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。     

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.     

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$rho$-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.     

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     

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.

     

多用户MIMO系统广播信道的连续块对角化预编码算法

针对块对角化(BD)算法无法满足各个用户的需要、串行优化(SO)算法排序复杂、容量较低的问题,提出了一种连续块对角化(SBD)算法.该算法按照各用户的信道条件、服务质量(QoS)需求给用户定义不同的优先级,并按优先级次序进行块对角化,后续用户在对高优先级用户及同优先级用户不干扰的条件下采用块对角化法抵消共信道干扰(CC...     

MIMO Wireless Linear Precoding

This article provides a tutorial of linear precoding for a frequency- flat, single-user MIMO wireless system, examining both theoretical foundations and practical issues. The article first discusses principles for CSIT (channel-side information at the transmitter) acquisition and develops a dynamic CSIT model, which spans perfectly to statistical CSIT, taking into account channel temporal variation. It then presents the capacity benefits of CSIT and information theoretic arguments for exploiting the CSIT by linear precoding. A precoded system structure is then described, involving an encoder and a linear precoder. Criteria for designing the precoder are then discussed, followed by specific designs for different CSIT scenarios.     

基于协作多点下行传输的非线性鲁棒预编码

对于协作多点系统,下行信道信息误差会大幅降低联合传输的性能。为了避免下行信道信息误差对联合传输的影响,本文利用其二阶统计特性,设计了非线性鲁棒预编码算法。由于协作多点系统的特点和非线性鲁棒预编码的结构会导致用户间的性能差异,本文通过优化非线性鲁棒预编码算法的连续干扰消除先后顺序,从而改善性能最差用户的误码率,降低非线性鲁棒预编码算法的平均误码率。仿真结果表明当下行信道信息误差存在时,本文所提出的非线性鲁棒预编码性能优于传统的线性和非线性预编码性能。仿真结果还表明优化排序能提高非线性鲁棒预编码的性能增益。     

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.     

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。     

NGB-W广播信道估计实现算法设计

针对下一代广播电视网无线系统(NGB-W)广播接收信道估计,提出了一种基于二次一维维纳滤波的信道估计实用算法.该算法实时估计信道多普勒频偏、时延扩展和噪声方差等参数,并根据参数估计值分别从离线获得的预选集中选择时域和频域的一维维纳滤波系数.通过Cocentric System Studio(CCSS)平台仿真,给出了参数估计对算法性能的影响,以及所提信道估计算法的均方误差和误块率性能.仿真结果表明该算法在不同移动速度下,与采用理想插值系数信道估计相比性能损失不超过0.4 dB,与理想信道估计相比性能损失在1 dB以内.     

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.     

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.     

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。     

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     

全双工信息与能量同传系统的鲁棒性预编码及高能效时隙分配方案

最近全双工信息与能量同传系统（FD-SWIPT）受到高度重视,区别于现有研究,本文在最大化多天线FD-SWIPT系统的和速率的同时,考虑了其鲁棒性和能量效率,并提出了一种FD-SWIPT系统的鲁棒性预编码及高能效时隙分配方案.由于优化涉及的因素很多,这是一个多个变量的非凸优化问题,在数学上很难求解.首先,为减少全双工系统中自干扰对和速率造成的影响,基于奇异值分解及最小均方误差算法对系统自干扰进行消除;然后,固定时隙分配因子,在自干扰信道存在估计误差的情况下,基于一阶泰勒凸逼近对原优化问题进行鲁棒预编码设计,并给出相应的迭代算法;进一步,提出了不同约束条件下的时隙分配方案,并推导了不同方案下的时隙分配因子的最优解.最后,通过仿真实验与现有结果比较,验证了本文方案的性能优势.