Space-Time Transmission using Tomlinson-Harashima Precoding
Space-Time Transmission using Tomlinson-Harashima Precoding
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发表时间：
2002
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通讯作者：
R. Fischer;C. Windpassinger;A. Lampe;J. Huber
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作者：
R. Fischer;C. Windpassinger;A. Lampe;J. Huber
本文提出了 Tomlinson-Harashima 预编码，一种非线性预均衡技术，用于多输入/多输出信道上的传输。这里执行空间均衡，即多用户干扰的均衡，或者组合的空间/时间均衡，而不是均衡符号间干扰（时间均衡）。结果表明，与 SISO 对应物一样，这种 MIMO 预编码比线性预均衡和超决策反馈均衡（如 BLAST 类方案中所做的那样）具有显着优势。使用信道编码，MIMO 预编码能够以比竞争方案更低的编码延迟实现更高的功率效率。关键词：BLAST、决策反馈均衡、MIMO 信道、空时编码、Tomlinson-Harashima 预编码 一、引言 在过去几年中，对高速无线传输的需求显着增加，并激发了人们对所谓的多输入/多输出（MIMO）系统的兴趣。在这些传输方案中，类似 BLAST（贝尔实验室分层时空）方法（发射器和接收器具有多个天线的系统）目前发挥着最突出的作用。这种特别的兴趣源于 Foschini 和 Gans [17] 的结果，他们表明频谱效率（对于大信噪比）原则上可以随着发射 ( NT ) 和接收 ( NR ) 天线数量的最小值线性增长。一般来说，MIMO传输方案可以通过基本关系y＝Hx+n来描述。这里，x表示包括NT个并行数据流的发送符号的发送向量。这些流可能是由于高速率数据信号的并行（即分层）编码，或者它们可能属于不同且独立的用户。维度NR的向量y和n分别表示接收符号的向量和干扰的向量。 MIMO信道的特征在于其NR NT 信道矩阵H 。除了 MIMO 信道的信息论研究 [29]、[25]、[26]、[33]、[6] 之外，还开展了大量工作来为各种实际场景提出可行的接收器。 MIMO 信道传输的主要困难是并行数据流的分离或均衡，即恢复传输矢量 x 中在接收器侧产生干扰的分量。分离数据流最明显的策略是接收器侧的线性均衡。这里，决策向量由r = H 1 (l) y 生成，其中H 1 (l) 表示信道矩阵H 的左（伪）逆。众所周知，线性均衡会受到噪声增强的影响，因此功率效率较差。这个缺点可以通过空间决策反馈均衡（DFE）[17]，[34]来克服。不幸的是，在 DFE 中可能会发生错误传播。此外，由于需要立即做出决定，因此信道编码的应用需要一些巧妙的交织，这反过来又引入了显着的延迟。最后，不同的作者 [30]、[1]、[4] 提出了迭代（Turbo）检测器。上述方法仅在接收器侧需要信道状态信息(CSI)。如果CSI（部分）在发射机处也可用，则可以通过预均衡来分离用户。假设发射机处的CSI完美，通过将数据向量a与发射机处的信道矩阵H的（伪）右逆H 1 (r)相乘，可以完全避免接收机侧的用户干扰[3]。不是直接通过信道 (x = a) 传输数据符号 a，而是将预失真版本 x = H 1 (r)a 馈送到信道中。然而，这种迫零线性预均衡会遭受与接收器侧线性均衡相同的功率效率损失。这里，平均发射功率没有增强噪声，而是增加了相同的系数。最后，信道均衡的任务可以在发射机和接收机之间分配。一种流行的策略是基于通道矩阵 H 的奇异值分解（SVD），即将其写为 H = U V ，其中 U 和 V 是酉矩阵并且是对角矩阵。在发射机应用 V H 并在接收机应用 UH 生成独立的并行通道 [28]、[24]。这里，与线性（预）均衡相比，既没有增加发射功率，也没有增强信道噪声。 MIMO 系统中的空间均衡（信道矩阵 H）与符号间干扰 (ISI) 信道上的单输入/单输出 (SISO) 传输的时间均衡紧密相关（信道传递函数 H(z)）。每个均衡策略在其他领域都有其直接对应的策略。表 I 中描述了这些类比。接收器处的线性均衡和发射器处的线性预均衡的对应关系是直接的。 MIMO 信道的奇异值分解可以用正交频率来识别。 表 I. FORISI 信道和 MIMO 信道的相应均衡策略。 ISI 通道 H(z) MIMO 通道 H（时间均衡）（空间均衡） 接收器处线性 接收器处线性均衡 通过 1=H(z) 发送器处通过 H 1 (l) 线性均衡 发送器/接收器处通过 1=H(z) 线性预均衡 通过 H 1 (r) 线性预均衡 OFDM/DMT，矢量编码 SVD 接收器处非线性 DFE 发送器/接收器处矩阵 DFE Tomlinson-Harashima 预编码 用于 ISI 信道上的 MIMO 信道分割复用 (OFDM) 或离散多音 (DMT) 传输的预编码。准确地说，SVD对应的是一种称为向量编码的策略，例如[23]、[11]，其中基于某些信道矩阵的特征向量在发射机和接收机处处理连续符号块。在这两种情况下，都会将底层信道划分为并行独立的子信道，这也是计算信道容量时的理论概念。决策反馈均衡是接收端的非线性均衡策略。 MIMO 通道的对应部分是用于空间均衡的矩阵 DFE。在SISO传输中，DFE的反馈部分可以转移到发射机，从而产生称为汤姆林森-原岛预编码（THP）的方案。众所周知，忽略平均发射功率的微小增加，DFE 和 THP 的性能是相同的，但由于 THP 是一种发射器技术，因此可以避免接收器处的错误传播。此外，可以以与理想加性高斯白噪声（AWGN）或平坦衰落信道相同的方式应用信道编码方案。此外，已经表明（例如[35]、[12]）DFE（一种非线性但时不变的技术）的性能与多载波传输（OFDM/DMT）（一种线性但时变的策略）的性能相同。实际上，传输方案的实际选择取决于很多因素，例如实现的复杂性、固有延迟或传输信号的峰均功率比。在本文中，我们想要提出一种用于 MIMO 信道的非线性预编码方案。与 SISO 传输一样，它与矩阵 DFE 相对应，并且反映了 SVD 与 THP 与多载波传输相同的对偶性。当然，预编码需要发送端的CSI。目前，为了概述 MIMO 预编码的主要原理，我们假设完美的 CSI 是可用的。 [14] 解决了发送端 CSI 必须有多准确的问题。本文的结构如下：第二部分介绍了一般通道模型，并对 BLAST 进行了简短概述。基于此，第三节提出了针对 MIMO 信道的 TomlinsonHarashima 预编码。为了说明 MIMO 预编码的优点，第四节给出了未编码和编码传输的仿真结果。第五节给出了总结。通道模型和爆炸
In this paper, Tomlinson-Harashima precoding, a nonlinear pre-equalization technique, is proposed for transmission over multiple-input/multiple-output channels. Instead of equalizing intersymbol interference (temporal equalization) here spatial equalization, i.e., equalization of the multi-user interference, or combined spatial/temporal equalization is performed. It is shown that this MIMO precoding—like its SISO counterpart—offers significant advantages over linear pre-equalization and over d ecisionfeedback equalization, as is done in BLAST-like schemes. Us ing channel coding, MIMO precoding is able to achieve higher power efficiencies at lower coding delays