MIMO-OFDM系统中反馈降低算法

本文针对MIMO-OFDM波束赋形系统中基于子载波递归反馈编码算法反馈负载过大和基于簇递归反馈编码算法出现跟踪错误传播问题,提出一种新的周期性递归反馈编码算法。该方法利用簇波束向量之间的冗余相关性进一步降低反馈量。同时,通过周期性地搜索初始码书避免了跟踪错误的传播问题。另外,还提出了一种修订分簇反馈降低方法,接收端只当码字发生变化时才反馈最优码字及其子载波索引给发送端,否则不反馈任何信息。仿真结果表明这两种方法可以有效地降低反馈量,并且保证了系统性能。     

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。     

一种基于方向标记的有限反馈量化方法

随着天线数目和反馈比特数的增加,大规模多输入多输出（Multiple-Input Multiple-Output,MIMO）信道向量量化的复杂度大幅增加。为此,提出了一种基于方向标记的有限反馈量化方法。该方法将码本中码字进行分组,每组选取一个向量作为方向标记向量,在进行量化时,信道向量首先与各组方向标记向量进行比较,将与信道向量最接近的方向标记向量所在组选为待选码本组;在待选码本组内进行下一步量化,最终选出与其最接近的量化向量为最优码字。复杂度分析与仿真结果表明,所提方法缩小了待选码字的数量从而降低了计算复杂度,是系统性能与计算复杂度的一种折中。     

有限反馈MISO-OFDM系统中最大化容量的波束成形

该文提出了一种在有限反馈条件下多输入单输出正交频分复用(MISO-OFDM)系统中基于最大化容量的波束成形方案。将OFDM符号的所有子载波分成若干簇,从码本中选择能够最大化该簇每个子载波平均容量的码字,作为该簇的波束成形向量。在低信噪比区域,求出了最优波束成形向量的闭合解;鉴于在高信噪比区域无法求出闭合解,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以降低搜索最优解时的计算复杂度。仿真结果表明,在典型参数设置下,所提方案能够取得比其他已有方案更高的容量和更低的误码率。     

时间相干信道下波束赋形系统的有限反馈方法

该文提出一种新的基于树形码书的有限反馈方法,由于相邻帧的时间相干性,信道向量的量化码字可建模为一阶有限状态马尔可夫链,当前帧信道向量被量化到前一帧最大转移概率码字的子码字上,该子码字的索引以1 bit反馈给发射端。链路仿真结果表明本文所提方法相比普通反馈方法可明显改善误码率性能,某些条件下还可降低反馈速率。     

两跳中继分布式预编码码字选择方案

针对两跳分布式预编码MIMO中继系统,为了克服码字选择复杂度较高的缺点,提出一种基于单跳信道右奇异特征向量反馈的最小距离准则码本选择策略。首先给出基于均方误差矩阵的两跳分布式预编码设计方法,选取单跳信道右奇异特征向量作为反馈量,利用RVQ码本对其量化,最后采用最小距离准则对码字进行选择。仿真结果表明,在反馈比特数目相同的情况下,得到的系统BER性能与现有算法相近,但系统的和速率性能优于已有算法,且计算复杂度降低大约一半。     

一种基于码本轮转的有限反馈量化方法

大规模多输入多输出（Multiple-Input Multiple-Output,MIMO）系统中随着天线数目的增加,其反馈比特数将随之大幅度增加。为此,提出了一种基于码本轮转的有限反馈量化方法。该方法中,用户在前一时刻得到最佳码字之后,在码本中选取轮转区域构成虚拟码本,判断当前时刻的信道向量,满足轮转条件的用户将虚拟码本轮转到码本起始位置,在虚拟码本中进行量化;不满足轮转条件的用户在原始码本中进行量化,选出当前时刻的最优码字。反馈比特数分析与仿真结果表明,所提方法可轮转的虚拟码本减少了量化码字的数量,从而减少了反馈比特数,是系统性能与反馈比特数的一种折中。     

Rician信道下基于信道均值信息的自适应反馈方案

在多天线多用户下行系统中,当信道为莱斯(Rician)衰落时,基于瑞利(Rayleigh)信道假设设计出的有限反馈方法将会导致系统反馈开销的浪费。该文提出了一种适用于Rician信道的自适应反馈方案。该方案根据各用户信道的均值信息计算出相应的信道方向分布函数,然后利用其函数设计判决门限来调整各用户的量化反馈码本,使各用户量化码本中的码字矢量更加集中在用户信道矢量方向周围。另外,该方案可以自适应于不同的信道分布,在保证一定的量化误差下,根据信道均值的大小自适应调节各用户的反馈比特数,显著减少了用户的反馈量。仿真结果表明,与基于Rayleigh信道假设的有限反馈方案相比,该文提出的自适应反馈方案在不降低系统的吞吐率性能的前提下显著降低了用户的反馈开销。     

多用户MIMO系统中基于快速匹配调度的有限反馈SDMA

提出了一种能高效利用多用户分集和空分复用增益的有限反馈空分多址(SDMA,space division multiple access)方法。首先利用子空间扰动的方法构造了一种具有分簇结构的多用户预编码码本。基于该码本,进一步给出了一种新型的多用户机会调度算法,该算法利用码本的簇结构实现对信道条件匹配的用户组进行快速的机会调度,同时确定被调度用户的首选码字。仿真结果表明,在蜂窝网络中,与传统的有限反馈SDMA方法相比,所提方法可以在不明显增加反馈开销的前提下显著提高系统吞吐量。     

多基站协作系统中有限反馈策略及其码本设计

该文针对基于中央控制单元和大容量光纤骨干网连接而成的多基站集中调度协作系统所引起的高系统复杂度和高实现成本等问题,分析了一种可由现存蜂窝无线系统平滑过渡的多基站分布式协作MIMO系统结构及其信号传输特性。在此基础上,给出了该系统结构中基于信道量化码字索引信息的低速率有限反馈策略,讨论了对应的码本设计与构造准则,并提出了一种基于弦距离矢量量化准则的量化码本空间构造与实现算法。通过性能分析表明,该有限反馈策略获得的系统性能可明显优于模拟的导频重传方法,同时也好于基于欧几里德距离量化准则构造的码本空间性能。     

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"     

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     

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     

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.     

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     

A performance analysis framework for limited feedback beamforming in correlated fading

Limited or finite rate, feedback is an efficient way to implement beamforming in multiple antenna systems using frequency division duplexing. Unfortunately, closed-form performance analysis of limited feedback beamforming has not been investigated. This paper provides an analytical framework for the correlated limited feedback beamforming problem by treating selection of the beamforming vector from the codebook as a multibranch selection problem.     

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.     

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.      

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.