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.      

一种分布式多入多出(MIMO)信道的容量研究

分布式MIMO系统结合了点对点MIMO信道与分布式天线系统两者的特点，能改善链路的质量，提高覆盖面积。本文提出了一种包含路径损耗、阴影衰落与小尺度衰落的分布式MIMO信道模型，分析推导了采用该模型时的分布式MIMO信道容量。通过计算机仿真，研究分析了阴影衰落、Rice信道因子K等因素对分布式MIMO上行信道容量的影响，得出了分布式MIMO信道容量空间分布的特点。     

On the Capacity of Free-Space Optical Intensity Channels

Upper and lower bounds are derived on the capacity of the free-space optical intensity channel. This channel has a nonnegative input (representing the transmitted optical intensity), which is corrupted by additive white Gaussian noise. To preserve the battery and for safety reasons, the input is constrained in both its average and its peak power. For a fixed ratio of the allowed average power to the allowed peak power, the difference between the upper and the lower bound tends to zero as the average power tends to infinity and their ratio tends to one as the average power tends to zero. When only an average power constraint is imposed on the input, the difference between the bounds tends to zero as the allowed average power tends to infinity, and their ratio tends to a constant as the allowed average power tends to zero.     

On the Outage Capacity of Correlated Multiple-Path MIMO Channels

The use of multiple-antenna arrays can dramatically increase the throughput of wireless communication systems. Thus, it is important to characterize the statistics of the mutual information for realistic correlated channels. Here, a mathematical approach is presented, using the method of replicas, that provides analytic expressions not only for the average, but also for the higher moments of the distribution of the mutual information for the most general zero-mean Gaussian multiple-input multiple-output (MIMO) channels when the channel is known at the receiver. These channels include multitap delay paths, and channels with covariance matrices that cannot be written as a Kronecker product, such as general dual-polarized correlated antenna arrays. This approach is formally valid for large antenna numbers, in which case all cumulant moments of the distribution, other than the first two, scale to zero. In addition, it is shown that the replica-symmetric result is valid if the variance of the mutual information is positive and finite. In this case, it is shown that the distribution of the mutual information tends to a Gaussian, which enables the calculation of the outage capacity. These results are quite accurate even for few antennas, which makes this approach applicable to realistic situations.     

On the Capacity of Time-Varying Channels With Periodic Feedback

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel-state information (CSI) is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals. The system capacity is investigated in two cases: 1) finite-state Markov channel, and 2) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.     

在相关信道下MIMO-OFDM信道容量的分析

利用中心Wishart矩阵的性质得到相关信道下的多输入/输出正交频分复用系统(Multiple Input Multiple out-put;Orthogonal Frequency Division Multiplexing,MIMO OFDM)的信道容量的上下界限,同时分析天线相关对信道容量的影响。假设接收端有完全的信道状态信息(CSI),而发射端没有任何的CSI的情况下得到了信道容量的上下界限,通过仿真说明得到的界限是紧凑的,同时说明信道相关如何降低信道容量。     

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。     

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     

Maximum Likelihood Sequence Estimation for Randomly Dispersive Channels

Receiver designs for maximum likelihood sequence estimation of digital data transmission through randomly dispersive channels are developed. The random channels are constrained to have finite memory of durationLin the sense that the casual minimum mean square error estimate of the channel output at any given time is a function of only the most recentLTseconds of observations. Examples of the channels included are the time varying Rayleigh, Rician and lognormal fading channels whose covariance functions have finite support, phase unsynchronized channels which satisfy the finite-memory constraint and point process channels. The information sequence may be either a stream of independent, equally-likely symbols of binary orM-ary alphabets or the output sequence of a trellis or convolutional encoder.     

