Nakagami信道的中断容量分析

本文讨论了Nakagami-m衰落信道系统的中断容量性能,在发射端未知信道信息,接收端的信道估计存在误差时,给出了计算中断容量上界和下界的表达式,它们是接收端的估计误差和信道参数的函数,仿真结果表明随着估计误差的增大中断容量的上界和下界同时降低,但是中断容量的下界随着信道参数的增大而增大,上界随着信道参数的增大而减小。     

Channel capacity and error exponents of variable rate adaptivechannel coding for Rayleigh fading channels

We have evaluated the information theoretical performance of variable rate adaptive channel coding for Rayleigh fading channels. The channel states are detected at the receiver and fed back to the transmitter by means of a noiseless feedback link. Based on the channel state informations, the transmitter can adjust the channel coding scheme accordingly. Coherent channel and arbitrary channel symbols with a fixed average transmitted power constraint are assumed. The channel capacity and the error exponent are evaluated and the optimal rate control rules are found for Rayleigh fading channels with feedback of channel states. It is shown that the variable rate scheme can only increase the channel error exponent. The effects of additional practical constraints and finite feedback delays are also considered. Finally, we compare the performance of the variable rate adaptive channel coding in high bandwidth-expansion systems (CDMA) and high bandwidth-efficiency systems (TDMA)     

Capacities of time-varying multiple-access channels with sideinformation

We determine the capacity regions for a class of time-varying multiple-access channels (TVMACs), when the underlying channel state evolves in time according to a probability law which is known to the transmitters and the receiver. Additionally, the transmitters and the receiver have access to varying degrees of channel state information (CSI) concerning the condition of the channel. Discrete-time channels with finite input, output, and state alphabets are considered first. The special case of a TVMAC, with the channel state process being a time-invariant, indecomposable, aperiodic Markov chain, shows a surprising anomaly in that imperfect transmitter CSI can cause the capacity under some distributions for the initial state to be strictly larger than that under a stationary distribution for the initial state. We also study a time-varying multiple-access fading channel with additive Gaussian noise, when various amounts of CSI are provided to the transmitters and perfect CSI is available to the receiver, and the fades are assumed to be stationary and ergodic. Implications for transmitter power control are discussed     

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.      

Gallager?s Exponent for MIMO Channels: A Reliability-Rate Tradeoff

In this paper, we derive Gallager's random coding error exponent for multiple-input multiple-output (MIMO) Rayleigh block-fading channels, assuming no channel-state information (CSI) at the transmitter and perfect CSI at the receiver. This measure gives insight into a fundamental tradeoff between the communication reliability and information rate of MIMO channels, enabling to determine the required codeword length to achieve a prescribed error probability at a given rate below the channel capacity. We quantify the effects of the number of antennas, channel coherence time, and spatial fading correlation on the MIMO exponent. In addition, the general formulae for the ergodic capacity and the cutoff rate in the presence of spatial correlation are deduced from the exponent expressions. These formulae are applicable to arbitrary structures of transmit and receive correlation, encompassing all the previously known results as special cases of our expressions.     

Exact BER analysis for M-QAM modulation with transmit beamforming under channel prediction errors

Significant throughput improvements can be obtained in multiple-inputmultiple-output (MIMO) fading channels by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. In general, accurate channel state information (CSI) is required to achieve these performance gains. In this paper, we analyze the impact of channel prediction error on the bit error rate (BER) of combined beamforming and MRC in slow Rayleigh fading channels. Exact closed-form BER expressions are obtained in terms of elementary functions. Numerical results show that imperfect CSI causes little BER degradation using channel prediction of moderate complexity.     

Random coding error exponents for flat fading channels withrealistic channel estimation

There has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realistic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI. Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied     

Joint channel estimation and resource allocation for MIMO systems-part I: single-user analysis

Multiple antenna systems are known to provide very large data rates, when the perfect channel state information (CSI) is available at the receiver. However, this requires the receiver to perform a noise-free, multi-dimensional channel estimation, without using communication resources. In practice, any channel estimation is noisy and uses system resources. We shall examine the trade-off between improving channel estimation and increasing the achievable data rate. We consider transmitside correlated multi-input multi-output (MIMO) channels with block fading, where each block is divided into training and data transmission phases. The receiver has a noisy CSI that it obtains through a channel estimation process, while the transmitter has partial CSI in the form of covariance feedback. In Part I of this two-part paper, we consider the single-user case, and optimize the achievable rate jointly over parameters associated with the training phase and data transmission phase. In particular, we first choose the training signal to minimize the channel estimation error, and then, develop an iterative algorithm to solve for the optimum system resources such as time, power and spatial dimensions. Specifically, the algorithm finds the optimum training duration, the optimum allocation of power between training and data transmission phases, the optimum allocation of power over the antennas during the data transmission phase.     

