Capacity Analysis for Continuous-Alphabet Channels With Side Information, Part I: A General Framework

Capacity analysis for channels with side information at the receiver has been an active area of interest. This problem is well investigated for the case of finite-alphabet channels. However, the results are not easily generalizable to the case of continuous-alphabet channels due to analytical difficulties inherent with continuous alphabets. In the first part of this two-part paper, we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver. For this purpose, we establish novel necessary and sufficient conditions for weak* continuity and strict concavity of the mutual information. These conditions are used in investigating the existence and uniqueness of the capacity-achieving measures. Furthermore, we derive necessary and sufficient conditions that characterize the capacity value and the capacity-achieving measure for continuous-alphabet channels with side information at the receiver.     

Capacity of Time-Varying Channels With Causal Channel Side Information

We derive the capacity of time-varying channels with memory that have causal channel side information (CSI) at the sender and receiver. We obtain capacity of block-memoryless and asymptotically block-memoryless channels with block-memoryless or weakly decorrelating side information. Our coding theorems rely on causal generation of the codewords relative to the causal transmitter CSI. The CSI need not be perfect, and we consider the case where the transmitter and receiver have the same causal CSI as well as the case where the transmitter CSI is a deterministic function of the receiver CSI. For block-memoryless and asymptotically block-memoryless channels, our coding strategy averages mutual information density over multiple transmission blocks to achieve the maximum average mutual information. We apply the coding theorem associated with the block-memoryless channel to determine the capacity and optimal input distribution of intersymbol interference (ISI) time-varying channels with causal perfect CSI about the time-varying channel. The capacity of this channel cannot be found through traditional decomposition methods     

Capacity of the Class of MIMO Channels With Incomplete CDI—Properties of Mutual Information for a Class of Channels

This paper is concerned with multiple-input multiple-output (MIMO) wireless channel capacity, when the probability distribution of the channel matrix p(H) is not completely known to the transmitter and the receiver. The partial knowledge of a true probability distribution of the channel matrix p(H) is modelled by a relative entropy D(middot||middot) such that D(p||p_nom) les d, d ges 0, where d is the distance from the so-called nominal channel matrix distribution p_nom(H). The capacity of this compound channel is equal to the maximin of the mutual information, where the minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. The existence of a minimizing probability distribution is proved, and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution p_nom(H) and parameter d. A number of properties of the mutual information, minimized over the set of channel distributions, are derived. Specifically, upper and lower bounds are derived for the minimized mutual information, while its convexity with respect to d is shown. In the case of the Rayleigh fading, an explicit formula for the capacity and the optimal transmit covariance matrix are derived.     

Rayleigh环境下MIMO系统容量分析

研究了多输入多输出(MIMO)系统Rayleigh衰落信道矩阵的特征值以及天线空间相关性对信道容量的影响.Monte-Carlo数值仿真结果表明:MIMO系统能极大提高Rayleigh衰落环境中的系统容量,且容量随最小收发天线数目的增加而线性增加,但由于相关性对信道矩阵特征值及其统计分布的影响较大,因此可导致MIMO系统容量的损失.     

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。     

Multiple-Antenna Signaling Over Fading Channels With Estimated Channel State Information: Capacity Analysis

Multiple-antenna concepts for wireless communication systems promise high spectral efficiencies and improved error rate performance by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the capacity of Rayleigh and Ricean block-fading channels. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. The training symbols are used to estimate the channel state information (CSI) at the receiver by means of an arbitrary linear estimation filter. No CSI is assumed at the transmitter. Our analysis is based on an equivalent system model for training-based multiple-antenna systems which specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent, multiplicative noise. This model includes the special cases of perfect CSI and no CSI. We present new upper and lower bounds on the maximum instantaneous mutual information to compute ergodic and outage capacities, and extend previous results to arbitrary (and possibly mismatched) linear channel estimators and to correlated Ricean fading. Several numerical results for single- and multiple-antenna systems with estimated CSI are included as illustration.     

接收机准确估计信道条件下MIMO系统的信道容量分析

文中考虑独立Rayleigh衰落环境下的单用户点对点多输入多输出系统,假定接收端能准确估计信道状态信息,推导出系统的容量公式,相比单天线系统,多天线系统能取得更大的容量,当输入信号是高斯分布时,系统容量随着发射天线和接收天线数目的最小值线性增加,如果发送端完全知道信道状态信息,采用注水原理的功率分配策略,可以获得更高的容量增益,最后推导出各态历经容量的数学表达式.     

