Recursive and Trellis-Based Feedback Reduction for MIMO-OFDM with Rate-Limited Feedback

We investigate an adaptive MIMO-OFDM system with a feedback link that can only convey a finite number of bits. We consider three different transmitter configurations: i) beamforming applied per OFDM subcarrier, ii) precoded spatial multiplexing applied per subcarrier, and iii) precoded orthogonal space time block coding applied per subcarrier. Depending on the channel realization, the receiver selects the optimal beamforming vector or precoding matrix from a finite-size codebook on each subcarrier, and informs the transmitter through finite-rate feedback. Exploiting the fact that the channel responses across OFDM subcarriers are correlated, we propose two methods to reduce the amount of feedback. One is recursive feedback encoding that selects the optimal beamforming/precoding choices sequentially across the subcarriers, and adopts a smaller-size time-varying codebook per subcarrier depending on prior decisions. The other is trellis-based feedback encoding that selects the optimal decisions for all subcarriers at once along a trellis structure via the Viterbi algorithm. Our methods are applicable to different transmitter configurations in a unified fashion. Simulation results demonstrate that the trellis-based approach outperforms the recursive method as well as an existing interpolation-based alternative at high signal-to-noise-ratio, as the latter suffers from "diversity loss"     

太赫兹超大规模3D MIMO系统中的波束斜视补偿技术

太赫兹通信技术凭借超大带宽的优势成为未来6G的关键技术之一。超大规模天线技术可以提供巨大的空间分集,提升频谱效率,同样在6G无线通信系统中起到关键作用。在基于移相器的大规模MIMO（multiple-input multiple-output）混合预编码中,由于太赫兹频段的超大带宽,不同频率的子载波信道具有不同的等效空间方向,发射端波束形成时,将带来严重的波束斜视问题。与此同时,随着天线规模的不断增长,超大规模天线技术的应用更进一步扩大了波束斜视造成的影响。针对超大规模天线阵列带来的波束斜视现象放大问题,本文利用3D MIMO平面天线阵列来改善这一状况。为进一步改善太赫兹频段超大带宽引起的波束斜视,在3D大规模MIMO系统的基础上,本文提出了基于两层移相器结构的混合预编码方案,利用第二层移相器,对不同频率的子载波进行补偿。实验结果表明,本方法可以有效地弥补波束斜视带来的阵列增益损失,实现接近最优的系统性能。      

Codebook‐Based Precoding for SDMA‐OFDMA with Spectrum Sharing

This paper focuses on codebook‐based precoding for space‐division multiple access/orthogonal frequency‐division multiple access (SDMA‐OFDMA) systems aiming to guarantee high throughput for their users as well as to mitigate interference to fixed satellite service (FSS). A systematic design of SDMA codebook for subband‐based OFDMA is proposed, which forms multiple orthogonal beams with common spatial null in the direction of a victim FSS earth station (ES). The design enables both transmitter and receiver to independently construct identical codebook by sharing only on the direction angle of an FSS ES, which takes fewer overhead bits than Gram‐Schmidt process, a general method satisfying our design criterion. A system‐level throughput evaluation shows that the proposed precoding provides superior performance over existing spectrum sharing method, that is, subband deactivation. The spectrum sharing analysis shows that the proposed precoding, even with an estimation error of the direction angles of an FSS ES, causes lower interference than existing precoding, knockdown precoding.     

Adaptive precoding and power allocation in distributed antenna systems with limited feedback

This paper introduces the limited feedback precoding into the distributed antenna system and proposes to adapt the predetermined orthogonal space time block codes to the available channel state information at the transmitter. The optimal representation of precoding information, namely the precoder, with least bits therefore becomes the key problem. Inspired by the characteristics of the distributed antenna system, we focus our work on the precoder construction, adaptable in response to the large and small scale fading, such that the symbol error probability is significantly reduced over that of a fixed, non‐adaptive, independent and identically distributed precoder codebook design. Furthermore, a suboptimal power‐loading strategy is presented by minimizing the derived tight upper bound on the average pairwise error probability of the precoded orthogonal space time block codes, which approaches the optimal performance asymptotically without additional channel knowledge other than the available feedback information. We prove that the proposed precoded orthogonal space time transmission scheme can achieve full diversity order. In particular, the robustness of our proposed transmission scheme to channel estimation error and feedback delay is respectively investigated in some detail, and numerical results show that it obviously improves the link reliability and obtains substantial gains even with few bits of feedback in comparison with conventional antenna selection scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

基于码本的有限反馈非酉矩阵预编码多用户MIMO系统

该文提出了一种基于码本的有限反馈非酉矩阵预编码下行多用户MIMO系统。该方案根据用户反馈的信道信息SINR在发送端进行调度和预编码来提高系统容量。预编码的码本设计依据格拉斯曼空间装箱原理,并将码本中的向量按其相关性构成非酉矩阵来提高预编码增益和抑制多用户共道干扰。新方案反馈量少、复杂度低,在相同情况下比传统的单用户MIMO系统和基于码本的酉矩阵预编码多用户MIMO系统都具有更好的性能。     

