Performance analysis of maximum likelihood detection in a MIMOantenna system

We provide an analysis of the performance of maximum likelihood detection (MLD) over flat fading channels in a wireless multiple input-multiple output (MIMO) antenna system. A tight union bound with an asymptotic form on the probability of symbol error rate (SER) for MIMO MLD systems with two-dimensional signal constellations (such as QAM and PSK) is introduced. Using this analytic bound, the performance of the MIMO antenna system is demonstrated quantitatively with respect to channel estimation, constellation size, and antenna configuration     

Frequency Offset Estimation and Training Sequence Design for MIMO OFDM

This paper addresses carrier frequency offset (CFO) estimation and training sequence design for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems over frequency selective fading channels. By exploiting the orthogonality of the training sequences in the frequency domain, integer. CFO (ICFO) is estimated. With the uniformly spaced non-zero pilots in the training sequences and the corresponding geometric mapping, fractional CFO (FCFO) is estimated through the roots of a real polynomial. Furthermore, the condition for the training sequences to guarantee estimation identifiability is developed. Through the analysis of the correlation property of the training sequences, two types of sub-optimal training sequences generated from the Chu sequence are constructed. Simulation results verify the good performance of the CFO estimator assisted by the proposed training sequences.     

On the capacity of OFDM-based spatial multiplexing systems

This paper deals with the capacity behavior of wireless orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing systems in broad-band fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a physically motivated multiple-input multiple-output (MIMO) broad-band fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that, in the MIMO case, unlike the single-input single-output (SISO) case, delay spread channels may provide advantages over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and higher multiplexing gain than MIMO flat fading channels     

Achievable information rates of multi-antenna systems over frequency-selective fading channels with constrained inputs

Information rates of multiple-input multiple-output (MIMO) systems over frequency-selective fading channels are computed under the constraint of independent identically distributed inputs chosen from a finite alphabet. The method uses a simulation based approach that employs the sum-product algorithm. The setting includes as special cases the single-input single-output systems over frequency-selective fading channels and the MIMO systems over flat fading channels. Both ergodic and nonergodic channels are considered, and examples are provided for the case of binary signaling.     

Semi-blind maximum-likelihood joint channel/data estimation for correlated channels in multiuser MIMO networks

The aim of this paper is to investigate receiver techniques for maximum likelihood (ML) joint channel/data estimation in flat fading multiple-input multiple-output (MIMO) channels, that are both (i) data efficient and (ii) computationally attractive. The performance of iterative least squares (LS) for channel estimation combined with sphere decoding (SD) for data detection is examined for block fading channels, demonstrating the data efficiency provided by the semi-blind approach. The case of continuous fading channels is addressed with the aid of recursive least squares (RLS). The observed relative robustness of the ML solution to channel variations is exploited in deriving a block QR-based RLS-SD scheme, which allows significant complexity savings with little or no performance loss. The effects on the algorithms’ performance of the existence of spatially correlated fading and line-of-sight paths are also studied. For the multi-user MIMO scenario, the gains from exploiting temporal/spatial interference color are assessed. The optimal training sequence for ML channel estimation in the presence of co-channel interference (CCI) is also derived and shown to result in better channel estimation/faster convergence. The reported simulation results demonstrate the effectiveness, in terms of both data efficiency and performance gain, of the investigated schemes under realistic fading conditions.     

空时编码多载波码分多址MIMO系统下行频率选择性信道盲估计

基于子空间方法的无线信道盲估计由于其算法的固有特性,使得估计结果与实际信道之间存在一个不确定复系数,无法得到无线信道的精确估计。在利用子空间分解方法对空时编码多输入多输出MC-CDMA系统下行频率选择性信道盲估计的基础上,利用发射符号的有限码集特性,将单载波系统下的模糊复系数盲辨识方法推广到多载波多输入多输出系统,从而得到信道的精确估计。Monte-Carlo仿真表明,在信噪比较低的情况下,本方法的信道估计误差仍然较小。     

Subspace-based noise variance and SNR estimation for MIMO OFDM systems

This paper proposes a subspace-based noise variance and Signal-to-Noise Ratio （SNR） estimation algorithm for Multi-Input Multi-Output （MIMO） wireless Orthogonal Frequency Division Multiplexing （OFDM） systems. The special training sequences with the property of orthogonality and phase shift orthogonality are used in pilot tones to obtain the estimated channel correlation matrix. Partitioning the observation space into a delay subspace and a noise subspace, we achieve the measurement of noise variance and SNR. Simulation results show that the proposed estimator can obtain accurate and real-time measurements of the noise variance and SNR for various multipath fading channels, demonstrating its strong robustness against different channels.     

