Robust Linear Receivers for Multiaccess Space–Time Block-Coded MIMO Systems: A Probabilistically Constrained Approach

Traditional multiuser receiver algorithms developed for multiple-input–multiple-output (MIMO) wireless systems are based on the assumption that the channel state information (CSI) is precisely known at the receiver. However, in practical situations, the exact CSI may be unavailable because of channel estimation errors and/or outdated training. In this paper, we address the problem of robustness of multiuser MIMO receivers against imperfect CSI and propose a new linear technique that guarantees the robustness against CSI errors with a certain selected probability. The proposed receivers are formulated as probabilistically constrained stochastic optimization problems. Provided that the CSI mismatch is Gaussian, each of these problems is shown to be convex and to have a unique solution. The fact that the CSI mismatch is Gaussian also enables to convert the original stochastic problems to a more tractable deterministic form and to solve them using the second-order cone programming approach. Numerical simulations illustrate an improved robustness of the proposed receivers against CSI errors and validate their better flexibility as compared with the robust multiuser MIMO receivers based on the worst case designs.     

PERFORMANCE OF THE ZERO FORCING PRECODING MIMO BROADCAST SYSTEMS WITH CHANNEL ESTIMATION ERRORS

In this paper, the effect of channel estimation errors upon the Zero Forcing (ZF) precoding Multiple Input Multiple Output Broadcast (MIMO BC) systems was studied. Based on the two kinds of Gaussian estimation error models, the performance analysis is conducted under different power allocation strategies. Analysis and simulation show that if the covariance of channel estimation errors is independent of the received Signal to Noise Ratio (SNR), imperfect channel knowledge deteriorates the sum capacity and the Bit Error Rate (BER) performance severely. However, under the situation of orthogonal training and the Minimum Mean Square Error (MMSE) channel estimation, the sum ca- pacity and BER performance are consistent with those of the perfect Channel State Information (CSI) with only a performance degradation.     

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.     

Matrix Coded Modulation: A New Non-coherent MIMO Scheme

This paper describes a new space-time coding scheme for non-coherent multi-antenna multi-input multi-output (MIMO) systems. This new MIMO scheme merges error-correcting and space-time coding functions by transmitting invertible matrices, so this scheme has been called “Matrix Coded Modulation” or “MCM”. Coherent systems require channel state information (CSI) at the transmitters and/or at the receivers, and their performances strongly depend on the channel estimation. For example, in systems using Orthogonal frequency division multiplexing, the channel estimation requires the insertion of pilot-symbols in the transmitted frame which implies a spectral efficiency loss of the global system that increase with the number of transmit antennas. The existing non-coherent schemes such as the differential space-time modulation leads to performance degradation compared to coherent systems in which perfect CSI is assumed. Decoding in the MCM scheme is performed iteratively, based on a specified detection criteria. In the proposed MCM scheme, decoding can be achieved with or without CSI at the receiving antennas. As the space-time coding function is merged with the error-correcting code, the euclidean distances distribution between modulated signals based on the detection criteria is strongly linked to the Hamming weights distribution of the channel error-correcting code used in the MCM scheme. Moreover, a low-complexity decoding algorithm is described and compared to the existing differential schemes.     

VLST系统中ZF检测算法的研究

垂直分层空时码(VLST)是贝尔实验室提出的一种基于MIMO传输方式的空时码系统,其中,迫零检测算法(ZF)、最小均方误差检测算法(MMSE)和最大似然检测算法(ML)是常用的3种检测算法。着重对经典的ZF检测算法进行了深入的数学分析,并通过matlab仿真试验,给出了该算法在不同的调制方法、不同的信道估计误差下的性能分析,为构造实际VLST系统给出了理论依据     

Matrix Coded Modulation: A New Non-coherent MIMO Scheme

This paper describes a new space-time coding scheme for non-coherent multi-antenna Multi-Input Multi-Output (MIMO) systems. This new MIMO scheme merges error-correcting and space-time coding functions by transmitting invertible matrices, so this scheme has been called “Matrix Coded Modulation” or “MCM”. Coherent systems require Channel State Information (CSI) at the transmitters and/or at the receivers, and their performances strongly depend on the channel estimation. For example, in systems using Orthogonal Frequency Division Multiplexing, the channel estimation requires the insertion of pilot-symbols in the transmitted frame which implies a spectral efficiency loss of the global system that increase with the number of transmit antennas. The existing non-coherent schemes such as the Differential Space-Time Modulation leads to performance degradation compared to coherent systems in which perfect CSI is assumed. Decoding in the MCM scheme is performed iteratively, based on a specified detection criteria. In the proposed MCM scheme, decoding can be achieved with or without CSI at the receiving antennas. As the space-time coding function is merged with the error-correcting code, the euclidean distances distribution between modulated signals based on the detection criteria is strongly linked to the Hamming weights distribution of the channel error-correcting code used in the MCM scheme. Moreover, a low-complexity decoding algorithm is described and compared to the existing differential schemes.     

