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.      

多天线广播信道模型安全性分析

在无线广播网络中,信道的广播特性会导致通信特别容易被窃听,通信中的防窃听问题就变得更加重要。根据多天线（MIMO）高斯广播信道模型（MGBC-CM）,并结合了MIMO块对角化预编码思想,建立了一种多天线广播信道可靠安全模型。基站在向用户发送数据之前先进行块对角化预编码,这样不仅可以消除用户之间数据的相互干扰,而且更重要的是还可以有效防止用户数据被窃听。仿真结果表明,该模型具有很好的保密性和安全性。     

下行链路广播信道能效优化鲁棒波束成形算法

针对多天线广播下行链路通信系统,研究了一种鲁棒能效联合波束成形和功率分配算法。首先,鲁棒能效优化问题描述为满足一定功率约束的系统和速率与系统消耗之比的最大化优化问题。其次,利用分数规划理论及用户速率与最小均方误差之间的关系,把所描述的分数规划优化问题转化成参数化多项式优化问题。然后,利用拉格朗日对偶及单调优化理论,提出了一种有效的鲁棒能效优化算法。数值仿真结果表明,相对于传统的非鲁棒能效优化算法,所提鲁棒能效优化算法可获得明显的能效性能增益。      

The p -Sphere Encoder: Peak-Power Reduction by Lattice Precoding for the MIMO Gaussian Broadcast Channel

A vector precoding scheme has been recently proposed for the multiple-input multiple-output (MIMO) Gaussian broadcast channel. This technique minimizes the instantaneous transmitted power of linearly precoded signals, but does not take into account the peak-to-average-power ratio (PAPR). In this paper, we present a modified vector precoding scheme, where a perturbation vector is chosen in order to take into account both the instantaneous power and the instantaneous peak power of the transmitted signal. This is obtained by minimizing the p-norm of the transmitted signal for pges2. For this reason, the scheme is referred to as the p-sphere encoder. We demonstrate the performance of the proposed scheme applied to a MIMO independent, identically distributed Rayleigh fading downlink channel with simple channel inversion. We show that by choosing pges2, the proposed p-sphere encoder yields a tradeoff between power efficiency, PAPR reduction, and complexity. In particular, with eight antennas, the proposed algorithm significantly reduces the tail of the PAPR distribution, with very small degradation in terms of bit-error rate with respect to standard vector precoding     

The$p$-Sphere Encoder: Peak-Power Reduction by Lattice Precoding for the MIMO Gaussian Broadcast Channel

A vector precoding scheme has been recently proposed for the multiple-input multiple-output (MIMO) Gaussian broadcast channel. This technique minimizes the instantaneous transmitted power of linearly precoded signals, but does not take into account the peak-to-average-power ratio (PAPR). In this paper, we present a modified vector precoding scheme where a perturbation vector is chosen in order to take into account both the instantaneous power and the instantaneous peak power of the transmitted signal. This is obtained by minimizing the$rho$-norm of the transmitted signal, for$rhogeq 2$. For this reason, the scheme is referred to as the$rho$-sphere encoder. We demonstrate the performance of the proposed scheme applied to a MIMO i.i.d. Rayleigh fading downlink channel with simple channel inversion. We show that by choosing$rhogeq 2$, the proposed$rho$-sphere encoder yields a tradeoff between power efficiency, PAPR reduction, and complexity. In particular, with eight antennas, the proposed algorithm significantly reduces the tail of the PAPR distribution with very small degradation terms of bit-error rate with respect to standard vector precoding.     

Tomlinson-Harashima Precoding for Broadcast Channels with Uncertainty

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.     

Robust Tomlinson-Harashima Precoding for Two-Way Relaying

Most of the non-linear transceivers, which are based on Tomlinson-Harashima (TH) precoding and have been proposed in the literature for two-way relay systems, assume perfect channel state information (CSI). In this paper, a novel and robust TH precoding scheme has been investigated for two-way relay systems, with multiple antennas at the transceiver and relay nodes. We assume imperfect CSI and the channel uncertainty is bounded by a spherical region. The minimum mean square error at the destinations is used as the design criterion and we develop an iterative method to solve this nonconvex problem to obtain TH precoding matrices at the transmitter, linear precoding matrix at the relay and linear equalizer at the destination nodes, where each subproblem is convex. Simulations are provided to evaluate the performance and to validate the efficiency of the proposed scheme.