On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory

For a stationary additive Gaussian-noise channel with a rational noise power spectrum of a finite-order L, we derive two new results for the feedback capacity under an average channel input power constraint. First, we show that a very simple feedback-dependent Gauss-Markov source achieves the feedback capacity, and that Kalman-Bucy filtering is optimal for processing the feedback. Based on these results, we develop a new method for optimizing the channel inputs for achieving the Cover-Pombra block-length- n feedback capacity by using a dynamic programming approach that decomposes the computation into n sequentially identical optimization problems where each stage involves optimizing O(L ²) variables. Second, we derive the explicit maximal information rate for stationary feedback-dependent sources. In general, evaluating the maximal information rate for stationary sources requires solving only a few equations by simple nonlinear programming. For first-order autoregressive and/or moving average (ARMA) noise channels, this optimization admits a closed-form maximal information rate formula. The maximal information rate for stationary sources is a lower bound on the feedback capacity, and it equals the feedback capacity if the long-standing conjecture, that stationary sources achieve the feedback capacity, holds     

On the Capacity of IEEE 802.11 DCF with Capture in Multipath-Faded Channels

In this paper, we estimated the influence of capture effect over the capacity of IEEE 802.11b DCF within a single picocell. The channel utilization is examined analytically by introducing two capture models based on Rayleigh-distributed envelopes of the captured and the interfering frames divided into two local-mean power classes. Simulations in a pure Rician-faded channel depict the conditions under which both Rayleigh-faded capture models can be used to accurately predict the peak network capacity. Unlike the RTS/CTS handshake access mode, Basic access mode is significantly sensitive to the capture ratio, i.e., the receiver design. The packet size threshold over which it is convenient to switch from Basic to RTS/CTS handshake access scheme is also sensitive to the capture effect.     

On the Capacity and Energy Efficiency of Training-Based Transmissions Over Fading Channels

In this paper, the capacity and energy efficiency of training-based communication schemes employed for transmission over a priori unknown Rayleigh block-fading channels are studied. Initially, the case in which the product of the estimate error and transmitted signal is assumed to be Gaussian noise is considered. In this case, it is shown that bit energy requirements grow without bound as the signal-to-noise ratio (SNR) goes to zero, and the minimum bit energy is achieved at a nonzero SNR value below which one should not operate. The effect of the block length on both the minimum bit energy and the SNR value at which the minimum is achieved is investigated. Flash training and transmission schemes are analyzed and shown to improve the energy efficiency in the low-SNR regime. In the second part of this paper, the capacity and energy efficiency of training-based schemes are investigated when the channel input vector in each coherence block is subject to peak power constraints. The capacity-achieving input structure is characterized and the magnitude distribution of the optimal input is shown to be discrete with a finite number of mass points. The capacity, bit energy requirements, and optimal resource allocation strategies are obtained through numerical analysis. The improvements in energy efficiency when on-off keying (OOK) with fixed peak power and vanishing duty cycle is employed are studied.     

On Noncoherent MIMO Channels in the Wideband Regime: Capacity and Reliability

We consider a multiple-input multiple-output (MIMO) wideband Rayleigh block-fading channel where the channel state is unknown to both the transmitter and the receiver and there is only an average power constraint on the input. We compute the capacity and analyze its dependence on coherence length, number of antennas and receive signal-to-noise ratio (SNR) per degree of freedom. We establish conditions on the coherence length and number of antennas for the noncoherent channel to have a "near-coherent" performance in the wideband regime. We also propose a signaling scheme that is near-capacity achieving in this regime. We compute the error probability for this wideband noncoherent MIMO channel and study its dependence on SNR, number of transmit and receive antennas and coherence length. We show that error probability decays inversely with coherence length and exponentially with the product of the number of transmit and receive antennas. Moreover, channel outage dominates error probability in the wideband regime. We also show that the critical as well as cutoff rates are much smaller than channel capacity in this regime     

On the Capacity of Underlay Multihop Cognitive Relaying Over Generalized-K Composite Fading Channels

Cognitive radio (CR) is one of the candidate enabling technologies for future wireless communication systems. This paper is devoted to analyze the capacity of underlay cognitive multihop relaying over independent and non-identically distributed generalized-K fading channels. In doing so, we derive upper and lower-bounded expressions for the ergodic capacity and the outage probability of the secondary user (SU), respectively. By using these expressions, new insights in the performance of the cognitive multihop amplify-and-forward relaying are revealed. The obtained results provide interesting details on the joint effect of shadowing and multipath fading on the capacity of the SU in relay-assisted underlay CR networks. The analytical results are verified by Monte-Carlo simulations for different fading conditions.     