Soft‐output MMSE V‐BLAST receiver with MMSE channel estimation under correlated Rician fading MIMO channels

For wireless multiple‐input multiple‐output (MIMO) communications systems, both channel estimation error and spatial channel correlation should be considered when designing an effective signal detection system. In this paper, we propose a new soft‐output MMSE based Vertical Bell Laboratories Layered Space‐Time (V‐BLAST) receiver for spatially‐correlated Rician fading MIMO channels. In this novel receiver, not only the channel estimation errors and channel correlation but also the residual interference cancellation errors are taken into consideration in the computation of the MMSE filter and the log‐likelihood ratio (LLR) of each coded bit. More importantly, our proposed receiver generalizes all existing soft‐output MMSE V‐BLAST receivers, in the sense that, previously proposed soft‐output MMSE V‐BLAST receivers can be derived as the reduced forms of our receiver when the above three considered factors are partially or fully simplified. Simulation results show that the proposed soft‐output MMSE V‐BLAST receiver outperforms the existing receivers with a considerable gain in terms of bit‐error‐rate (BER) performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Multiuser channel estimation and tracking for long-code CDMA systems

Channel estimation techniques for code-division multiple access (CDMA) systems need to combat multiple access interference (MAI) effectively. Most existing estimation techniques are designed for CDMA systems with short repetitive spreading codes. However, current and next-generation wireless systems use long spreading codes whose periods are much larger than the symbol duration. We derive the maximum-likelihood channel estimate for long-code CDMA systems over multipath channels using training sequences and approximate it using an iterative algorithm to reduce the computational complexity in each symbol duration. The iterative channel estimate is also shown to be asymptotically unbiased. The effectiveness of the iterative channel estimator is demonstrated in terms of squared error in estimation as well as the bit error rate performance of a multistage detector based on the channel estimates. The effect of error in decision feedback from the multistage detector (used in the absence of training sequences) is also shown to be negligible for reasonable feedback error rates using simulations. The proposed iterative channel estimation technique is also extended to track slowly varying multipath fading channels using decision feedback. Thus, an MAI-resistant multiuser channel estimation and tracking scheme with reasonable computational complexity is derived for long-code CDMA systems over multipath fading channels.     

On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel Estimation Error

By employing spatial multiplexing, multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. Zero-forcing (ZF) detection is a simple and effective technique for retrieving multiple transmitted data streams at the receiver. However the detection requires knowledge of the channel state information (CSI) and in practice accurate CSI may not be available. In this letter, we investigate the effect of channel estimation error on the performance of MIMO ZF receivers in uncorrelated Rayleigh flat fading channels. By modeling the estimation error as independent complex Gaussian random variables, tight approximations for both the post-processing SNR distribution and bit error rate (BER) for MIMO ZF receivers with M-QAM and M-PSK modulated signals are derived in closed-form. Numerical results demonstrate the tightness of our analysis     

A lower bound on achievable rate of MRT precoding in multicell multiuser massive MIMO networks with Rician flat fading

A multicell multiuser massive multiple‐input‐multiple‐output (MIMO) network with Rician flat fading is considered. Given channel reciprocity, non‐orthogonal uplink channel training in conjunction with minimum mean square error channel estimation at the base stations are used to acquire channel state information. In the forward link, using maximal ratio transmission precoding, base stations send data to corresponding users. In this paper, first, a closed‐form expression for signal to interference and noise ratio and a lower bound on achievable rate are obtained for arbitrary number of base station antennas. Then, using random matrix theory, a simplified approximate expression for large number of base station antennas (i.e., massive MIMO scenario) are calculated. This simplified expression shows that in a multicell multiuser massive MIMO network with Rician flat fading, like Rayleigh fading, as the number of base station antennas goes to infinity, the effects of uncorrelated noise and intercell and intracell interferences tend to zero. The only factor limiting the performance of system is the correlated intercell interference, that is, pilot contamination, due to non‐orthogonality of channel training sequences in adjacent cells. Numerical results show that our obtained closed‐form expression is a good lower bound on sum‐rate for various system parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

莱斯衰落信道下大规模MIMO系统中的信道估计方法

日趋重要的高速移动工具,如高速铁路、无人驾驶飞机等,大多都处在开阔地带.由于视距传播的存在,瑞利衰落模型已经不能很好地描述该环境下的信道情况,而莱斯衰落信道模型由视距分量和多径分量组成,更能准确地表述上述信道变化.基于此模型,在大规模天线系统下,在已存在的基于叠加训练序列信道估计方法的基础上,提出了改进的信道估计方法和对应的解码方法.改进后的信道估计方法分为直射分量已知和未知两种情况,分别推导了相应的信道估计公式和解码方法.数值仿真结果验证了本文所提方案性能的优越性.     