Analysis of Tomlinson–Harashima Precoding in Multiuser MIMO Systems With Imperfect Channel State Information

Tomlinson–Harashima precoding (THP) is a successive pre-equalization technique that arranges all the receivers into a group of layers and then suppresses the interlayer interference in sequence at the transmitter. There are two basic THP structures according to the positions of the diagonal weighted filter—decentralized at the receivers or centralized at the transmitter—which are denoted dTHP or cTHP, respectively. In this paper, the investigation of THP in downlink multiuser multiple-input–multiple-output (MIMO) systems with imperfect channel state information (CSI) is performed. The interference power caused by imperfect CSI is first derived, and then, the comparison between the two basic THP structures and the linear zero-forcing (ZF) precoding is carried out in terms of the interference power and the system capacity. Furthermore, the cases with different CSI errors among users are considered, through which the independence of the interference power among layers or subchannels is presented, including the cases with single-antenna and multiantenna receivers. Analytical and simulation results indicate that with imperfect CSI, THP leads to less interference power than linear-ZF, and dTHP leads to larger system capacity than cTHP and linear-ZF.      

基于MIMO信道估计误差模型的功率分配与自适应调制算法

该文分析了瑞利平坦衰落信道下,信道估计误差对采用迫零接收的MIMO系统性能的影响,提出了一种以系统有效吞吐量最大化为目标的功率分配与自适应调制算法。为了减少信道估计误差对实际系统性能的影响,该算法对发送端估计的信噪比进行修正,并以此作为功率分配和自适应调制的依据。在系统总功率受限的条件下,对发端多天线的功率分配结合了空域注水定理和比特分配,并尽量保证调制阶数高的数据符号所在天线的功率。仿真结果表明,该算法实现较简单,获得的系统有效吞吐量接近于最优值,适用于实际系统。     

Adaptive Channel Estimation Using Pilot-Embedded Data-Bearing Approach for MIMO-OFDM Systems

Multiple-input multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) systems employing coherent receivers crucially require channel state information (CSI). Since the multipath delay profile of channels is arbitrary in the MIMO-OFDM systems, an effective channel estimator is needed. In this paper, we first develop a pilot-embedded data-bearing (PEDB) approach for joint channel estimation and data detection, in which PEDB least-square (LS) channel estimator and maximum-likelihood (ML) data detection are employed. Then, we propose an LS fast Fourier transform (FFT)-based channel estimator by employing the concept of FFT-based channel estimation to improve the PEDB-LS one via choosing a certain number of significant taps for constructing a channel frequency response. The effects of model mismatch error inherent in the proposed LS FFT-based estimator when considering noninteger multipath delay profiles and its performance analysis are investigated. The relationship between the mean-squared error (MSE) and the number of chosen significant taps is revealed, and hence, the optimal criterion for obtaining the optimum number of significant taps is explored. Under the framework of pilot embedding, we further propose an adaptive LS FFT-based channel estimator employing the optimum number of significant taps to compensate the model mismatch error as well as minimize the corresponding noise effect. Simulation results reveal that the adaptive LS FFT-based estimator is superior to the LS FFT-based and PEDB-LS estimators under quasi-static channels or low Doppler's shift regimes     

MIMO iterative receiver SNR estimation strategies for link to system interfacing

This paper presents link to system (L2S) interfacing technique for multiple input and multiple output (MIMO) iterative receivers. In L2S interfacing, usually the post detection signal to noise ratio (SNR)‐based frame error rate lookup tables (LUT) are used to predict the link level performance of receivers. While L2S interfacing for linear MIMO receivers can be conveniently implemented, it is more challenging for MIMO iterative receivers due to unavailability of the closed form SNR expressions. In this paper, we propose three methods for post detection SNR estimation for MIMO iterative receivers. The first is based on the QR decomposition of the channel matrix, the second relies on the residual noise calculation based on the soft symbols, and the third exploits the closed form SNR expressions for linear receivers. A link to system interface model for iterative receivers is developed for evaluating the reference curves for different modulation and coding schemes, and results are validated by comparing the simulated and predicted frame error rates. It is shown that linear and residual noise‐based SNR approximations result in a very good prediction performance whereas the performance of QR decomposition‐based method degrades for higher order modulations and coding schemes. This paper presents link to system interfacing technique for MIMO iterative receivers. A link to system interface model for iterative receivers is developed for evaluating the reference curves for different modulation and coding schemes, and results are validated by comparing the simulated and predicted frame error rates. Three post detection SNR evaluation schemes have been proposed for link to system interfacing all of which give good prediction performance especially at lower order modulation.     