Space–Time Constellation Design for Partial CSI at the Receiver

The design of signal constellations for a communication system using multiple transmitter antennas over a Rayleigh-fading channel is considered under the assumption that no channel state information (CSI) is available at the transmitter and the receiver has acquired a CSI estimate with known error covariance. This setup encompasses the well-studied scenarios of perfect and no channel knowledge at the receiver and allows a smooth transition between these two cases. The data detection performance as a function of the CSI error covariance is analyzed and used to investigate the design of training blocks if such blocks are transmitted to provide CSI to the receiver. Moreover, two approaches to design constellations adapted to the error covariance of the receiver CSI are presented. Whereas the first approach is based on a generic gradient search method, the second approach uses an appropriate combination of constellations designed for perfect and no CSI at the receiver. Simulations confirm the benefits of the presented designs.     

Practical robust uniform channel decomposition scheme for CSI mismatch in limited feedback MIMO systems

Uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) is assumed to be available at both the transmitter and receiver side. In practice, CSI can be obtained by channel estimation at receiver and conveyed to transmitter via a limited-rate feedback channel. In such case, the implementation of traditional UCD by treating the imperfect CSI as perfect CSI cause significant performance degradation due to inevitable channel estimation error and vector quantization error. To overcome this problem, a practical robust UCD scheme was proposed in this paper, which includes two steps, firstly, a matching architecture was proposed to eliminate the mismatch between CSI at receiver (CSIR) and CSI at transmitter (CSIT), secondly, an MMSE based robust UCD scheme considering channel estimation error and vector quantization error as an integral part of the design was derived. Simulation results show that the proposed practical robust UCD scheme is capable of improving the BER performance greatly in the context of channel estimation error and vector quantization error compared with the traditional UCD scheme.     

Capacity of correlated MIMO Rayleigh channels

Abstract-This paper presents some exact results on the capacity of multiple-input-multiple-output (MIMO) channels subject to correlated Rayleigh fading when perfect channel state information (CSI) is known at the receiver. The authors focus on the semicorrelated scenario in which correlation exists either at the transmitter or at the receiver., They consider two cases: 1) the transmitter does not have any CSI and as such allocates power equally among transmitter antennas and 2) the transmitter only knows the statistical distribution of the channel. The first case derives the moment generating function (MGF) of the mutual information (MI) and then deduces from this MGF the mean MI. The authors also study the cumulative distribution function (CDF) of the MI, which can serve as an upper bound to the outage probability under the capacity versus outage formulation when the channel is nonergodic. The second case studies the capacity achieved by optimum power-loading and beamforming schemes based on covariance feedback. Numerical results illustrate that the full capacity of MIMO systems can be preserved even for relatively high values of correlation coefficients.     

Fading Channel Prediction for Mobile Radio Adaptive Transmission Systems

Adaptive transmission methods can potentially aid the achievement of high data rates required for mobile radio multimedia services. To realize this potential, the transmitter needs accurate channel state information (CSI) for the upcoming transmission frame. In most mobile radio systems, the CSI is estimated at the receiver and fed back to the transmitter. However, unless the mobile speed is very low, the estimated CSI cannot be used directly to select the parameters of adaptive transmission systems, since it quickly becomes outdated due to the rapid channel variation caused by multipath fading. To enable adaptive transmission for mobile radio systems, prediction of future fading channel samples is required. Several fundamental issues arise in the design and testing of fading prediction algorithms for adaptive transmission systems. These include complexity, robustness, choice of an appropriate channel model for algorithm validation, channel estimation and noise reduction required for reliable prediction, and design and analysis of adaptive transmission methods aided by fading prediction algorithms. We use these criteria in the review of recent advances in the area of fading channel prediction. We also demonstrate that reliable fading prediction makes adaptive transmission feasible in diverse wireless communication systems.     