than competing schemes. Keywords—BLAST, decision-feedback equalization, MIMO channel, space-time coding, Tomlinson-Harashima precoding I. I NTRODUCTION THE demand for high-rate wireless transmission significantly increased over the last years and stimulated the interest in so-called m ultiple-input/multipleoutput (MIMO) systems. Among these transmission schemes, BLAST-like (B ell Laboratories La yered Space-Time) approaches—systems with multiple antennas at transmitter and receiver—currently play the most prominent role. This particular interest is due to the results of Foschini and Gans [17] who showed that the spectral efficiency can (for large signal-to-noise ratios) in principle grow linearly with the minimum over the number of transmit ( NT) and receive ( NR) antennas. In general, a MIMO transmission scheme can be described by the basic relation y =Hx+n. Here,x designates the transmit vector which comprises the transmit symbols ofNT parallel data streams. These streams can be due to a parallel (i.e., layered) encoding of a highrate data signal, or they may belong to different and independent users. The vectors y andn of dimensionNR denote the vector of received symbols, and the vector of disturbances, respectively. The MIMO channel is characterized by itsNR NT channel matrixH . Besides information theoretic studies of MIMO channels [29], [25], [26], [33], [6], numerous work has been done to propose feasible receivers for various practical scenarios. The main difficulty for transmission over MIMO channels is the separation or equalization of the parallel data streams, i.e., the recovery of the components of the transmitted vector x which interfere at the receiver side. The most obvious strategy for separating the data streams is linear equalization at the receiver side. Here, the decision vector is generated by r = H 1 (l) y, where H 1 (l) denotes the left (pseudo) inverse of the channel matrixH . It is well-known that linear equalization suffers from noise enhancement and hence has poor power efficiency. This disadvantage can be overcome by spatial decision-feedback equalization (DFE) [17], [34]. Unfortunately, in DFE error propagation may occur. Moreover, since immediate decisions are required, the application of channel coding requires some clever interleaving which in turn introduces significant delay. Finally, iterative (Turbo) detectors have been presented by various authors [30], [1], [4]. The above methods require c hannel state information (CSI) only at the receiver side. If CSI is (partly) also available at the transmitter, the users can be separated by means of pre-equalization. Assuming perfect CSI at the transmitter, interference of the users at the receiver side can be completely avoided by a multiplication of the data vector a with the (pseudo) right inverse H 1 (r) of the channel matrixH at the transmitter [3]. Instead of transmitting the data symbols a directly over the channel (x = a), the pre-distorted version x = H 1 (r)a is fed into the channel. However, this zero-forcing linear pre-equalization suffers from the same loss in power efficiency as linear equalization at the receiver side. Here, instead of enhancing the noise, average transmit power is increased by the same factor. Finally, the task of channel equalization can be split among transmitter and receiver. A popular strategy is based on the s ingular value decomposition (SVD) of the channel matrixH, i.e., writing it asH = U V , whereU andV are unitary matrices and is diagonal. ApplyingV H at the transmitter and UH at the receiver independent, parallel channels are generated [28], [24]. Here, in contrast to