多用户下行链路收发机鲁棒性优化算法

该文提出了一种多用户MIMO系统中预矩阵及其匹配接收矩阵的鲁棒性优化算法。针对信道估计误差构造均方误差代价函数,在发射功率受限的约束条件下联合设计发射和接收矩阵,推导出了采用线性多用户MMSE接收时的最优收发机迭代算法。仿真表明,系统具有良好的鲁棒性。     

载波频率偏移下分布式MIMO系统性能分析

文中针对载波频率偏移对分布式MIMO系统的性能进行了仿真分析,仿真结果表明：载波频率偏移和不理想的信道估计会对系统性能产生较大影响;高阶调制更容易受到载波频率偏移的影响;ZF和MMSE译码算法与传统的Alamouti译码算法相比对于载波频率偏移更加稳健,当｜w-2-w-1｜取值较大时,采用ZF和MMSE译码性能要好于传统的Alamouti译码算法;随着各链路载波频率偏移差别｜w-2-w-1｜的减小,传统的Alamouti译码算法性能不断改善。     

基于有限反馈的MIMO系统鲁棒性均匀信道分解

 在MIMO系统中,当假设发送端和接收端已知完美信道状态信息的情况下,均匀信道分解(UCD)被证明在误码率性能上是最优的且是容量无损的.然而在实际系统中,接收端或发送端获得的信道信息通常存在着一定的估计误差.本文提出一种基于有限反馈的鲁棒性均匀信道分解方案,在设计方案中充分考虑了信道估计误差的影响,并利用香农率失真定理和广义Lloyd矢量量化算法(GLA)得到了信道估计误差的近似值,使得本文提出的方案有很好的实用性.仿真结果表明与传统均匀信道分解方案相比,本文提出的鲁棒性均匀信道分解方案有效地降低了系统的误码平层,提高了系统容量.     

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.     

短波通信多组空时编码中等效MIMO模型ZF解码

面向短波通信提出了多组空时编码( MGSTC )的一种等效多输入多输出( MIMO )模型迫零( ZF)解码算法。该算法以降低运算复杂度为目的,将原多时隙MIMO系统拆分为多个多时隙单输入多输出( SIMO)系统并分别等效为多个新的单时隙MIMO系统模型,通过各自左乘等效信道矩阵的共轭转置后进行最大比合并( MRC)以及ZF解码获得发送信号估计值,避免了球形解码( SD)中对高阶矩阵的QR分解。仿真结果表明,与虚拟MIMO模型SD解码算法相比,等效MIMO模型ZF解码算法在误码率( BER)性能1 dB损耗的情况下,运算量降低一个数量级以上。     

Robust AM-MIMO based on minimized transmission power

We propose a design of minimizing transmission power adaptive modulation (AM) that utilizes imperfect channel state information (I-CSI) in multi-input and multi-output (MIMO) systems. By taking channel estimation errors into account, the proposed algorithm provides the quality of services (QoS) closed to the expected values when larger channel estimation error occurs. Furthermore, we, make comparison between the proposed algorithm and the ideal one based on perfect CSI assumption, and present the simulations results to illustrate the performance advantages at last.     

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.     

MIMO系统的信号检测算法分析

MIMO已成为当今4G中的主流技术,其接收端的信号检测性能决定着其能否在提升信道容量的同时减少误码率。因此,文中研究了MIMO系统中4种主要的信号检测算法,包括ZF、MMSE、ZF-SIC和MMSE-SIC算法。[JP2]通过在不同的收发天线数和不同接收天线数下各自的误码率,对4种检测算法进行了分析。[JP]结果表明,MMMSE-SIC检测性能最佳,ZF-SIC、MMSE次之,ZF最差。     

双向MIMO中继网络中采用信道独立预编码的自干扰消除技术

双向中继网络在提高频谱效率的同时会引入额外的自干扰,本文针对放大转发（AF）模式下双向多输入多输出（MIMO）中继网络中的自干扰抵消问题,从消除信道估计误差引入的剩余自干扰着手,提出一种采用信道独立预编码的盲干扰抵消（BIC）方案。新方案在源节点对信息进行行空间预编码,从而构建不依赖于MIMO信道矩阵的期望信号子空间和自干扰子空间,实现未知信道状态下自干扰抵消和期望信号分离,从而消除非理想信道估计带来的剩余自干扰信号。在此基础上,以最大化有效信噪比为目标设计最佳预编码,通过推导可达和速率的闭合表达式,分析不同方案下信道估计误差对可达和速率的影响。仿真结果表明,新方案在不同的信道估计误差下,能够实现完美自干扰消除,其检测性能和容量均优于基于信道估计的自干扰消除方案。      

Deep learning-based channel estimation for wireless ultraviolet MIMO communication systems

To solve the problems of pulse broadening and channel fading caused by atmospheric scattering and turbulence, multiple-input multiple-output(MIMO) technology is a valid way. A wireless ultraviolet(UV) MIMO channel estimation approach based on deep learning is provided in this paper. The deep learning is used to convert the channel estimation into the image processing. By combining convolutional neural network(CNN) and attention mechanism(AM), the learning model is designed to extract the depth f...