Novel Transmit Beamforming Schemes for Time-Selective Fading Multiantenna Systems

Transmit beamforming has been widely adopted for wireless systems with multiple transmit antennas. For a block fading channel, the Grassmannian beamformer has been shown to provide very good performance for finite rate feedback. However, the original Grassmannian beamformer does not take the time domain correlation of the channel fading into consideration. In this paper, based on a first-order autoregressive (AR1) dynamic fading model, we develop two new classes of beamforming algorithms that exploit the interframe correlations in the channel fading. We first introduce an algorithm based on a standard predictive vector quantization (PVQ) approach, and the resulting PVQ beamformer accomplishes superior power delivery at the receiver. However, the error performance of the PVQ beamformer is not satisfactory at high signal-to-noise ratios, and it also has a high implementation complexity. To resolve these issues, we then develop a novel successive beamforming (SBF) algorithm. The new SBF scheme uses the knowledge of the previous fading blocks to aid the beamforming codebook design of the current fading block. The beamforming codebook is constructed based on the successive partition of the surface of a spherical cap. The new SBF scheme accomplishes nearly the same performance as that of the PVQ beamformer, and it has a much simpler implementation. Through numerical simulations, we demonstrate that the proposed beamformers outperform the other previously proposed beamformers at various fading scenarios     

On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

The theory of multiple-input–multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input–single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beamforming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.      

On the performance of random vector quantization limited feedback beamforming in a MISO system

In multiple antenna wireless systems, beamforming is a simple technique for guarding against the negative effects of fading. Unfortunately, beamforming requires the transmitter to have knowledge of the forward-link channel which is often not available a priori. One way of overcoming this problem is to design the beamforming vector using a limited number of feedback bits sent from the receiver to the transmitter. In limited feedback beamforming, the beamforming vector is restricted to lie in a codebook that is known to both the transmitter and receiver. Random vector quantization (RVQ) is a simple approach to codebook design that generates the vectors independently from a uniform distribution on the complex unit sphere. This correspondence presents performance analysis results for RVQ limited feedback beamforming     

Combining Beamforming and Space-Time Coding Using Noisy Quantized Feedback

The goal of combining beamforming and spacetime coding is to obtain full-diversity order and to provide additional received power (array gain) compared to conventional space-time codes. In this work, a class of code constellations is proposed, called generalized partly orthogonal designs (PODs) and both high-rate and low-rate feedback information is incorporated with possible feedback errors. A binary symmetric channel (BSC) model characterizes feedback errors. Two cases are studied: first, when the BSC bit error probability is known a priori to the transmission ends, and second, when it is not known exactly. Based on a minimum pairwise error probability (PEP) design criterion, we design a channel optimized vector quantizer (COVQ) for feedback information and a precoder matrix codebook to adjust the transmission codewords. The attractive property of our combining scheme is that it converges to conventional space-time coding with low-rate and erroneous feedback and to directional beamforming with high-rate and error-free feedback. This scheme also shows desirable robustness against feedback channel modeling mismatch.     

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.     

MIMO-OFDM系统中基于簇的有限反馈方法

本文针对有限反馈MIMO-OFDM波束形成系统,研究了基于簇的有限反馈方法。利用簇内相邻子载波信道的频率相干性,提出了一种低复杂度的信道均值分簇法,该方法以平均信道响应在给定码本中选择最佳簇波束形成向量。此外,利用簇波束形成向量之间的剩余相关性,还提出了递归反馈和基于格的反馈两种反馈速率降低方法,即将前一簇码字的邻域内码字作为当前簇的新码本,从而大幅度降低反馈比特数。仿真结果表明信道均值分簇法能以较低的计算复杂度获得较佳的BER性能,反馈降低方法相对传统分簇方法能进一步降低反馈速率,递归反馈方法有一定性能损失,而基于格的反馈方法性能损失可忽略不计。      

用于MIMO广播信道的带多波束选择的正交随机波束成形算法

本文提出一种基于有限反馈的波束和用户选择方案,在这种方案中,用户端利用一个随机正交码本对其信道方向信息(CDI)进行量化,计算其最大信号与干扰加噪声功率比(SINR),并把这些信息反馈给基站;基站根据接收到的这些反馈信息,按照和容量最大的准则选择出多个正交波束以及相应的多个用户.和sharif等人最近提出的方案相比,我们提出的方案能根据系统参数,如用户数和信噪比(SNR),对选择的波束成形矢量及其对应的用户的数量和集合进行调整,当用户数量较小时,和容量性能得到了很大的提升,同时避免了选择波束成形矢量时的用户冲突,另外,基站也不需要广播波束成形矢量给各个用户.     