linear (pre-)equalization neither transmit power is increased, nor channel noise is enhanced. Spatial equalization in MIMO systems (channel matrix H) is tightly related to temporal equalization for single-input/single-output (SISO) transmission over intersymbol-interference (ISI) channels (channel transfer functionH(z)). Each equalization strategy has its direct counterpart in the other domain. The analogies are depicted in Table I. The correspondences for linear equalization at the receiver and linear pre-equalization at the transmitter are immediate. Singular value decomposition for MIMO channels can be identified with o rthogonal frequencyTABLE I. CORRESPONDING EQUALIZATION STRATEGIES FORISI CHANNELS AND MIMO CHANNELS. ISI channel H(z) MIMO channel H (temporal equalization) (spatial equalization) linear at receiver linear equalization via 1=H(z) linear equalization via H 1 (l) at transmitter linear pre-equalization via 1=H(z) linear pre-equalization via H 1 (r) at transmitter/receiver OFDM/DMT, vector coding SVD non-linear at receiver DFE matrix DFE at transmitter/receiver Tomlinson-Harashima precoding precoding for MIMO channels division multiplexing (OFDM) or discrete multitone (DMT) transmission over ISI channels. To be precise, SVD corresponds to a strategy called vector coding, e.g. [23], [11], where blocks of consecutive symbols are processed at transmitter and receiver based on the eigenvectors of some channel matrix. In both cases, a partitioning of the underlying channel into parallel independent sub-channels is performed, which is also the theoretical concept when calculating the channel capacity. Decision-feedback equalization is a non-linear equalization strategy at the receiver side. Its counterpart for MIMO channels is a matrix DFE for spatial equalization. In SISO transmission, the feedback part of the DFE can be transferred to the transmitter, leading to a scheme known asTomlinson-Harashima precoding (THP) . It is well known that neglecting a very small increase in average transmit power, the performance of DFE and THP is the same, but since THP is a transmitter technique, error propagation at the receiver is avoided. Moreover, channel coding schemes can be applied in the same way as for the ideal additive white Gaussian noise (AWGN) or flat fading channel. Furthermore, it has been shown (e.g. [35], [12]) that the performance of DFE, which is a non-linear but timeinvariant technique, is identical to that of multicarrier transmission (OFDM/DMT), which is a linear but timevariant strategy. In practice, the actual choice of transmission scheme depends on many points, such as complexity of implementation, inherent delay, or peak-toaverage power ratio of the transmit signal. In the present paper we want to present a non-linear precoding scheme for MIMO channels. Like in SISO transmission, it is the counterpart to matrix DFE and reflects the same duality to SVD as THP to multicarrier transmission. Of course, precoding requires CSI at the transmitter side. For the moment, in order to outline the main principles of MIMO precoding, we assume that perfect CSI is available. The question of how accurate the CSI has to be at the transmitter side is addressed in [14]. The paper is organized as follows: In Section II the general channel model is introduced and a short overview of BLAST is given. Based on this, TomlinsonHarashima precoding for MIMO channels is presented in Section III. In order to illustrate the advantages of MIMO precoding, simulation results for uncoded and coded transmission are presented in Section IV. A summary is given in Section V. II. CHANNEL MODEL AND BLAST