Subcarrier grouping with environmental sensing for MIMO‐OFDM systems over correlated double‐selective fading channels

Multiple‐Input, Multiple‐Output (MIMO)‐orthogonal frequency division multiplexing (OFDM) is a promising technique in 5G wireless communications. In high‐mobility scenarios, the transmission environments are time‐varying and/or the relative moving velocity between the transmitter and receiver is also time‐varying. In the literature, most of previous works mainly focused on fixed subcarrier group size and precoded the MIMO signals with unitary channel state information. In this way, the subcarrier grouping may naturally lead to big loss of channel capacity in high‐mobility scenarios because of the channel state information difference on the subcarriers in each group. To employ the MIMO‐OFDM technique, adaptive subcarrier grouping scheme may be an efficient way. In this paper, we first consider MIMO‐OFDM systems over double‐selective i.i.d. Rayleigh channels and investigate the quantitative relation between subcarrier group size and capacity loss theoretically. With developed theoretical results, we also propose an adaptive subcarrier grouping scheme to satisfy the preset capacity loss threshold by adjusting grouping size with the sensed environmental information and mobile velocity. Theoretical analysis and simulation results show that to achieve a better system capacity, a sparse scattering, lower signal‐to‐noise ratio, and lower velocity as well as properly large antenna number are matched with larger subcarrier group size. One important observation is that if the antenna number is too large and higher than a threshold, which will not bring any additional gain to the subcarrier grouping. That is, the system capacity loss will converge to a lower bound expeditiously with respect to antenna number, which is given in theory also. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved Multiuser MIMO Unitary Precoding Using Partial Channel State Information and Insights from the Riemannian Manifold

Multiple-input multiple-output (MIMO) systems can be leveraged to increase capacity in fading channels. Especially in multiuser downlink communication systems, it has been shown that knowledge of channel state information at the transmitter (CSIT) is critical to leverage the capacity gain available from multiple antennas. When duplexing is performed using time division, CSIT can often be successfully obtained when channel reciprocity is available. CSIT acquisition, however, is much more difficult in frequency division duplexing. Sending feedback on the uplink has been shown to be a powerful technique to improve downlink performance in single user MIMO systems. The basic idea is to restrict the CSIT to a B bit codebook so that the mobiles can easily transmit these bits on the uplink. In this paper, we consider the multiuser downlink model with unitary precoding when there is a codebook consisting of 2^B unitary matrices that the precoder is restricted to lie in. This codebook is designed offline and known to both the basestation and all users. Each user sends back signal-to-interference plus noise ratio (SINR) information along with binary feedback about the unitary precoder. Based on the CSIT received on the uplink, the basestation selects one of the unitary matrices in the codebook to maximize the sum-rate. For this set-up, we first analyze the sum-rate performance of the unitary precoding scheme. We then show that the codebook of unitary precoders represents a collection of points in a special kind of manifold and show how the achievable sum-rate performance relates to the minimum distance of the codebook points in this space. Finally, we present a framework for constructing the codebook to maximize this minimum distance. Monte Carlo simulation results are presented to show the sum-rate performance of the proposed codebook design.     

Quantized Principal Component Selection Precoding for Spatial Multiplexing with Limited Feedback

In this paper, for spatial multiplexing with limited feedback, a quantized principal component selection (QPCS) precoding scheme is proposed that achieves comparable capacity to the closed-loop multiple-input multiple-output (MIMO) and furthermore adapts to various fading channel conditions without any additional feedback bits and transmit channel state information (CSI). We propose a systematic design method for a codebook consisting of a finite number of unitary matrices based on a maximizing minimum distance criterion in the one- dimensional angular domain and show that the method outperforms the Grassmannian subspace packing method in various fading channel conditions. The proposed QPCS precoding scheme allows for adjustment of the precoding matrix based on limited feedback information on the principal vectors approximating a MIMO channel in the angular domain according to various channel conditions. Furthermore, for practical implementation of the QPCS precoding scheme, we propose a structured precoder optimization procedure and show that the proposed procedure induces a negligible capacity loss compared with the exhaustive precoder optimization, even with considerably reduced complexity.     