     

无线通信中的线性预编码技术应用与研究

为了研究单用户分组传输系统设计的问题，基于线性预编码技术下的无线频率选择性信道，证明在有限冲击响应滤波器信道中，采用线性预编码技术可以获得很好的信道均衡。分组传输中的线性预编码是指一个线性空间到另外一个线性空间的变换，以循环前缀或迫零方式的冗余码片可以消除分组间干扰。同时OFDM系统也可以采用线性预编码技术，结果表明在很多方面采用线性预编码技术的OFDM系统将优于传统的OFDM系统。     

Optimum Linear Constellation Precoding for Space Time Wireless Systems

Space Time Constellation Rotating Codes (STCRs) achieve a rate of 1 symbol/s/Hz and enjoy a diversity N _tN_r for arbitrary number of transmit and receive antennas N _t and N _r over quasi static fading channels. Optimum Unitary STCRs based on Algebraic design tools, which achieve the upper bound on coding gain for all linear precoders over Quadrature Amplitude Modulation (QAM) and Pulse Amplitude Modulation (PAM), are known only when the number of transmit antennas is power of two. In this paper we design optimum unitary LCPs for even number of transmit antennas. We also present some unitary precoders for odd number of transmit antennas which clearly out-perform the existing unitary non-optimum precoders. Performance results corroborate our analysis. Manav R. Bhatnagar was born in Moradabad, India in 1976. He did his B.E. in Electronics in 1997 and Master of Technology in Communications Engineering in 2005 from Indian Institute of Technology Delhi, India. He has worked as lecturer in Moradabad Institute of Technology, Moradabad, India from 1998--2003. He is currently pursuing PhD from Indian Institute of Technology Delhi, India. His research interests include Routing in Optical Networks, Signal Processing in Wireless Communications and Image Processing. He is a member of the IEEE. R Vishwanath was born in Hyderabad, India in 1982. He did his B.E. in Electronics and Communications Engineering from Birla Institute of Technology, Ranchi, India in 2002 and Master of Technology in Communications Engineering in 2005 from Indian Institute of Technology Delhi, India. Currently he is pursuing PhD from Indian Institute of Technology Delhi, India. His research interests include Routing in Optical Networks, Signal Processing, Wireless Communications and Image Processing. He is a member of the IEEE.     

Blind Channel Estimation for OFDM Systems via a Generalized Precoding

In this paper, we consider the problem of blind channel estimation for single-input-single-output (SISO) orthogonal frequency-division multiplexing (OFDM) system via second-order statistics only. Based on the assumption that the transmitted symbols are independent and identically distributed, we develop a simple blind channel estimation technique for OFDM systems by utilizing a generalized linear nonredundant block precoding. Instead of using partial information from the signal covariance matrix, as done in previous works where a specific precoder is designed and only one column of the signal covariance matrix is exploited, our work jointly considers all the information contained in the signal covariance matrix. Compared to the popular subspace-based blind channel estimation methods, the proposed algorithm is much more computationally efficient. A design criterion of the precoders by which the performance can be improved is provided, and the closed-form stochastic Crameacuter-Rao bound is derived. The numerical results clearly show the effectiveness of our proposed algorithm, as well as its improvement over the existing techniques     

On the Discrete Memoryless Partially Cooperative Relay Broadcast Channel and the Broadcast Channel With Cooperating Decoders

We derive two inner bounds on the rate region of the partially cooperative relay broadcast channel. The first inner bound is based on the Cover and El Gamal generalized strategy for the original relay channel, while the second inner bound is based on the strategy proposed recently by Chong, Motani, and Garg, for the relay channel, which combines backward decoding and simultaneous decoding. Both rate regions subsume the inner bound reported by Liang and Kramer which is based just on the decode-and-forward strategy for the common message. A broadcast channel with cooperating decoders is a broadcast channel wherein the receivers, once observing their outputs, may exchange messages via a pair of channels with specified capacities. An achievable rate region for this model is derived based on the first coding strategy for the partially cooperative relay broadcast channel. This region subsumes the Dabora and Servetto rate region. A converse result is proved for this model based on the converse result of Nair and El Gamal for the broadcast channel and Willems's converse proof for the multiple-access channel with cooperating encoders.     

