Performance of Orthogonal Beamforming for SDMA With Limited Feedback

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.     

空间相关莱斯衰落信道下基于部分信道信息的多用户预编码与调度算法

在空间相关的莱斯衰落信道模型下,针对多用户MIMO(Multiple-Input Multiple-Output)系统潜在的多用户分集增益和空间分集增益,该文提出了一种基于部分信道信息的多用户预编码与调度算法。结合部分瞬时信道信息和统计信息,利用约束最大似然估计对各用户信道矢量进行估计,然后利用估计的各用户信道调度多个用户进行预编码。仿真结果表明,该方案以较少的反馈开销,获得了较大的性能增益。     

Opportunistic Beamforming over Rayleigh Channels with Partial Side Information

In recent years, diversity techniques have evolved into highly attractive technology for wireless communications in different forms. For instance, the channel fluctuations of the users in a network are exploited as multiuser diversity by scheduling the user with the best signal-to-noise ratio (SNR). When fading is slow, beamforming at a multiple antenna transmitter is used to induce artificial channel fluctuations to ensure multiuser diversity in the network. Such a beamforming scheme is called opportunistic beamforming since the transmitter uses random beamforming to artificially induce opportunism in the network [1]. Opportunism requires a large number of users in the system in order to reach the performance of the true beamforming that uses perfect channel state information (CSI). In this paper we investigate the benefit of having partial CSI at an opportunistic transmitter. In the investigation, we focus on the maximum normalized SNR scheduling where user?s feedback consists of SNR relative to its channel gain. We show that opportunism can be beneficially used to increase the average throughput of the system. Simulations support the analytical average throughput results obtained as the amount of CSI and the number of users vary.     

Reduced-feedback linear precoding with stable performance for the time-varying MIMO broadcast channel

This work explores the performance of a multiple-input multiple-output broadcast channel where both the transmitter and receivers have outdated channel knowledge due to node motion or other time-variations in the communication channel. A performance analysis based on measured channel responses reveals significant throughput degradation for optimal linear and nonlinear precoding strategies unless the channel state information (CSI) is frequently fed back to the transmitter. The paper then develops a linear beamforming precoding strategy based on channel distribution information in the form of a full spatial correlation matrix for each user. This algorithm is shown to provide highly stable communication, with a throughput that is higher than that for optimal precoders operating on outdated CSI, in a time-variant environment, indicating that this approach can operate with significantly reduced feedback frequency. Furthermore, the paper demonstrates the use of the well-known Kronecker and Weichselberger models to parameterize the full correlation matrix to enable further reduction in the amount of feedback data required for implementation of the new beamforming technique.     

一种多输入多输出系统中有限反馈预编码的自适应跟踪测度

该文提出一种新的适用于无线相关信道中有限反馈预编码多输入多输出系统的预编码矩阵自适应跟踪测度。由于该测度在统计意义下对信道的相关性与预编码矩阵变化的关系具有更优化的描述,所以基于该测度的方案在保持较低反馈信息量的前提下,能够进一步改善预编码系统性能。文中给出优化自适应跟踪测度的理论推导。系统仿真分别针对无线信道的频域相关和时域相关,并结合空间分集和空间复用两类系统结构予以讨论,并验证了理论分析结果。另外,由于该测度方案算法复杂度更低,所以更具工程实用价值。     

统计和瞬时CSI混合的3D MIMO预编码

本文针对分别具有统计信道状态信息（Channel State Information,CSI）和瞬时CSI的用户,研究了两类用户在三维多输入多输出（Three-Dimension Multiple-Input Multiple-Output,3D MIMO）系统中的下行链路传输模式,解决了混合利用统计和瞬时CSI的下行预编码的设计问题。利用3D MIMO信道的克罗内克积的性质,提出了一种用于最小化基站总发射功率的扩展迫零预编码的方法,并分别求解其最优水平预编码矩阵和最优垂直预编码矩阵。仿真结果表明,该方案具有更低的复杂度和良好的速率。      

MIMO-OFDMA波束成形的反馈设计

MIMO-OFDMA的波束成形算法中,接收机需要反馈信道状态信息。当系统用户、子载波、天线数增加时,反馈量随之线性增长。为了限制反馈量在一个固定的限度之下,文中提出一种预设门限的反馈算法。接收机在确定每个子载波上的最优波束成形矢量及相应的信噪比之后,只有当信噪比大于门限时,才反馈最优波束成形矢量的索引及相应的信噪比值。该算法可以大大降低反馈量,同时保证频谱利用率几乎不变。     

Optimal bandwidth allocation for the data and feedback channels in MISO-FDD systems

In frequency-division duplex (FDD) systems, channel-state information (CSI) is estimated by the receiver and then fed back to the transmitter through a feedback link, which inevitably requires additional bandwidth and power. In this letter, we jointly study optimal bandwidth allocation between the data channel, modeled as a flat-fading multiple-input single-output (MISO) channel, and the feedback channel for maximum average throughput in the data channel using a beamforming scheme. We consider two models of the partial CSI at the transmitter (CSIT): the noisy CSIT, modeled as jointly Gaussian with the actual channel state, and the quantized CSIT. In the first model, we use distortion-rate theory to relate the CSIT accuracy to the feedback-link bandwidth. In the second model, we derive a lower bound on the achievable rate of the data channel based on the ensemble of a set of random quantization codebooks. We show that in the MISO flat-fading channel case, beamforming based on feedback CSI can achieve an average rate larger than the capacity without CSIT under a wide range of mobility conditions.     

