Average channel capacity for Rayleigh fading spread spectrum MIMO systems

In this paper, a novel approach to the problem of estimating the average channel capacity (in the Shannon sense) assigned to each user of a spread spectrum (SS) multiple‐input multiple‐output (MIMO) system operating in a Rayleigh fading environment, is presented. The analysis leads to a closed‐form expression which fully conforms to the upper bound of the channel capacity value of a non‐fading AWGN channel when the transmitted signal bandwidth tends to infinity proving the validity of the described analysis. Copyright © 2006 John Wiley & Sons, Ltd.     

Asymptotic spectral efficiency of multicell MIMO systems with frequency-flat fading

The spectral efficiency of multiple-input multiple-output (MIMO) systems operating in multicell frequency-flat fading environments is studied for situations in which co-channel interference is the dominant channel impairment instead of ambient noise. The following detectors are analyzed: the joint optimum detector, a group linear minimum-mean-square-error (MMSE) detector and its generalized version, a group MMSE successive interference cancellation detector, and an adaptive multiuser detector, with the focus on their large-system asymptotic (nonrandom) expressions. Analytical and numerical results based on these asymptotic multicell MIMO spectral efficiencies are explored to gain insights into the behavior of interference-limited multicell MIMO systems.     

基于频谱效率的低复杂度自适应MIMO系统

在一定的误比特率(BER)下,使用自适应MQAM调制可以最大化MIMO系统的频谱效率。通过不同的算法可以得到自适应调制MIMO系统的离散速率频谱效率(DRSE)。为了进一步提高频谱效率,提出了一种基于DRSE,在不同的算法之间进行切换的低复杂度自适应机制。研究了在两种2×2信道下即:独立同分布(i.i.d)的平坦瑞利衰落信道和空间相关的瑞利衰落信道,自适应MIMO系统在正交空时块编码(OSTBC)和空间复用(SM)之间切换的自适应机制。仿真结果表明,通过选择一种最优的调制模式及发射模式的组合方式,此切换算法可以使系统的频谱效率得到有效提高,同时只增加有限的反馈信息,降低了系统复杂度。     

On the capacity of Rayleigh fading cooperative systems under adaptive transmission

In this letter, the use of adaptive source transmission with amplify-and-forward relaying is proposed. Three different adaptive techniques are considered: (i) optimal simultaneous power and rate adaptation; (ii) constant power with optimal rate adaptation; (iii) channel inversion with fixed rate. The capacity upper bounds of these adaptive protocols are derived for the amplify-and-forward cooperative system over both independent and identically distributed (i.i.d.) Rayleigh fading and non-i.i.d. Rayleigh fading environments. The capacity analysis is based on an upper bound on the effective received signal-to-noise ratio (SNR). The tightness of the upper bound is validated by the use of a lower bound and by Monte Carlo simulation. It is shown that at high SNR the optimal simultaneous power and rate adaptation and the optimal rate adaptation with constant power provide roughly the same capacity. Channel inversion is shown to suffer from a deterioration in capacity relative to the other adaptive techniques.     

Mutual information statistics for dual MIMO systems in correlated Rayleigh fading

In this letter, we derive very simple and exact expressions for the mutual information (MI) distributions under isotropic Gaussian input of dual multiple-input multiple-output (MIMO) systems, where the minimum number of antennas at either side of the wireless link is two, in a semicorrelated Rayleigh fading environment with correlation at the dual-antenna side only. Furthermore, exact closed-form expressions for the MI moments (mean, variance), and other higher order statistics, such as the skewness and kurtosis, are derived. The proposed methodology for evaluating the MI statistics, is easily extendable to other multielement antenna settings such as single-input multiple-output (SIMO), multiple-input single-output (MISO) and dual MIMO systems for both uncorrelated and semicorrelated Rayleigh fading, where correlation can be assumed at the side with the largest number of antennas.     