Estimating the Ergodic Capacity of Log-Normal Channels

In this paper, we first provide a very accurate estimation of the capacity of a single-input single-output system operating in a log-normal environment. Then, hinging on the fact that the sum of log-normal Random Variables (RV) is well approximated by another log-normal RV, we apply the obtained results to find the capacity of Maximum Ratio Combining and Equal Gain Combining in a log-normal environment. The capacity in an interference-limited environment is also investigated in this paper. The analytical expressions obtained match perfectly the capacity given by simulations.     

Capacity Bounds for Sticky Channels

The capacity of sticky channels, a subclass of insertion channels where each symbol may be duplicated multiple times, is considered. The primary result is to provide nearly tight numerical upper and lower bounds for the independent and identically distributed (i.i.d.) duplication channel.     

On the Capacity of Secondary Networks Over Opportunistic Spectrum Access in Rayleigh Fading Channels

In this paper the effect of the opportunistic spectrum access on the spectrum utilization is studied in terms of the secondary network capacity measured at the secondary receiver. A mathematical model is developed to represent the secondary network capacity in Rayleigh fading channel. An exact analytical solution for the capacity is derived for both sensing and accessing fading channels. A numerical evaluation of the channel capacity is presented for different channel sensing and accessing schemes. The effects of detection and accessing channel parameters on the capacity are investigated. The analytical results that are validated by substantial simulations showed how the utilization of the network can be increased significantly by the suggested opportunistic spectrum accessing technique. It was found that when having a good sensing system with a high secondary user signal to noise ratio, accessing the licensed band increases and drives the spectrum utilization to its maximum. In addition, this work shows how the capacity can be positively affected by three factors: the secondary accessing channel, the primary user interference and the desired quality of service (QoS) of primary user. The awareness of a proper sensing scheme can maximize the spectrum utilization without degrading the QoS of primary users.     

On the Derivation of the Exact, Closed-Form Capacity Formulas for Receiver-Sided Correlated MIMO Channels

This paper solves the problem of finding a closed-form expression for the average information-theoretic capacity of wireless systems with an arbitrary number of transmitter and receiver antennas. It is assumed that only the receivers have (perfect) knowledge of the channel state and that fading correlation is receiver-sided. The main purpose of the paper is accomplished by introducing a few very simple concepts and performing some clear-cut algebraic manipulations, making the presentation virtually self-contained. The results show a substantial capacity reduction in the presence of correlation between receiver antennas. It is also shown that employing linear arrays with nonuniform spacings may improve the system capacity, and a simple technique to exploit this possibility is presented. Isotropic and nonisotropic propagation scenarios are studied.      

Feedback Capacity of Stationary Gaussian Channels

The feedback capacity of additive stationary Gaussian noise channels is characterized as the solution to a variational problem in the noise power spectral density. When specialized to the first-order autoregressive moving-average noise spectrum, this variational characterization yields a closed-form expression for the feedback capacity. In particular, this result shows that the celebrated Schalkwijk-Kailath coding achieves the feedback capacity for the first-order autoregressive moving-average Gaussian channel, positively answering a long-standing open problem studied by Butman, Tiernan-Schalkwijk, Wolfowitz, Ozarow, Ordentlich, Yang-Kavc?ic?-Tatikonda, and others. More generally, it is shown that a k-dimensional generalization of the Schalkwijk-Kailath coding achieves the feedback capacity for any autoregressive moving-average noise spectrum of order k. Simply put, the optimal transmitter iteratively refines the receiver's knowledge of the intended message. This development reveals intriguing connections between estimation, control, and feedback communication.