Peak‐to‐average power ratio reduction of a hidden training sequence‐aided precoding scheme for MIMO‐OFDM

We analyze a peak‐to‐average power ratio (PAPR) reduction property based on a hidden training sequence‐aided precoding scheme for MIMO‐OFDM systems. In addition to the benefits of a hidden training sequence‐aided precoding scheme such as improvement in bandwidth efficiency and frequency diversity gain, we address that power amplifier efficiency can be improved without any additional complexity burden. By mathematically analyzing PAPR of the precoded MIMO‐OFDM signal with a hidden training sequence, we demonstrate that PAPR reduction can be obtained by varying the allocated power to the hidden training sequence. Because of the low PAPR property of this scheme, it is possible to utilize a low‐cost power amplifier, resulting in the reduction in the total cost for hardware implementation. Copyright © 2014 John Wiley & Sons, Ltd.     

Zero‐forcing and codebook based beamforming scheme for practical usage of multiuser MIMO‐OFDM with uplink channel sounding

Since the concept of the multiuser multiple input multiple output (MU‐MIMO) system has been introduced for enhancement of capacity and flexibility, it has been accepted in various wireless standards. To enjoy the benefits of the MU‐MIMO system, full or partial channel information is necessary at the transmitter, but how to use the full or partial feedback information in the practical system perspective has not been investigated well. In this paper, we analyze the interference of full usage concurrent transmission codebook based on the MU‐MIMO systems and also investigate the usage of channel information for a codebook based scheme and a zero‐forcing beamforming (ZFBF) scheme. Based on the analytic results, we propose two adaptive schemes for the practical usage perspective in MU‐MIMO‐OFDM systems. Firstly, we propose an adjustable uplink channel sounding scheme, which depends on the number of users in a given cell/sector in frequency division duplexing system, with ZFBF MU‐MIMO‐OFDM systems. Secondly, we propose an adaptive switching scheme, which depends on signal‐to‐noise ratio, between the codebook based scheme and the ZFBF scheme. The performance of the proposed scheme is evaluated with computer simulations, and the simulation results show that the proposed scheme provides the enhanced throughput over entire signal‐to‐noise‐ratio regions. Copyright © 2014 John Wiley & Sons, Ltd.     

一种OFDM中继系统的有限反馈预编码方法

基于正交频分复用的放大转发协作中继系统,为了减少系统误比特率、增加信道容量和增强实用性,该文提出一种实用的源节点预编码和中继节点预编码的联合优化有限比特反馈的预编码方法。利用3节点构成的两个下行链路,实现两跳协作通信方式;采用SVD分解和QR(orthogonal triangular)分解相结合设计预编码,其中源节点预编码每帧只要一个;优选量化码本,把预编码矩阵量化后反馈到发射端。仿真结果表明,该方案能提高平均和速率、降低误码率和改善中断概率特性,且反馈比特数较少具有更好的实用价值。     

Bat algorithm–based beamforming for mmWave massive MIMO systems

In this paper, an optimized analog beamforming scheme for millimeter‐wave (mmWave) massive MIMO system is presented. This scheme aims to achieve the near‐optimal performance.by searching for the optimized combination of analog precoder and combiner. In order to compensate for the occurrence of attenuation in the magnitude of mmWave signals, the codebook‐dependent analog beamforming in conjunction with precoding at transmitting end and combining signals at the receiving end is utilized. Nonetheless, the existing and traditional beamforming schemes involve a more difficult and complicated search for the optimal combination of analog precoder/combiner matrices from predefined codebooks. To solve this problem, we have referred to a modified bat algorithm to find the optimal combination value. This algorithm will explore the possible pairs of analog precoder/combiner as a way to come up with the best match in order to attain near‐optimal performance. The analysis shows that the optimized beamforming scheme presented in this paper can improve the performance that is very close to the beam steering benchmark that we have considered.     

多小区MIMO系统中基于泄漏的多用户下行链路预编码新算法

针对多小区MIMO系统的多用户下行链路预编码设计是未来移动通信系统研究的重要内容之一。本文在蜂窝多小区MIMO通信环境下,基于信漏噪声比(Signal-to-Leakage-Noise Ratio,SLNR)最大准则,提出了改进的多用户下行链路线性预编码算法。通过在优化目标中考虑接收端白化滤波器的影响,该预编码算法实现了对用户间干扰和小区间干扰(OCI)的同步抑制消除;在求解预编码矩阵优化问题时,本文基于QR分解提出了一种新的低复杂度求解算法,该算法能以较低的计算复杂度实现系统性能的有效提升。仿真实验结果表明,本文的改进SLNR线性预编码算法能有效抑制小区间干扰(OCI)的影响,使多小区MIMO系统获得更高的和速率(Sum Rate)容量。      

一种提高部分反馈预编码MIMO系统安全性能方案

MIMO(Mutiple-In Mutiple-Out,多输入多输出)技术是无线移动通信领域智能天线技术的重大突破。无线通信的广播特性容易引起信息泄露,开展研究提高无线通信网络安全性能的课题十分必要。目前,MIMO系统中的预编码技术已成为无线通信领域的研究热点。本文将介绍一种加密技术控制下通过旋转码本提高预编码系统安全性能的方案。通过仿真,验证了该方案可以使无线通信可靠性接近1,并且该方案的设计思想可以推广到其他预编码系统中。     