Channel Adaptive Quantization for Limited Feedback MIMO Beamforming Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques. In the absence of full channel knowledge at the transmitter, the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low-rate feedback channel. In the literature, quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution, commonly the uncorrelated Rayleigh distribution. When the channel is not uncorrelated Rayleigh, however, these quantization strategies result in a degradation of the receive signal-to-noise ratio (SNR). In this paper, switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution. The codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel. The convergence properties of the codebook selection algorithm are studied assuming a block-stationary model for the channel. In the case of a nonstationary channel, it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in SNR. Simulation results show that in the case of correlated channels, the SNR performance of the link can be significantly improved by adaptation, compared with nonadaptive quantization strategies designed for uncorrelated Rayleigh-fading channels     

Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels

The full diversity gain provided by a multi-antenna channel can be achieved by transmit beamforming and receive combining. This requires the knowledge of channel state information (CSI) at the transmitter which is difficult to obtain in practice. Quantized beamforming where fixed codebooks known at both the transmitter and the receiver are used to quantize the CSI has been proposed to solve this problem. Most recent works focus attention on limited feedback codebook design for the uncorrelated Rayleigh fading channel. Such designs are sub-optimal when used in correlated channels. In this paper, we propose systematic codebook design for correlated channels when channel statistical information is known at the transmitter. This design is motivated by studying the performance of pure statistical beamforming in correlated channels and is implemented by maps that can rotate and scale spherical caps on the Grassmannian manifold. Based on this study, we show that even statistical beamforming is near-optimal if the transmitter covariance matrix is ill-conditioned and receiver covariance matrix is well-conditioned. This leads to a partitioning of the transmit and receive covariance spaces based on their conditioning with variable feedback requirements to achieve an operational performance level in the different partitions. When channel statistics are difficult to obtain at the transmitter, we propose a universal codebook design (also implemented by the rotation-scaling maps) that is robust to channel statistics. Numerical studies show that even few bits of feedback, when applied with our designs, lead to near perfect CSI performance in a variety of correlated channel conditions.     

Enhanced Unitary Beamforming Scheme for Limited-Feedback Multiuser MIMO Systems

In this letter, we consider practical downlink multiuser multiple-input multiple-output systems where each user has multiple antennas and codebook-based limited channel feedback is available at base station. We propose a preprocessing scheme for downlink transmission where a unitary beamforming matrix is used. Firstly, we propose how to construct the unitary matrix that maximizes sum rate. Secondly, we propose a codebook-based channel feedback method for the proposed beamforming method. Numerical results show that the proposed scheme outperforms conventional zero-forcing beamforming scheme in terms of sum rate.     

Novel limited feedback scheme under the MIMO broadcast system

By deducing the distribution of the normalized channel covariance matrix, a novel limited feedback scheme is proposed under multiple users (MU) multiple-input multiple-output (MIMO) broadcast channel (BC) system. The proposed scheme has advantages in three aspects. First, it has no constraints on the number of users or antennas. Second, each user's feedback bits are independent of the number of receiving antennas. Third, the proposed scheme avoids the storage of large-size codebook on the transceivers. Simulation results show that the performance of the proposed scheme is close to the perfect channel state information (CSI) case and it just needs a small number of feedback bits.     

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.     

Grassmannian beamforming for MIMO amplify-and-forward relaying

We consider the problem of beamforming codebook design for limited feedback half-duplex multiple-input multiple output (MIMO) amplify-and-forward (AF) relay system. In the first part of the paper, the direct link between the source and the destination is ignored. Assuming perfect channel state information (CSI), we show that the source and the relay should map their signals to the dominant right singular vectors of the source-relay and relay-destination channels. For the limited feedback scenario, we prove the appropriateness of Grassmannian codebooks as the source and relay beamforming codebooks based on the distributions of the optimal source and relay beamforming vectors. In the second part of the paper, the direct link is considered in the problem model. Assuming perfect CSI, we derive the optimization problem that identifies the optimal source beamforming vector and show that the solution to this problem is uniformly distributed on the unit sphere for independent and identically distributed (i.i.d) Rayleigh channels. For the limited feedback scenario, we justify the appropriateness of Grassmannian codebooks for quantizing the optimal source beamforming vector based on its distribution. Finally, a modified quantization scheme is presented, which introduces a negligible penalty in the system performance but significantly reduces the required number of feedback bits.     

The Effect of Finite Rate Feedback on CDMA Signature Optimization and MIMO Beamforming Vector Selection

We analyze the effect of finite rate feedback on code-division multiple-access (CDMA) signature optimization and multiple-input multiple-output (MIMO) beamforming vector selection. In CDMA signature optimization, for a particular user, the receiver selects a signature vector from a codebook to best avoid interference from other users, and then feeds the corresponding index back to the specified user. For MIMO beamforming vector selection, the receiver chooses a beamforming vector from a given codebook to maximize the instantaneous information rate, and feeds back the corresponding index to the transmitter. These two problems are dual: both can be modeled as selecting a unit norm vector from a finite size codebook to ldquomatchrdquo a randomly generated Gaussian matrix. Assuming that the feedback link is rate limited, our main result is an exact asymptotic performance formula where the length of the signature/beamforming vector, the dimensions of interference/channel matrix, and the feedback rate approach infinity with constant ratios. The proof rests on the large deviations of the underlying random matrix ensemble. Further, we show that random codebooks generated from the isotropic distribution are asymptotically optimal not only on average, but also in probability.     