Outage Behavior of Discrete Memoryless Channels Under Channel Estimation Errors

Communication systems are usually designed by assuming perfect channel state information (CSI). However, in many practical scenarios, only a noisy estimate of the channel is available, which may strongly differ from the true channel. This imperfect CSI scenario is addressed by introducing the notion of estimation-induced outage (EIO). We derive a single-letter characterization of the maximal EIO rate and prove an associated coding theorem and its strong converse for discrete memoryless channels (DMCs). The transmitter and the receiver rely on the channel estimate and the statistics of the estimate to construct codes that guarantee reliable communication with a certain outage probability. This ensures that in the non-outage case the transmission meets the target rate with small error probability, irrespective of the quality of the channel estimate. Applications of the EIO capacity to a single-antenna (nonergodic) Ricean fading channel are considered. The EIO capacity for this case is compared to the EIO rates of a communication system in which the receiver decodes by using a mismatched maximum-likelihood (ML) decoder. The effects of rate-limited feedback to provide the transmitter with quantized CSI are also investigated.      

Robust Uniform Channel Decomposition and Power Allocation for MIMO Systems with Imperfect CSI

In point to point MIMO systems, uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) are assumed to be available at both the transmitter and the receiver side. However, in practice, CSI can be obtained at the transmitter if there is reciprocity between the forward and reverse channels in time division duplex (TDD) systems or can be conveyed from the receiver to the transmitter via a feedback channel. In any case, channel estimation error is inevitable. In this paper, a novel robust UCD scheme and corresponding optimal robust power allocation are proposed, which are capable of improving the BER performance in the context of imperfect CSI compared with the conventional UCD scheme and the robust precoding scheme proposed by Amir D. Dabbagh and David J. Love. Simulation results show that the MIMO channel capacity of the proposed robust UCD scheme is higher than that of the conventional UCD scheme. By deriving and analyzing the MIMO channel capacity lower bound of the robust UCD scheme, we prove that our proposed robust UCD scheme is capacity lossless in a channel estimation error existing MIMO system.     

Optimum Receiver for a Realistic Transmit–Receive Diversity System in Correlated Fading

A transmit–receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path, is considered. The imperfect channel state information (CSI) is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum-likelihood (ML) sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect CSI and the transmit weight vector, is derived for the system. For the case of $M$-ary phase-shift keying (MPSK), an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained, with the transmit weight vector chosen to minimize this conditional SEP. For the receive-only and transmit-only correlation scenarios with ill-conditioned eigenvalues of the receive and transmit covariance matrices (that is, some of the eigenvalues are very small), we derive expressions for the diversity gain. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading. These results show that the optimum receiver typically has about a 0.5-dB gain over a conventional receiver when the correlation coefficient exceeds 0.5 and the number of receive antennas is much larger than the number of transmit antennas.      

Channel estimation and long-range prediction of fast fading channels for adaptive OFDM system

This correspondence presents the channel estimation and long-range prediction technique for adaptive-orthogonal-frequency-division-multiplexing (AOFDM) system. The efficient channel loading is accomplished by feeding the accurately predicted channel-state-information (CSI) back to transmitter. The frequency-selective wireless fading channel is modelled as a tapped-delay-line-filter governed by a first-order autoregressive (AR1) process; and an adaptive channel estimator based on the generalised-variable-step-size least-mean-square (GVSS-LMS) algorithm tracks AR1 correlation coefficient. To compensate for the signal fading due to channel state variations, a modified-Kalman-filter (MKF)-based channel estimator is utilised. In addition, channel tracking is also performed for predicting future CSI at receiver, based on the numeric-variable-forgetting-factor recursive-least-squares (NVFF-RLS) algorithm. Subsequently, adaptive bit allocation for AOFDM system is employed by using predicted CSI at transmitter. Here, the proposed combination of GVSS-LMS and MKF algorithms for robust channel estimation and the NVFF-RLS algorithm for efficient channel prediction is incorporated. The performance validation of presented method is carried out by using different channel realisations through simulation, and also by comparing it with fixed step-size LMS, MKF and fixed forgetting-factor RLS algorithm based conventional techniques. Eventually, the reliable performance of underlying AOFDM system can be achieved in terms of the lower mean squared estimation/prediction errors and alleviated symbol error rate.     