Robust and consistent pilot designs for frequency offset estimation in MIMO OFDM systems

This paper presents pilot designs for consistent frequency offset estimation of MIMO OFDM systems in frequency selective fading channels. We derive the sufficient consistency condition for the pilots in MIMO OFDM systems to yield unambiguous estimation, and present corresponding consistent pilot designs. We discuss robustness of the frequency offset estimation against outliers at low to moderate SNR values and present an efficient criterion to choose robust and consistent pilots. Furthermore, we develop pilot designs which satisfy both consistency over a limited frequency offset estimation range and the optimal channel estimation condition in MIMO OFDM systems. Simulation results corroborate that both the consistent pilot design condition and the robustness criterion are efficient in choosing pilot patterns yielding better frequency offset estimation performance.     

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。      

Cross-layer based transmit antenna selection for decision-feedback detection in correlated Ricean MIMO channels

In this paper, we investigate a cross-layer transmit antenna selection (AS) approach for the decision-feedback detector (DFD) over spatially correlated flat Ricean fading multiple-input multiple-output (MIMO) channels. Closed-form expressions for the system throughput with both perfect and imperfect channel estimation are derived. Considering a training-based channel estimation technique, we show that the capacity-based AS is more robust to imperfect channel estimation. However, in all cases, the cross-layer AS delivers higher throughput gains than the capacity-based AS.     

Performance Analysis of Rate-Adaptive Modulation with Imperfect Estimation in Space?CTime Coded MIMO System

Based on the imperfect estimation information, the performance analysis of multi-input multi-out (MIMO) systems with rate-adaptive modulation and space?Ctime coding over flat Rayleigh fading channels is presented in this paper. The fading gain value is partitioned into a number of regions by which the modulation is adapted according to the region the fading gain falls in. Under a target bit error rate (BER) and constant power constraint, the fading gain region boundaries are given. By utilizing the minimum mean squared error estimation, the correlation between the channel gains and their estimates, which contributes to imperfect channel information, is evaluated. With this correlation, the probability density function of fading gain is obtained. Based on these results, the closed-form expressions for the SE and average BER are derived in detail, respectively. The theoretical expressions will be more accurate than the existing schemes, and they include perfect estimation as a special case. Numerical results show that the SE and BER of the system with imperfect estimation are worse than those with perfect estimation due to the estimation error. Moreover, the simulation results for SE and BER are in good agreement with the theoretical analysis.     

基于毫米波通信的混合MIMO系统的信道估计

作为5G的一项关键技术,毫米波通信要求提出专有的信道估计和预编码算法,为此,针对毫米波MIMO系统的窄带平坦衰落信道研究下行信道估计方案.由于毫米波系统的稀疏特性,将稀疏多径信道的信道估计转化为稀疏信号的重建,基于压缩感知设计适用于毫米波通信系统的信道估计方案,深入研究了正交匹配追踪算法.仿真结果显示,它可以高概率地恢复信号,与传统的最小二乘法比较,能获得更好的信道估计性能.     

Progressive Linear Precoder Optimization for MIMO Packet Retransmissions Exploiting Channel Covariance Information

This work investigates the design of linear precoders for ARQ packet retransmissions in multi-input multi-output (MIMO) systems. We consider transmitter precoder design based on partial MIMO channel information in the form of their covariance feedback. Our objective is to maximize the ergodic mutual information provided by multiple (re)transmissions of a packet subject to transmission power constraint. We propose a set of near-optimal successive linear ARQ precoders for flat fading MIMO channels. This progressive linear ARQ precoder combines the appropriate power loading and the reverse-order pairing of singular values in the current retransmission with previous transmissions. This reverse-order pairing is a special feature unique to our sequential ARQ preceding approach with demonstrated performance gains.     

On the design of space-time and space-frequency codes for MIMO frequency-selective fading channels

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.     

Shannon capacity of STBC in Rayleigh fading channels

Space-time block coding (STBC) is a powerful transmit diversity scheme for multiple antenna systems. A closed-form expression for the Shannon capacity of MIMO systems is derived using STBC under independent and quasi-static flat Rayleigh fading channels. The Shannon capacity of STBC over such channels is expressed as a finite sum of functions that are easy to evaluate, thereby avoiding the need for numerical integration or Monte Carlo simulation.