Capacity Analysis of MIMO Group-Broadcast Channels with Time-Division Scheduling

This paper investigates the ergodic sum capacity for a MIMO group-broadcast channel with time-division scheduling (TDS). In this scheme, the overall user set is divided into subgroups, among which a single user subgroup which maximizes the instantaneous sum capacity will be scheduled at a time. In order to characterize the TDS performance, we first derived an asymptotic bound to the full capacity obtained by dirty paper coding (DPC). This bound is a closed-form expression and performs well for different system configurations. Further concerning practical precoding techniques, we studied its achievable sum capacity by using block-diagonalization (BD) and zero-forcing (ZF) precoding. Based on these results, the achieved scheduling gain by TDS over random scheduling is analyzed. We also compared the scheduling gains under different transmission strategies including DPC, BD, and ZF precoding. The results reveal that TDS provides the largest scheduling gain for the system with ZF precoding. Finally, we also discussed the effect of the group cardinality on the performance of TDS. Numerical results show the tightness of derived capacity bounds and verify the correctness of our analysis.     

Capacity and Random-Coding Exponents for Channel Coding With Side Information

Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence, and the channel is selected by a hypothetical adversary. Partial information about the state sequence is available to the encoder, adversary, and decoder. The design of the transmitter is subject to a cost constraint. Two families of channels are considered: 1) compound discrete memoryless channels (CDMC), and 2) channels with arbitrary memory, subject to an additive cost constraint, or more generally, to a hard constraint on the conditional type of the channel output given the input. Both problems are closely connected. The random-coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder, which may be thought of as an empirical generalized maximum a posteriori decoder. For channels with arbitrary memory, the random-coding exponents are larger than their CDMC counterparts. Applications of this study include watermarking, data hiding, communication in presence of partially known interferers, and problems such as broadcast channels, all of which involve the fundamental idea of binning     

Capacity With Causal and Noncausal Side Information: A Unified View

In this correspondence, we identify the common underlying form of the capacity expression that is applicable to both cases where causal or noncausal side information is made available to the transmitter. A genie-aided outerbound is developed that states that when a genie provides n bits of side information to a receiver the resulting capacity improvement cannot be more than n bits. Using the genie-bound we are able to bound the relative capacity advantage of noncausal side information over causal side information for both the single user point-to-point channel as well as the multiple-access channel (MAC) with independent side information at the transmitters. Applications of these capacity bounds are demonstrated through examples of random access channels. Interestingly, the capacity results indicate that the excessive MAC layer overheads common in present wireless systems may be avoided through coding across multiple-access blocks. It is also shown that even one bit of side information at the transmitter can result in unbounded capacity improvement     

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.     

Measured MIMO Capacity and Diversity Gain With Spatial and Polar Arrays in Ultrawideband Channels

This paper experimentally investigates the performance of multiple-input multiple-output (MIMO) systems in indoor ultrawideband (UWB) channels. The improvement in robustness and information rate due to spatial and polar antenna arrays is evaluated. The subchannel correlation, power gains of supported eigenmodes, and branch power ratios are analyzed. The polar arrays are found to experience lower correlation than that of spatial arrays. SNR gains of up to 3 and 5 dB are reported with 1times2 and 1times3 spatial arrays, respectively; the latter is shown to double the coverage range. The mutual information capacity is found to scale almost linearly with the MIMO array size, with very low variance. It is confirmed that the device compactness achieved by the polar array comes with only a small penalty in the achievable capacity and SNR gain compared to the spatial array. The multiple-antenna UWB techniques explored in this paper offer the potential for high-data-rate, robust communications.     

On the Expected Rate of Slowly Fading Channels With Quantized Side Information

We study a multiple-layer variable-rate system employing quantized feedback to maximize the expected rate over a single-input single-output slowly fading Gaussian channel. The transmitter uses partial channel-state information, which is obtained via an optimized resolution-constrained feedback link, to adapt the power and to assign code layer rates, subject to different power constraints. To systematically design the system parameters, we develop a simple iterative algorithm that successfully exploits results in the study of parallel broadcast channels. We present the necessary and sufficient conditions for single-layer coding to be optimal, irrespective of the number of code layers that the system can afford. Unlike in the ergodic case, even coarsely quantized feedback is shown to improve the expected rate considerably. Our results also indicate that with as little as one bit of feedback information, the role of multilayer coding reduces significantly     

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     

Capacity Bounds for Broadcast Channels With Confidential Messages

This paper studies capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. Both inner and outer bounds are proposed to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszar and Korner's rate equivocation region for broadcast channels with a single confidential message, Liu 's achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand-Pinsker's achievable rate region for general broadcast channels. The proposed outer bounds, together with the inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including the less noisy, deterministic, and semideterministic broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.     

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。     

基于不同调度算法的多用户分集MIMO中继信道容量分析

采用平均容量性能来定量分析多用户分集多输入多输出(MIMO)中继信道,中继节点使用放大转发(Amplify-and-forward,AF)协议将接收到的源节点的发送信号重发给目的节点.研究了多用户MIMO中继信道的不同调度算法,即容量公平、最大特征根、最小特征根调度策略和空间独立性调度算法,结果表明空间独立性调度算法有...     

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 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.