无线广播监测网

本文主要介绍了中央无线广播监测网的组成,分析了其系统体系结构、技术特点及所采用的关键技术。     

Vector Precoding for Wireless MIMO Systems and its Replica Analysis

This paper studies a nonlinear vector precoding scheme which inverts the wireless multiple-input multiple-output (MIMO) channel at the transmitter so that simple symbol-by-symbol detection can be used in lieu of sophisticated multiuser detection at the receiver. In particular, the transmit energy is minimized by relaxing the transmitted symbols to a larger alphabet for precoding, which preserves the minimum signaling distance. The so-called replica method is used to analyze the average energy savings with random MIMO channels in the large-system limit. It is found that significant gains can be achieved with complex-valued alphabets. The analysis applies to a very general class of MIMO channels, where the statistics of the channel matrix enter the result via the R-transform of the asymptotic empirical distribution of its eigenvalues. Moreover, we introduce polynomial-complexity precoding schemes for binary and quadrature phase-shift keying in complex channels by using convex rather than discrete relaxed alphabets. In case the number of transmit antennas is more than twice the number of receive antennas, we show that a convex precoding scheme, despite its polynomial complexity, outperforms NP-hard precoding using the popular Tomlinson-Harashima signaling.     

An Efficient Multimode Quantized Precoding Technique for MIMO Wireless Systems

Multimode quantized precoding (QP) can provide full diversity gain or high capacity gain by adapting the number of substreams, as well as the precoding matrix, according to the instantaneous channel condition with low-rate feedback. Conventional multimode QP (MM-QP), however, does not consider the adaptive rate allocation among substreams; thus, it cannot have the additional gain by adaptive modulation. Furthermore, it is computationally complex since exhaustive matrix inversions are required to determine the optimal mode. In this paper, we propose an efficient MM-QP system that improves the performance of a conventional system in terms of error rate and has a lower computational complexity than the conventional system. First, we define the rate-partitioning vector as the mode and control the rate among substreams and the number of substreams according to the channel instantaneous condition. Second, to reduce the computational complexity for the receiver to determine the optimal mode, the simplified mode-selection technique using estimates of the modal metric is proposed. In the proposed mode-selection technique, the optimal mode can be obtained by several multiplication and division operations. Finally, the mode-reduction technique eliminating the less-frequently used modes is proposed, which leads to a significant reduction of the feedback information with negligible performance loss. In numerical experiments, it was verified that the proposed MM-QP system gives a better error-rate performance than the conventional system, with much less computational complexity for the same amount of feedback information.      

Design of Parallel Tomlinson–Harashima Precoders

Like decision feedback equalizers (DFEs), Tomlinson-Harashima precoders (TH precoders) contain nonlinear feedback loops, which limit their use for high-speed applications. Unlike in DFEs, where the output levels of the nonlinear devices are finite, in TH precoders the output levels of the modulo devices are either infinite or finite but very large. Thus, it is difficult to apply look-ahead and pre-computation techniques to speed up TH precoders, which were successfully applied to design parallel and pipelined infinite impulse response (IIR) filters and DFEs in the past. However, a TH precoder can be viewed as an IIR filter with an input equal to the sum of the original input to the TH precoder and a finite-level compensation signal. Based on this point of view, a novel parallel architecture is proposed to speed up TH precoders. This architecture can be used in many high-speed applications, such as 10-Gb Ethernet over copper.     

MIMO多中继系统中基于不完全信道状态信息的预编码算法研究

针对配置多个中继节点的多输入多输出（Multiple-input Multiple-Output,MIMO）系统,提出一种不完全信道状态信息（Imperfect channel state information,CSI）下基于最小均方误差（Minimum Mean-Squared Error,MMSE）准则的预编码设计方案,该方案综合考虑各个节点天线之间的相关性及信道估计误差。由于各个中继端预编码矩阵之间可视为相互独立,故将约束优化问题转化为若干半正定规划问题,继而通过内点法或CVX工具箱求解预编码矩阵,然后采用求导法推导出接收端处理矩阵。最后利用迭代算法交替迭代来联合优化预编码矩阵和接收端处理矩阵,直到算法收敛。仿真结果表明,与未能综合考虑各个节点的预编码算法相比,本文提出的算法能明显改善系统BER性能。      

New Design for Linear Precoding over STBC in the Presence of Channel Correlation

In order to account for spatial correlation in a multiple input multiple output (MIMO) channel using precoding over space-time block codes (STBC), an approach was proposed for the design of a linear precoder (H. Sampath and A. Paulraj, 2002). This approach works well for orthogonal STBC but fails in the case of non-orthogonal STBC. Based on a min-max problem formulation, a new design of the linear precoder is proposed in this paper. Simulation results in the case of quasi-orthogonal STBC (ABBA) are presented in order to show the gain over the conventional design approach and the non-precoded system     

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。