Analysis of capacity and coverage region for Rayleigh fading MIMO relay channel

In this paper, we consider Rayleigh fading MIMO relay channel with channel state information at the receivers. First, we extend the previously obtained results for the ergodic capacity of uncorrelated and semi‐correlated MIMO channels and derive closed‐form expressions for the capacity bounds of MIMO relay channel. Next, we study this channel from a new point of view, maximizing coverage region for a desired transmission rate, and investigate the optimal relay location in the sense of maximizing coverage region. However, in order to overcome the mathematical complexity in desired transmission rate analysis, because of the randomness of the multiple antenna channel matrices, we evaluate this rate by using an existing exact formula and also by an approximation we find in the high signal‐to‐noise ratio regime. Numerical results show a perfect match between the Monte Carlo simulations and the obtained analytical closed‐form expressions and also confirm the effectiveness of our approach in cooperative vehicular communication for determining optimal relay location at which the coverage region is maximum. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymptotic spectral efficiency of MIMO multiple-access wireless systems exploring only channel spatial correlations

In this paper, we use the replica method originally developed in statistical physics to investigate the asymptotic sum-rate of a Gaussian antenna-array-based multiple-input multiple-output (MIMO) multiple-access (MA) wireless channel having spatial correlations at both the transmitters and the receiver. Through numerical experiments, the asymptotic solution can consistently produce highly accurate ergodic results for MIMO-MA systems with only a few antenna elements at each transmitter and receiver. This offers the asymptotic solution important practical values in analyzing and designing a MIMO multiple access system that makes best use of the wireless channel structure. Furthermore, with the asymptotic solution, we provide an efficient optimization algorithm to determine the asymptotic optimum transmit signal covariance matrices when only the slow-varying channel spatial covariance information is available.     

Impact of channel prediction on adaptive coded modulation performance in Rayleigh fading

Adaptive coded modulation (ACM) is a promising tool for increasing the spectral efficiency of time-varying mobile channels while maintaining a predictable bit-error rate (BER). An important restriction in systems with such a transmission scheme is that the transmitter needs to have accurate channel-state information (CSI). Earlier analysis of ACM systems usually assumes that the transmitter has perfect knowledge of the channel or that the CSI is accurate but outdated. In this paper, we investigate the effects of predicting the CSI using a linear fading-envelope predictor in order to enhance the performance of an ACM system. For the case in which multidimensional trellis codes are used on Rayleigh-fading channels, we obtain approximative closed-form expressions for BER and average spectral efficiency. Numerical examples are given for the case of Jakes correlation profile and maximum a posteriori-optimal predictor coefficients.     

相关衰落信道MIMO STBC分集增益与多用户自适应OFDMA研究

首先沿用经典的分集增益特性分析了在已知与未知多输入多输出（MIMO）信道状况的条件下空时分组码（STBC）接收机的性能,从而揭示了相关衰落下信道矩阵的秩和特征值扩展对分集增益与编码增益等极其重要的影响;接着提出了一种与多天线STBC等效的单发单收（SISO）模型,将复杂的分集增益指标转换为直观的SNR指标,明确表示出接收机SNR与信道相关矩阵之间的关系,并以此为基础,提出一种实用的多用户MIMO-OFDM系统STBC编码优化的子载波资源分配OFDMA方法,进一步提高频谱效率与系统性能.     

Rayleigh衰落信道下多载波DS-CDMA系统性能分析

本文基于多载波传输技术，提出了一种多载波码分多址模型。并在Rayleigh衰落信道下对其误码性能进行了分析。分析及仿真结果表明，系统具有降低多址干扰的能力，同传统的单载波直接序列码分多址系统相比，能支持更大的用户容量。本系统能满足第三代移动通信系统对高速数据传输的要求。     