Transmission Scheme for 2D Antenna Array MIMO Systems with Limited Feedback

Three-dimensional (3D) multiple-input multiple-output (MIMO) systems exploit spatial richness and provide another degree of freedom to transmit signals and eliminate spatial interference. Currently, however, there is no 3D codebook for two-dimensional (2D) antenna array MIMO systems with limited feedback. In this paper, based on the existing 2D codebook, we present a limited feedback and transmission scheme for 2D antenna array MIMO systems. In this scheme, the mobile station (MS) has imperfect channel knowledge, and the base station (BS) only acquires partial information relating the channel instantiation. MS must feed back two channel state information (CSI) instances, i.e., the horizontal and vertical CSIs. After receiving the two CSI instances, the BS interpolates a new vertical precoding vector using the vertical CSI. Then, the BS re-constructs a 3D beamforming vector using horizontal and vertical precoding vectors and compensates the reported horizontal channel quality indicator. System level simulation is employed, and the simulation results show that the proposed method improves the system spectral efficiency and the cell-edge SE significantly.     

A Novel Uplink MIMO Transmission Scheme in a Multicell Environment

Uplink multiple-input multiple-output (MIMO) transmission scheme is developed for time division duplex (TDD) systems in a multicell environment. We propose a precoding scheme that maximizes the total achievable rate and works in the decentralized manner with only locally available channel state information (CSI) at each transmitter. We first establish and solve a decentralized optimization problem for the case of multiple-input single-output (MISO) channels, introducing a new precoding design metric called signal to generated interference plus noise ratio (SGINR). By extending the result to general MIMO channels, we propose an SGINR-based precoding scheme where the number of transmit streams is selected adaptively to the surrounding environments. Simulation results confirm that the proposed precoding scheme offers significant throughput enhancement in multicell environments.     

Precoding for Orthogonal Space–Time Block-Coded OFDM Downlink: Mean or Covariance Feedback?

This paper presents linear and nonlinear precoding design for error-rate improvement in orthogonal space–time block-coded (OSTBC) multiple-input–multiple-output (MIMO) orthogonal frequency-division-multiplexed (OFDM) downlink, where both the conditional mean of the channel gain matrix and the channel gain covariance matrix may be available at the transmitter. The conditional means of the channel matrix are derived for a general transmit-antenna-correlated frequency-selective fading MIMO channel with estimation errors and feedback delay. Mean-feedback linear precoding and nonlinear Tomlinson–Harashima precoding (THP) are developed to maximize the signal-to-noise power ratio (SNR). The intuition that when the mean feedback becomes accurate the mean-feedback precoding outperforms covariance precoding is confirmed. Dual-mode precoding is also proposed, in which the novel mean-feedback precoding or covariance precoding is adaptively chosen at the receiver. The precoding-mode switching metric is the maximized SNR, which is an indicator of the error rate. The receiver calculates its metric, selects the mode that achieves a higher SNR, and decides whether mean feedback is necessary. Our proposed precoders (both mean feedback and adaptive) significantly reduce the system error rate. Nonlinear precoding is shown to outperform linear precoding. Adaptive precoding outperforms both mean-feedback precoding and covariance precoding if individually applied in OSTBC OFDM.      

Outage probability of multiple-input single-output (MISO) systems with delayed feedback

We investigate the effect of feedback delay on the outage probability of multiple-input single-output (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect CSIR and (b) CSI estimated at the receiver using training symbols. With perfect CSIR, under a short-term power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BF-IC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BF-IC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a longterm power constraint, we show that BF-IC is better for low SNR and USPA is better at high SNR. With imperfect CSIR, we obtain an upper bound on the outage probability with USPA and BF-IC. Results show that the loss in performance due to imperfection in CSIR is not significant, if the training power is chosen appropriately.     