Reliable adaptive modulation aided by observations of another fading channel

Adaptive transmission techniques, such as adaptive modulation and coding, adaptive power control, adaptive transmitter antenna diversity, etc., generally require precise channel estimation and feedback of channel state information (CSI). For fast vehicle speeds, reliable adaptive transmission also requires long-range prediction of future CSI, since the channel conditions are rapidly time variant. In this paper, we propose using past channel observations of one carrier to predict future CSI and perform adaptive modulation without feedback for another correlated carrier. We derive the minimum mean-square error (MMSE) long-range channel prediction that uses the time- and frequency-domain correlation function of the Rayleigh fading channel. An adaptive MMSE prediction method is also proposed. A statistical model of the prediction error that depends on the frequency and time correlation is developed and is used in the design of reliable adaptive modulation methods. We use a standard stationary fading channel model (Jakes model) and a novel physical channel model to test our algorithm. Significant gains relative to nonadaptive techniques are demonstrated for sufficiently correlated channels and realistic prediction range.     

Capacity of multiple-antenna systems with both receiver and transmitter channel state information

The capacity of multiple-antenna systems operating in Rayleigh flat fading is considered under the assumptions that channel state information (CSI) is available at both transmitter and receiver, and that the transmitter is subjected to an average power constraint. First, the capacity of such systems is derived for the special case of multiple transmit antennas and a single receive antenna. The optimal power-allocation scheme for such a system is shown to be a water-filling algorithm, and the corresponding capacity is seen to be the same as that of a system having multiple receive antennas (with a single transmitter antenna) whose outputs are combined via maximal ratio combining. A suboptimal adaptive transmission technique that transmits only over the antenna having the best channel is also proposed for this special case. It is shown that the capacity of such a system under the proposed suboptimal adaptive transmission scheme is the same as the capacity of a system having multiple receiver antennas (with a single transmitter antenna) combined via selection combining. Next, the capacity of a general system of multiple transmitter and receiver antennas is derived together with an equation that determines the cutoff value for such a system. The optimal power allocation scheme for such a multiple-antenna system is given by a matrix water-filling algorithm. In order to eliminate the need for cumbersome numerical techniques in solving the cutoff equation, approximate expressions for the cutoff transmission value are also provided. It is shown that, compared to the case in which there is only receiver CSI, large capacity gains are available with optimal power and rate adaptation schemes. The increased capacity is shown to come at the price of channel outage, and bounds are derived for this outage probability.     

Rateless coded Orthogonal Frequency Division Multiplexing system design based on intercarrier interference self‐cancelation

In this paper, we consider a rateless coded Orthogonal Frequency Division Multiplexing (OFDM) system under a quasistatic fading channel. During each transmission round, transmitter keeps transmitting to the receiver using Raptor code until the receiver feeds back an acknowledgement (ACK). On the other hand, frequency offset between the transmitter and receiver ruins the orthogonality of OFDM subcarriers and cause intercarrier interference (ICI). We resort to ICI self‐cancelation precoding to combat ICI, wherein the data symbol vectors are multiplied with some precoding matrix before transmission. To improve the system robustness, we jointly optimize the precoding matrix and the degree profile of Raptor code, with only statistical channel state information (CSI) being assumed at the transmitter. The optimization problem is formulated based on the extrinsic information transfer (EXIT) analysis of the decoding process at the receiver. The advantage of the proposed design is that the instant CSI is not required at the transmitter, which reduces the system overhead. Simulation results verify that the proposed scheme with the optimized precoding matrix and degree profile can effectively combat ICI and achieve good performance both in bit error ratio (BER) and average transmission rate.     

Achievable Rates with Imperfect Transmitter Side Information Using a Broadcast Transmission Strategy

rdquoWe investigate the performance of the broadcast approach for various fading distributions, which correspond to different models of partial transmit channel state information (CSI). The first model considered is the quantized limited feedback. In this model, the receiver can send as feedback only a finite number of bits describing the fading gain. We derive the optimal power allocation for the broadcast approach for the quantized feedback model. For a Rayleigh fading channel, numerical results here show that if the feedback word can be longer than one bit, the broadcasting gain becomes negligible, due to diminished channel uncertainty. The second partial transmit CSI model is a stochastic Gaussian model with mean and variance information, which is commonly used for modeling the channel estimation error. In a single-input single-output (SISO) channel, this model also corresponds to the Ricean fading distribution, for which we derive maximal achievable broadcasting rates. We further consider a multiple-input single-output (MISO) channel, and derive the optimal power allocation strategy in a broadcast approach. Numerical results here show that uniform power allocation is preferable over beamforming power allocation in the region where broadcasting gain over single level coding is non-negligible.