Parameter Estimation for Correlated MIMO Channels with Frequency-Selective Fading

In this paper, we address the problem of frequency offset and channel gain estimation for frequency-selective multi-input multi-output (MIMO) correlated fading channels. A maximum-likelihood (ML) frequency offset (FO) estimator is proposed by using the Bayesian approach. We show that the proposed FO estimator is efficient and asymptotically optimal. Based on the FO estimate, we derive the linear minimum mean square error (LMMSE) channel estimator and analytically investigate the effect of frequency offset estimation error on the mean square error (MSE) performance of the channel estimator. Finally, the performances of the FO and channel estimation are evaluated by simulation results.     

MIMO相关信道估计中训练序列的最优结构和最佳长度

针对存在空域相关性的多输入多输出（Multiple—Input Multiple—Output，MIMO）信道，首先设计了适用于任何给定长度的最优训练序列，该序列能够充分利用已知的信道相关信息，且具有估计均方误差最小化的特性．在此基础上，分析了相关信道下采用训练估计的数据传输机制所能达到的容量下界，得出了满足估计准确性和数据速率最优折中的最佳训练序列长度．最后，通过仿真验证了本文给出的训练序列的性能和最佳长度取值的有效性。     

Carrier Frequency Offset Estimation for MIMO over Spatially Correlated Flat-fading Channels

This paper deals with Carrier frequency offset （CFO） estimation for Multiple-input multiple-output （MIMO） systems. A Rayleigh fiat-fading channel model is considered and spatial correlation among channels corresponding to different pairs of transmit and receive antennas is taken into account. A Data-aided （DA） Maximum likelihood （ML）CFO estimator based on the marginal likeli- hood function is proposed. It can exploit spatial diversity and make use of the knowledge of spatial correlation by averaging the conditional likelihood function over all realizations of the channel. The Cramer-Rao bound （CRB） for the problem is derived as a benchmark. Simulation results are given to illustrate the performance of the pro- posed estimator. It is shown that its performance is close to the CRB at high Signal-to-noise ratio （SNR） region and improved with decrease of the spatial correlation and in- crease of the number of receive antennas.     

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。     

相关瑞利信道下的分集与复用折衷

多天线可以用来增加通信系统的分集增益或者复用增益，二者之间存在着基本的折衷关系。相关瑞利信道的折衷性能差于i．i．d瑞利衰落信道，并且相关矩阵降秩时，折衷性能进一步下降。本文给出了相关瑞利信道下分集增益和复用增益的最优折衷关系。     

The Performance of Multiuser Diversity Scheduling for MIMO Channels With Spatially Correlated Fading

We study a cellular network with one multiantenna base station and a number of multiantenna users. Correlated fading may exist at the base station or at the users, or at both sides. With time-varying fading, multiuser diversity is exploited by always allowing the base station to transmit to the user with the best channel. For this network, we find that if the number of transmitter antennas and the number of receiver antennas grow with a fixed ratio, the multiuser diversity gain will approximately remain constant.     

Model-Based Correlated Channels Estimation

In this paper we propose a noisy Multivariate Autoregressive (MVAR) process for modeling and estimating the correlated fading channels. The method can estimate joint MVAR processes and model parameters from noisy received signal. The proposed method is based on serial connection of two algorithms. In the first algorithm, we estimate MVAR model parameters. For this purpose, a combination of Yule–Walker equations is used. This combination is considered as a generalized eigenvalue problem; an estimate for receiver noise variance is obtained by solving this eigenvalue problem then Least-Squares method is used to estimate the MVAR model parameters. In the second algorithm, the fading process is estimated by using Kalman filter. Simulation results show that the proposed method has good performance compared with other existing methods.     

Optimum Receiver Design for Correlated Rician Fading MIMO Channels with Pilot-Aided Detection

Two structures based on pilot symbol-aided channel receiver estimation are considered for the separately-correlated Rician fading MIMO channel. Mismatched receiver, which A decodes the received signal by first using maximum-likelihood (ML) or mean- minimum error square (MMSE) estimation of the MIMO channel matrix, and then by assuming that the estimate is exact. An optimum receiver, which does not estimate explicitly the matrix but jointly channel processes the received pilot and samples assuming known channel distribution.     