一种多天线UWB系统中线性预编码算法

线性预编码提高了多天线UWB系统的传输速率和误码率性能。通过选择合适的参数,系统最大限度地达到最大吞吐量,而多天线技术提高了系统空间分集增益。针对传统的ZF算法限制误码率性能提高的问题,提出了一种新的预编码方案,实现简单。仿真结果表明,新算法进一步减小系统误码率,提高了系统性能,较传统的ZF算法性能更为优越。     

多用户MIMO-OFDM系统低速率CSI反馈方法及信道容量分析

该文针对闭环多用户MIMO-OFDM系统提出一种基于线性预测的低速率CSI (Channel State Information)反馈方法。根据相关带宽将OFDM子载波划分成多个子带,移动台对每个子带的CSI作线性预测,并对预测误差进行量化编码后反馈给基站;基站使用相同的线性预测滤波器将反馈来的预测误差恢复成CSI,然后在每个子带上通过迫零-波束赋形实现多用户空间复用。同时,该文还在采用注水定理分配发射功率的条件下,从理论上分析了下行链路信道容量。数值仿真结果显示,每个反馈数据的实部或虚部仅用1bit量化时,本方法仍能够以较高的精度恢复CSI。与目前3GPP LTE标准所采用的基于码书的反馈方案相比,该方法能够在反馈开销相同情况下,有效地抑制同信道干扰,大幅提高系统容量。     

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.      

Enhanced Multi-mode Transmission by User Scheduling in MISO Broadcast Channels with Finite-Rate Feedback

This paper investigates the user selection strategy in multiuser downlinks using zero-forcing beamforming (ZFBF) and finite-rate feedback (FRF). In order to mitigate the interference-limited effect in ZFBF-FRF systems, we propose an efficient user scheduling scheme combined with adaptive transmission mode selection strategy. In this scheme, each user first evaluates its preferred transmission mode and the corresponding achievable rate according to a derived tight lower bound of the rate. Given such information on the users through feedback, the BS then determines the global transmission mode of the system and selects users for simultaneous transmission. Asymptotic analysis shows that limited feedback beamforming to a single user is the best choice at both low and high SNR regimes. Simulation results demonstrate individual effects of different system parameters on the sum rate performance by the proposed scheme.     

利用公共信道部分反馈信道信息的多用户分集方案及其性能

通过定量分析利用随机波束成型技术的多用户分集系统的吞吐率性能,在此基础上提出利用公共信道部分反馈信道信息的多用户分集方案并分析了它的性能,证明通过设置合理的门限,部分反馈信道度量几乎不降低系统吞吐率,但可以大量节省上行反馈的开销,当采用合适的多址方式,在一定带宽下,系统可以容纳更多的用户。     

Power control for delay constrained multi‐channel communications using outdated CSI

In this paper, we study the power allocation scheme for a single user, multi‐channel system, e.g., orthogonal frequency‐division multiplexing (OFDM) systems, under time‐variant wireless fading channels. We assume the receiver feeds back perfectly estimated channel state information (CSI) to the transmitter after a processing delay. The objective of the power allocation is to maximize throughput subject to quality‐of‐service (QoS) constraint. The QoS measure of our consideration is a triplet of data rate, delay, and delay bound violation probability. A two‐step sub‐optimal power allocation scheme is proposed to address the impact of outdated CSI. In the first step, the total transmission power that can be used within one block is determined according to the summation of the channel gains of all the channels. In the second step, the total transmission power is allocated among all the channels. The proposed power control scheme is less sensitive to the feedback delay. Compared to the optimal power allocation scheme designed for the perfect CSI scenario, it has lower computational complexity while achieving comparable capacity. Copyright © 2010 John Wiley & Sons, Ltd.     

Hybrid beamforming design based on unsupervised machine learning for millimeter wave systems

This article proposes a hybrid beamforming design with reduced channel state information (CSI) feedback. We use a beam sweeping procedure to provide channel measurements and feed a CSI report scheme. Thereby, the base station (BS) can perform an adequate estimation of the channel characteristics with reduced signaling overhead. Consequently, we need short pilot sequences and very few precoding matrix indicators (PMIs) to properly describe channel behavior. Moreover, we also evaluate different user selection strategies based on unsupervised machine learning framework that exploits the channel information provided by the proposed beam sweeping scheme. Our performance evaluation indicates that the user selection based on fuzzy c‐means is able to efficiently explore the reduced CSI. The proposed hybrid beamforming scheme reduces the multi‐user interference and achieves significant gains in total data rate as channel conditions and interference environment becomes more challenging.     

Limited Feedback Beamforming Over Temporally-Correlated Channels

Feedback of quantized channel state information (CSI), called limited feedback, enables transmit beamforming in multiple-input-multiple-output (MIMO) wireless systems with a small amount of overhead. Due to its efficiency, beamforming with limited feedback has been adopted in several wireless communication standards. Prior work on limited feedback commonly adopts the block fading channel model where temporal correlation in wireless channels is neglected. In this paper, we consider temporally correlated channels and design single-user transmit beamforming with limited feedback. Analytical results concerning CSI feedback are derived by modeling quantized CSI as a first-order finite-state Markov chain. These results include the information rate of the CSI quantizer output, the bit rate a CSI feedback channel is required to support, and the effect of feedback delay on throughput. In particular, based on the theory of Markov chain convergence rate, feedback delay is proved to reduce the throughput gain due to CSI feedback at least exponentially. Furthermore, an algorithm is proposed for CSI feedback compression in time. Combining the results in this work leads to a new method for designing limited feedback beamforming as demonstrated by a design example.