series. Relying on the fact that the sum of log-normal Random Variables (RV) is well approximated by another lognormal RV, we further utilize the obtained results to approximate the capacity of diversity combining techniques in correlated lognormal fading channels. The results that we provide in this letter are an important tool for measuring the performance of communication links in a log-normal environment.     

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.     

BER Performance of Free-Space Optical Transmission with Spatial Diversity

Free space optical (FSO) communications is a cost-effective and high bandwidth access technique, which has been receiving growing attention with recent commercialization successes. A major impairment in FSO links is the turbulence- induced fading which severely degrades the link performance. To mitigate turbulence-induced fading and, therefore, to improve the error rate performance, spatial diversity can be used over FSO links which involves the deployment of multiple laser transmitters/receivers. In this paper, we investigate the bit error rate (BER) performance of FSO links with spatial diversity over log- normal atmospheric turbulence fading channels, assuming both independent and correlated channels among transmitter/receiver apertures. Our analytical derivations build upon an approximation to the sum of correlated log-normal random variables. The derived BER expressions quantify the effect of spatial diversity and possible spatial correlations in a log-normal channel.     

On the capacity of MIMO relay channels

We study the capacity of multiple-input multiple- output (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound under certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks.     

Energy Efficient Cooperation with Chip-Interleaved Transceivers in WSNs Over Frequency-Selective Fading Channels

Cooperative diversity techniques have been utilized to improve the energy efficiency of wireless sensor networks (WSNs) operating over flat fading channels in a considerable number of literature. However, wireless channels of WSNs operating in indoor environments are supposed to be characterised by frequency-selective fading. Theoretical analysis of energy efficient cooperative communications in WSNs operating in indoor environments are rarely addressed. Therefore, this paper studies the energy efficient cooperative communications in WSNs operating over frequency-selective fading channels. Closed-form bit error rate expressions are derived for systems over frequency-selective fading channels. In order to fully explore the energy conservation potential of cooperative communications, solutions of the optimal transmit power allocation and the partner node selection are provided. Moreover, it is proven that the communication quality can be greatly improved by using chip-interleaving techniques in WSNs subject to flat fading channels. Thus, this paper investigates the energy-saving potential of chip-interleaved transceivers in WSNs subject to frequency-selective fading. Numerical results show that significant energy savings can be achieved via cooperations with chip-interleaved transceivers in WSNs operating in indoor environments.

     

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.     

On Fading Margin in Ultrawideband Communications Over Multipath Channels

This work studies ultra wideband (UWB) communications over multipath residential indoor channels. We study the relationship between the fading margin and the transmitter–receiver separation distance for both the line of sight and the no line of sight scenarios. Impairments such as small scale fading as well as large scale fading are considered. Some implications of the results for UWB indoor network design are discussed.     

Tight closed-form approximation for the ergodic capacity of orthogonal STBC

In this letter we derive a simple and tight closed-form approximation for the ergodic capacity of orthogonal space-time block coding in arbitrary fading channels. The expression is an analytical function of the power covariance matrix of the channel. In the case of uncorrelated channels the expression only depends on the variances of the channel power gains. These channel statistics can be easily obtained from both analytical and physical fading channel models. Simulations results show the accuracy of the proposed expression     

On the Secrecy Capacity of Fading Channels

We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average signal-to-noise ratio (SNR) goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Overall, channel fading has a positive impact on the secrecy capacity and rate adaptation, based on the main channel CSI, is critical in facilitating secure communications over slow fading channels.      

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     

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.     

On the duality of Gaussian multiple-access and broadcast channels

We define a duality between Gaussian multiple-access channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimum-rate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well.     

On the capacity of OFDM-based spatial multiplexing systems

This paper deals with the capacity behavior of wireless orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing systems in broad-band fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a physically motivated multiple-input multiple-output (MIMO) broad-band fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that, in the MIMO case, unlike the single-input single-output (SISO) case, delay spread channels may provide advantages over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and higher multiplexing gain than MIMO flat fading channels     

Delay-limited capacity: multiple antennas, moment constraints, and fading statistics

Different performance measures are an important mean in order to analyze and design wireless communications systems. Examples of common performance measures are the ergodic capacity, the outage capacity, and the average mean-square error (MSE). In this work, we study the delay-limited capacity (DLC). The DLC depends on the properties of the fading channel, e.g. on the spatial correlation and on the line-of-sight (LOS) component. In this letter, we derive the DLC for the general class of parallel fading channels, including the multiple antenna channels under moment and long-term power constraint. We prove that the DLC is Schur-concave with respect to the spatial correlation in single-input multiple-output (SIMO), and multiple-input single-output (MISO). Bounds for the DLC of multiple-input multiple-output (MIMO) and parallel fading channels are derived and the impact of the the mean component and spatial correlation on these bounds is characterized.     

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 energy efficient cooperations in WSNs over frequency-selective channels

Energy efficient cooperations in wireless sensor networks (WSNs) subject to flat fading channels have attracted a considerable amount of attention recently. However, wireless channels of WSNs operating in indoor environments are supposed to have a frequency-selective nature, yet a comprehensive analysis of cooperative communications in these WSNs practically does not exist. Therefore, this paper has studied energy efficient cooperative communications over frequency-selective fading channels. Investigations of the energy efficient decode-and-forward and the adaptive decode-and-forward cooperations are provided in terms of the optimal power allocation and the partner selection region. The study is based on a network geometry of a fixed source node and a destination node with a range of potential partner node locations. Numerical results of optimal power allocation and the partner selection region are generated, and contour graphs of the resulting cooperative energy savings achieved from cooperations are provided using MATLAB. Results have indicated that cooperations can seek for potential partner nodes within a specified region to form energy efficient communications in WSNs operating in indoor environments. Furthermore, we have compared our results to the existing work which studies cooperations over flat fading channels, and several interesting findings have been revealed.     

Infinite-series representations associated with the bivariate rician distribution and their applications

Analytical expressions for the evaluation of the bivariate Rician cumulative distribution function (CDF), the covariance, and the characteristic function (CHF) are not known, despite their usefulness in wireless communications systems analysis. In this letter, motivated by the ability of the Rician model to describe fading in wireless communications, we derive infinite-series representations for the probability density function, the CDF, the covariance, and the CHF of two correlated Rician random variables. It is shown that the presented infinite-series expressions converge rapidly, and can be efficiently used to study several performance criteria for dual-diversity receivers operating over correlated Rician fading channels.     

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-OFDM系统无线衰落信道容量分析

推导了MIMO-OFDM系统在衰落信道下的各态历经容量、最优发送策略、使用等功率分配时的容量上界以及相对于单天线OFDM系统的容量增益。结果表明：天线数和平均接收信噪比是决定MIMO-OFDM系统信道容量的关键因素。天线数越多或者接收信噪比越大,信道的容量越大,信道容量几乎不受多径时延扩展的影响。慢衰落信道下的最大信道容量可以使用空-频两维注水算法得到,当接收信噪比足够大时,最大信道容量也可以用平均分配发送功率的方法逼近。