User scheduling based on angles with block diagonalization in MU‐MIMO broadcast

This paper investigates user selection scheme in the multiuser multiple‐input multiple‐output (MU‐MIMO) broadcast (BC) scene with block diagonalization precoding. Block diagonalization is a suboptimal but practical linear precoding method, which can eliminate the multiuser interference by turning the MU‐MIMO BC channel into parallel MIMO channels. With this precoding method, we propose the best user from the user subset to maximize the total throughput in the MU‐MIMO BC system. The angles between subspaces used in this paper are induced from n ‐inner product, an extension from norm space to the n ‐dimensional space, which characterizes the orthogonality between subspaces. One of the algorithms achieves good performance by comparing the capacity greedily, the other one attains high capacity by reducing the cardinality of the user subset to improve the orthogonality between the user channels, which could be seen as a complexity reduction algorithm with respect to the former one. Indeed, they are all based on the angles between subspaces. Analysis shows that both of the proposed algorithms have lower complexity and better performance than the classical algorithms. The numerical results also confirm our analysis.     

Capacity of a Multiple-Antenna Fading Channel With a Quantized Precoding Matrix

Given a multiple-input multiple-output (MIMO) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of random vector quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are independent and identically distributed (i.i.d.) and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter using $B$ bits. We first derive the large system capacity of beamforming (rank-one precoding matrix) as a function of $B$, where large system refers to the limit as $B$ and the number of transmit and receive antennas all go to infinity with fixed ratios. RVQ for beamforming is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. We subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic RVQ performance with optimal and linear receivers (matched filter and minimum mean squared error (MMSE)). Numerical examples show that these approximations accurately predict the performance of finite-size systems of interest. Given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback.      

Precoder Partitioning in Closed-loop MIMO Systems

We study unitary precoding for multistream MIMO systems with partial channel state information at the transmitter. We introduce a quantization scheme in which the full space of non-equivalent precoding matrices is partitioned into Grassmannian and orthogonalization parts. The Grassmannian part is used for maximizing the power after precoding and the orthogonalization part is used for removing cross talk between the data streams. We show that orthogonalization improves the attainable capacity when the receiver is linear. We give a parametrization for the non-equivalent orhogonalization matrices and a metric which measures the orthogonality of the transmission. Optimal orthogonalization codebooks for two-stream transmission are presented. When feedback is limited, the optimal partitioning of feedback bits between Grassmannian and orthogonalization parts becomes an issue. In correlated scenarios, the number of feedback bits may be significantly reduced by investing bits into the orthogonalization part.     

Improved Wideband Precoding with Arbitrary Subcarrier Grouping in MIMO‐OFDM Systems

Precoding in the multiple‐input multiple‐output orthogonal frequency division multiplexing system is investigated. In conventional wideband precoding (WBP), only one precoder, obtained from the decomposition of the subcarrier independent channel matrix, is used for all subcarriers. With an investigation of the relationship between the subcarrier independent channel matrix and the temporal/frequency channels, an improved WBP scheme is proposed for practical scenarios in which a part of subcarriers are allocated to a user. The improved WBP scheme is a generalized scheme of which narrow‐band precoding and conventional WBP schemes are special modes. Simulation results demonstrate that the improved WBP scheme almost achieves the optimum performance of a single precoder and outperforms the conventional WBP scheme in terms of the bit error ratio and ergodic capacity with slight complexity increase. The largest advantage of the improved WBP scheme on signal‐to‐noise ratio in simulation results is over 2.1 dB.     

Peak‐to‐average power ratio reduction in space–time coded MIMO‐OFDM via preprocessing

In this paper, we propose a trellis exploration algorithm based preprocessing strategy to lower the peak‐to‐average power ratio (PAPR) of precoded MIMO‐OFDM. We first illustrate the degradation in PAPR due to optimal linear precoding in MIMO‐OFDM systems. Then we propose two forms of multi‐layer precoding (MLP) schemes to reduce PAPR. In both schemes, the inner‐layer precoder is designed to optimize system capacity/BER performance. In the first MLP scheme (MLP‐I), a common outer‐layer polyphase precoding matrix is employed. In the second MLP scheme (MLP‐II), data stream corresponding to every transmit antenna is precoded with a different outer‐layer polyphase precoding matrix. Both outer‐layer precoders are custom designed using the trellis exploration algorithm by applying the aperiodic autocorrelation of OFDM data symbols as the metric to minimize. Simulation results indicate that both MLP schemes show superior PAPR performance over conventional MIMO‐OFDM with and without precoding. In addition, MLP better exploits frequency diversity resulting in BER performance gains in multi‐path environments. Copyright © 2010 John Wiley & Sons, Ltd.     

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.