Discrete Rayleigh fading channel modeling

In order to understand the behaviour of upper‐layer protocols and to design or fine tune their parameters over wireless networks, it is common to assume that the underlying channel is a flat Rayleigh fading channel. Such channels are commonly modeled as finite state Markov chains. Recently, hidden Markov models have also been employed to characterize these channels. In this paper, we study the different models that have been proposed along with the analysis of their validity. We start by presenting some preliminary concepts related to the modeling of the wireless communications channel. We then proceed to introduce finite state Markov channel models (FSMCs) along with the relations between them and the modulation schemes, error control protocols and channel coding. We propose and study the effects of taking into account the fading process in its characterization. We finish with a discussion on hidden Markov models for Rayleigh fading channel modeling. Copyright © 2004 John Wiley & Sons, Ltd.     

The impact of fading correlation on the error performance of MIMO systems over Rayleigh fading channels

This paper analyzes the impact of receive fading correlation on the error performance of a multiple-input multiple-output (MIMO) system that employs a zero-forcing detection scheme over frequency-nonselective Rayleigh fading channels. Error rate expressions as a function of the eigenvalues of the fading correlation matrix and the number of transmit and receive antennas are derived. Numerical results indicate that MIMO systems are resistant to receive fading correlation.     

Bi-directional LSTM based channel estimation in 5G massive MIMO OFDM systems over TDL-C model with Rayleigh fading distribution

In this work, a deep learning (DL)-based massive multiple-input multiple-output (mMIMO) orthogonal frequency division multiplexing (OFDM) system is investigated over the tapped delay line type C (TDL-C) model with a Rayleigh fading distribution at frequencies ranging from 0.5 to 100 GHz. The proposed bi-directional long short-term memory (Bi-LSTM) channel state information (CSI) estimator uses online learning during training and offline learning during the practical implementation phase. The design of the estimator takes into account situations in which prior knowledge of channel statistics is limited and targets excellent performance, even with limited pilot symbols (PS). Three separate loss functions (mean square logarithmic error [MSLE], Huber, and Kullback–Leibler Distance [KLD]) are assessed in three classification layers. The symbol error rate (SER) and outage probability performance of the proposed estimator are evaluated using a number of optimization techniques, such as stochastic gradient descent (SGD), momentum, and the adaptive gradient (AdaGrad) algorithm. The Bi-LSTM-based CSI estimator is trained considering a specific number of PS. It can be readily seen that by incorporating a cyclic prefix (CP), the system becomes more resilient to channel impairments, resulting in a lower SER. Simulations show that the SGD optimization approach and Huber loss function-trained Bi-LSTM-based CSI estimator have the lowest SER and very high estimation accuracy. By using deep neural networks (DNNs), the Bi-LSTM method for CSI estimation achieves a superior channel capacity (in bps/Hz) at 10 dB than long short-term memory (LSTM) and other conventional CSI estimators, such as minimum mean square error (MMSE) and least squares (LS). The simulation results validate the analytical results in the study.     

On multilevel coded MPSK for the Rayleigh fading channel

This paper presents a new upper bound on the pair-wise error probability of MPSK sequences for the Rayleigh fading channel when channel state information (CSI) is unavailable. This bound is derived by adding weight factors in computing symbol metrics. Simulation results show that the weight factors which optimize the upper bound likely optimize the error rate as well. Multilevel coded MPSK schemes for the Rayleigh fading channel are also devised. Results show that the added weight factors improve the error performance of these schemes in the case that CSI is unavailable     

On first-order Markov modeling for the Rayleigh fading channel

Previous models for the received signal amplitude of the flat-fading channel that use first-order finite-state Markov chains are examined. The stochastic properties of a proposed first-order model based on these models are examined. The limitations of using an information theoretic metric, which is sometimes used to justify a first-order Markov chain as a sufficient model for very slowly fading channels, are discussed. A simple method of qualitatively comparing autocorrelation functions is instead proposed. The usefulness of the first-order Markov chain in representing the flat-fading channel is examined by looking at two specific problems in wireless system applications that represent two disparate cases. The first case involves analysis over a short duration of time, relative to the inverse of the normalized Doppler frequency, while the second involves analysis over a long duration of time. Contrary to previous reports, the results indicate that first-order Markov chains are not generally suitable for very slowly fading channels. Rather, first-order Markov chains can be suitable for very slowly fading applications, which require analysis over only a short duration of time     