Design of the Periodic Training Sequence for Joint Channel and Frequency Estimation in MIMO Frequency-Selective Channels

This paper considers the design of a periodic training sequence (TS) for joint channel and frequency estimation in multiple-input, multiple-output (MIMO) frequency-selective channels. The design criterion for the periodic TS is to jointly minimize the mean-squared error (MSE) of the maximum likelihood channel estimation and the asymptotic Cramer-Rao bound (CRB) for the frequency estimation. This paper shows that all the TSs that minimize the MSE of the channel estimation have the same asymptotic CRB for the frequency estimation. Furthermore, they also minimize the asymptotic CRB as long as the channel is i.i.d. Rayleigh fading. The design of low-complexity frequency estimators based on the proposed periodic TS is also investigated. Finally, the performance of the proposed periodic TS is evaluated by simulation results.     

Design and Performance of Space–Time Codes for Spatially Correlated MIMO Channels

Space-time code (STC) designs classically rely on the assumption of independent and identically distributed (i.i.d.) Rayleigh channels. However, poor scattering conditions may have detrimental effects on the performance of STCs. In this letter, we derive code-design criteria leading to robust STCs in a large variety of slow-fading propagation conditions. No channel knowledge is assumed at the transmitter. Codes satisfying these criteria are shown to perform much better on real-world channels than codes designed only for i.i.d. channels. As examples, the robustness of various spatial multiplexing schemes, linear dispersion codes, and space-time trellis codes is discussed based on those criteria     

视距相关信道下考虑非理想CSI的多用户MIMO收发联合设计

在FDD模式多用户MIMO(Multi-input Multi-output)系统下行链路中,由于信道估计、反馈信道等存在误差,使得发送端获取理想信道状态信息(CSI,channel state information)十分困难。针对获得非理想CSI的多用户MIMO系统,考虑在基站和各用户的天线分别具有相关性并引入视距分量的信道条件下,提出了一种新的基于块对角化的MMSE准则收发联合设计算法。该算法首先通过块对角化消除用户间的共信道干扰,然后针对存在信道估计误差的用户信道依据MMSE准则分别迭代求解每个用户预编码和解码矩阵。论文设计出一种基于训练序列的信道估计误差算法,并获得等效信道模型,使得收发端获得的信道状态信息更有实际意义。本文假设反馈信道理想,发射端可以完整得到信道估计矩阵。在MMSE准则下,推导获得了Lagrange乘子的解析解,避免了求解非线性方程的复杂过程,显著降低了计算复杂度。和已有算法相比,该算法不仅可以获得良好的误码性能还可以对各用户进行独立优化,处理更加灵活。仿真分析了视距分量、信道相关性以及信道估计误差对算法性能的影响。仿真结果表明,该算法误码性能良好,算法收敛快,并且对信道估计误差带来的影响有较好的抑制作用。      

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.     

Throughput Analysis for Parallel ARQ over Correlated MIMO Channels

We treat the throughput analyses of parallel ARQ schemes over correlated MIMO channels with adaptive modulation and coding (AMC). To describe the packet transmission over multiple parallel logic channels, we extend the existing burst- error model for single channel to multiple parallel logic channels. Based on such a packet error model, we derive the throughput of different parallel ARQ protocols. Moreover, to describe the temporally correlated physical channel fading, we generalize the existing Markov model for single channel to multiple parallel channels for MIMO systems. Then we develop a method for calculating the packet-level model parameters from the parameters of the physical-layer model and the MIMO transceiver. Using the above hierarchical throughput analysis framework, we investigate the potential throughput gain or throughput loss of parallel ARQ over the conventional serial ARQ in MIMO systems. Our results reveal that as SNR increases, parallel ARQ can achieve higher throughput gain or less throughput loss compared to serial ARQ; parallel SW can achieve throughput gain in most of the MIMO scenarios but increasing the number of antennas does not always bring higher gain; parallel GBN with large number of antennas and independent buffers can achieve throughput gain; parallel SR incurs throughput loss.     

相关信道MIMO系统的白适应SD检测算法

文章提出一种适用于相关衰落信道的自适应SD检测算法,该算法能够根据信道状况和接收信号信噪比自适应地进行调整。仿真结果表明,该算法能在不明显降低SD检测性能的情况下降低算法的计算复杂度。     

Space–Time Turbo Equalization With Successive Interference Cancellation for Frequency-Selective MIMO Channels