Design and Analysis of MIMO Spatial Multiplexing Systems With Quantized Feedback

This paper investigates the problem of transmit beamforming in multiple-antenna spatial multiplexing (SM) systems employing a finite-rate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new criterion for designing the codebook of beamforming matrices that is based on minimizing an approximation to the capacity loss resulting from the limited rate in the feedback channel. Using the criterion, we develop an iterative design algorithm that converges to a locally optimum codebook. Under the independent identically distributed channel and high signal-to-noise ratio (SNR) assumption, the effect on channel capacity of the finite-bit representation of the beamforming matrix is analyzed. Central to this analysis is the complex multivariate beta distribution and tractable approximations to the Voronoi regions associated with the code points. Furthermore, to compensate for the degradation due to the equal power allocation assumption, we propose a multimode SM transmission strategy wherein the number of data streams is determined based on the average SNR. This approach is shown to allow for effective utilization of the feedback bits resulting in a practical and efficient multiple-input multiple-output system design.     

Resource Allocation of Limited Feedback in Clustered Wireless Mesh Networks

This paper focuses on resource allocation problem of limited feedback in OFDM-based clustered wireless mesh networks. Firstly, the channel quantization codebook is designed according to the equal probability quantizer and joint power, rate and channel quantization threshold codebook scheme (PRCQT) is proposed. Secondly, we deduce the subcarrier allocation criterion utilizing the Lagrange multiplier method. Finally, stochastic resource allocation scheme of limited feedback (SRALF) utilizing the stochastic optimization tools for OFDM-based clustered WMNs is proposed. Simulation results demonstrate SRALF+PRCQT scheme not only improves the network throughput, but also has advantage of limited feedback overhead.     

Performance analysis of MIMO beamforming with imperfect feedback

The quality of channel state information at the transmitter (CSIT) is critical to MIMO beamforming systems. However, in practical wireless systems, CSIT suffers from imperfections originating from quantization effects, feedback error and feedback delay. In this paper, we study the impact of feedback error and delay on the symbol error rate of MIMO beamforming systems with finite rate feedback. The feedback channel is modeled as a uniform symmetric channel. We derive an symbol error rate upper bound that is tight for a good beamformer. We also quantify the diversity gain and array gain loss due to the feedback error and delay. The codebook design method that is applicable to the beamforming systems with error or delay feedback is discussed. Both analytical and simulation results show that feedback error and delay will make the system behave badly at high signal‐to‐noise ratios. Copyright © 2012 John Wiley & Sons, Ltd.     

有限反馈MISO-OFDM系统中基于误码率的波束成形

该文提出了一种在有限反馈条件下多入单出正交频分复用(MISO-OFDM)系统中基于误码率的波束成形方案。将OFDM符号的所有子载波分成若干簇,从码本中选择能够最小化该簇每个子载波的平均误码率的码字,作为该簇的波束成形向量。此方案既能降低反馈量,又能取得较低误码率。同时,为避免所提方案中探求最优解时的穷尽搜索,还基于簇内不同子载波信道频响之间的相关性提出了一种简化的次优算法。仿真结果表明,在典型参数设置下,所提方案能够以较低计算复杂度取得比其他已有方案更好的误码率性能。     

Application of quasi-orthogonal space-time block codes in beamforming

It is well known that when channel information is available at the transmitter, transmit beamforming scheme can be employed to enhance the performance of a multiple-antenna system. Recently, Jongren et al. and Zhou-Giannakis proposed a new performance criterion based on partial channel side information at the transmitter. With this criterion, an optimal beamforming matrix was constructed for the orthogonal space-time block codes. However, the same method has not been applied to the recently proposed quasi-orthogonal space-time block codes (QSTBCs) due to the nonorthogonal nature of the quasi-orthogonal designs. In this paper, the issue of combining beamforming with QSTBCs is addressed. Based on our asymptotic analysis, we extend the beamforming scheme from Jongren et al. and construct the beamforming matrices for the quasi-orthogonal designs. The proposed beamforming scheme accomplishes high transmission rate as well as high-order spatial diversity. The new QSTBC beamformer can be presented as a novel four-directional or eight-directional eigen-beamformer that works for systems with four or more transmit antennas. Simulations for systems with multiple transmit antennas demonstrate significant performance improvement over several other widely used beamforming methods at various SNRs and for channels with different quality of feedback.     

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"