快衰落信道下的分布式MIMO差分检测方案

在快衰落分布式MIMO系统中,由于信道状态信息的快速变化,很难满足相邻空时码块的信道衰落系数保持不变,导致传统的分布式MIMO差分检测方案性能严重下降而不再适用。针对这一问题,提出了一种改进的分布式MIMO的差分检测方案。这种方案通过在发送端重组相位差分调制后的空时码矩阵,以一定的处理时延和额外的能量开销来降低信道的快速变化对系统性能的影响。理论分析与计算机仿真均表明,在快衰落环境中,与已有的分布式发射天线差分空时检测相比能够显著提高系统的误码性能。     

瑞利衰落时MIMO无线通信系统分集性能分析

针对多输入多输出（MIMO）无线通信系统提高系统性能的同时增加了系统的复杂度，提出了基于最大特征值传输的分集解决方案，在天线数量一定的情况下最大可能的提高系统的分集增益。对单输入多输出和多输入多输出的情况进行了数学分析，推导出了系统性能的变化范围，并且对分析的结果进行了数值仿真。     

Decision-directed estimation of MIMO time-varying Rayleigh fading channels

This paper presents a decision-directed (DD) maximum a posteriori probability (MAP) channel-estimation scheme for multiple-input multiple-output (MIMO) time-varying fading channels. With the estimate of the channel matrix for the current symbol interval, a zero-forcing (ZF) receiver is applied to detect the spatially multiplexed data on a symbol-by-symbol basis. Symbol decisions are then fed to the channel predictor for estimation of channel coefficients in future symbol intervals. Simulated error performance of a ZF receiver with the DD MAP and perfect channel estimates is provided and compared.     

MIMO-OFDM快衰落信道的稀疏自适应感知估计

在多输入多输出（MIMO）-正交频分复用（OFDM） 系统中,怎样在较高频谱利用率的情况下对快时变信道进行较为准确的估计是一个具有挑战性的课题。该文在利用压缩感知理论可提高系统频谱利用率的基础上,提出了一种适合于快时变环境下MIMO-OFDM 系统的稀疏自适应信道估计方法。该方法不再受到奈奎斯特采样频率条件约束,避免了传统导频辅助信道估计方法频谱利用率低的缺点。该文方法通过构建多天线群时频结构特征稀疏基,利用多天线间和群时变OFDM符号内信道冲激响应具有更强稀疏性的特点,对MIMO-OFDM快衰落信道进行稀疏变换。由于实际MIMO-OFDM快衰落信道往往处于频率选择性、时变性和多种干扰并存的复杂环境,受到干扰的信道参数对系统而言是未知,采用该方法克服了现有基于压缩感知理论的信道估计方法需要预先知道信道冲激响应稀疏度才能重构信道参数的不足,在信道稀疏度未知道的情况下,运用稀疏自适应的方法来对不同时频结构特征的信道参数进行估计。仿真结果表明所提估计方法具有对快时变信道参数估计的鲁棒性和较高频谱利用率,且均方误差小。      

Blind estimation and detection of space-time trellis coded transmissions over the Rayleigh fading MIMO channel

We present a joint channel estimation and detection method of space-time trellis codes (STTC) in the context of an unknown flat fading multiple-input multiple-output (MIMO) channel. A combined state-space model for the space-time code and the Rayleigh fading MIMO channel is introduced, in order to use deterministic particle filtering at the receiver side. An important feature of the proposed method is that the fading rate need not be known to the receiver. Monte-Carlo simulations show that the performances of the proposed scheme are close to decoding with perfect channel state information (CSI) using the Viterbi algorithm (VA).