This paper addresses the issue of iterative space–time equalization for multiple-input–multiple-output (MIMO) frequency-selective fading channels. A new soft equalization concept based on successive interference cancellation (SIC) is introduced for a space–time bit-interleaved coded modulation (STBICM) transmission. The proposed equalizer allows us to separate intersymbol interference (ISI) and multiantenna interference (MAI) functions. Soft ISI is successively suppressed using a low-complexity suboptimum minimum mean square error (MMSE) criterion. The decoupling of ISI and MAI offers more flexibility in the design of the whole space–time equalizer. Different multiantenna detection criteria can be considered, ranging from simple detectors to the optimal maximum a posteriori (MAP) criterion. In particular, we introduce two soft equalizers, which are called SIC/SIC and SIC/MAP, and we show that they can provide a good performance-to-complexity tradeoff for many system configurations, as compared with other turbo equalization schemes. This paper also introduces an MMSE-based iterative channel state information (CSI) estimation algorithm and shows that attractive performance can be achieved when the proposed soft SIC space–time equalizer iterates with the MMSE-based CSI estimator.      

Space–Time Code Design for Correlated Ricean MIMO Channels at Finite SNR

Space–time code (STC) designs commonly rely on the assumptions of independent and identically distributed (i.i.d.) Rayleigh channels (being either slow or fast fading) and high signal-to-noise ratio (SNR). However, it has been shown that poor scattering conditions can have detrimental effects on the performance of STCs and that the behavior of codes at high SNR is radically different from the finite SNR behavior. This calls for new design criteria that correctly predict the behavior of codes in correlated channels at finite SNR. In this paper, we investigate how spatially and temporally correlated Ricean fading affects the performance of STCs at finite SNR. We derive a code design criterion leading to robust STCs in a wide variety of propagation conditions and do not require any channel knowledge at the transmitter. Codes satisfying this criterion are shown to perform sensibly better in correlated channels than codes designed only for i.i.d. slow or fast Rayleigh-fading channels. Examples of space–time trellis codes and algebraic codes are proposed in order to illustrate the developed criterion.      

An Optimum Blind Receiver for Correlated Rician Fading MIMO Channels

A blind receiver scheme for narrowband separately- correlated Rician block fading coded MIMO systems is described. It is shown that this receiver (which can be interpreted as a limiting case of the optimum pilot-aided receiver) attains the maximum achievable throughput at sufficiently high E_b/N₀ ratio. The influence of the E_b/N₀ ratio and of the channel Rice factor on the receiver performance are studied and it is shown that, as either of these parameters increases, the advantage of the blind versus the pilot-aided receiver becomes more sensible. The results obtained support the intuition that, if the line-of-sight component is sufficiently strong, a blind scheme using only the knowledge of the fading statistics parameters matches or outperforms pilot- aided detection.     

Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels

The full diversity gain provided by a multi-antenna channel can be achieved by transmit beamforming and receive combining. This requires the knowledge of channel state information (CSI) at the transmitter which is difficult to obtain in practice. Quantized beamforming where fixed codebooks known at both the transmitter and the receiver are used to quantize the CSI has been proposed to solve this problem. Most recent works focus attention on limited feedback codebook design for the uncorrelated Rayleigh fading channel. Such designs are sub-optimal when used in correlated channels. In this paper, we propose systematic codebook design for correlated channels when channel statistical information is known at the transmitter. This design is motivated by studying the performance of pure statistical beamforming in correlated channels and is implemented by maps that can rotate and scale spherical caps on the Grassmannian manifold. Based on this study, we show that even statistical beamforming is near-optimal if the transmitter covariance matrix is ill-conditioned and receiver covariance matrix is well-conditioned. This leads to a partitioning of the transmit and receive covariance spaces based on their conditioning with variable feedback requirements to achieve an operational performance level in the different partitions. When channel statistics are difficult to obtain at the transmitter, we propose a universal codebook design (also implemented by the rotation-scaling maps) that is robust to channel statistics. Numerical studies show that even few bits of feedback, when applied with our designs, lead to near perfect CSI performance in a variety of correlated channel conditions.     

分集通道相关时MIMO雷达的检测算法

多输入多输出(MIMO)雷达利用波形分集或空间分集提高雷达性能,目标回波散射系数是全相关或者独立完全取决于阵列系统配置。然而,在有些情况下,雷达阵列系统配置导致散射系数部分相关,从而使MIMO雷达的检测性能受到影响。针对上述问题,文中研究了基于尼曼-皮尔逊准则下分集通道相关时MIMO雷达检测算法,推导检测概率与虚警概率的近似解析表达式,分析了分集通道相关性对MIMO雷达检测的影响。仿真结果验证了该算法的有效性。