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。     

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。     

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。     

中继辅助MIMO系统中基于有限反馈的分布式波束成形

对协作式中继辅助的多输入多输出通信系统中基于有限反馈的联合波束成形问题进行了研究.首先推导了接收信噪比的下界,并基于该下界建立联合波束成形的数学模型.其次推导了分布式波束成形的最优方案.最后针对该最优方案,设计了一个迭代算法,优化得到分布式波束成形码本,从而分布式中继站的波束成形可基于码本序号的有限反馈来进行.实验结果仿真表明,所设计的联合波束成形码本在反馈开销很小的情况下获得明显的性能增益.     

基于信道相关统计及有限反馈的多基站协作波束成型

为减少多基站协作波束成形系统中基站间的信息交换量和用户信道信息反馈量,提出一种基站联合利用有限反馈信道参数和信道空间相关矩阵估计信道矢量函数的方法;基于所估计的信道矢量函数,提出一种多基站协作扩展迫零波束成形算法。相比已有的多基站协作波束成形方案,所提算法能在反馈/回程开销和系统性能之间取得更合理的折中,计算仿真验证了所提算法的有效性。     

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.     

多小区多用户无线网络下行链路协同波束成形设计

在频率复用的多小区多用户无线网络中,为了获得较好的和速率性能,研究了降低同频干扰的协同波束成形设计问题。博弈论分析结果表明,性能最优的协同波束成形矢量是自私和利他策略的线性组合。提出了一种最大化和速率的波束成形矢量迭代算法,给出了基于信道状态统计量的组合系数的估计方法。最后,仿真评估了波束成形算法的性能,表明了所提迭代算法的收敛性。     

OFDM系统智能天线设计中的波束综合算法

基于自适应天线阵列理论。提出了一种新的可以应用于任意类型天线阵列的波束综合算法。根据与给定的参考波束的误差。引入虚拟干扰的概念，对目标波束图形状进行调整。应用本文提出的新算法，在主瓣和旁瓣位置都可以对波束进行有效的调节。最终获得阵列的最优权矢量，能够最小化目标波束图与参考波束图间的差异。理论分析与仿真结果表明与现有的同类算法相比，本算法能更有效地获得与参考波束基本相符的波束。在设计应用于OFDM智能天线系统时，通过对不同子载波频率上信号进行单独处理，利用该算法．进行波束综合，能够在整个有效频段，所有子载波上获得基本一致的阵列输出。     

基于循环子向量优化的波束成形接收机设计

针对新一代无线通信技术应用中对低能耗、低算力的应用需求，提出一种基于循环子向量优化（CSVO）算法的低复杂度波束成形接收机设计。CSVO算法根据最小均方误差（MMSE）准则推导产生，特点是在波束成形中可以灵活地选择拟优化波束向量的维度大小，降低计算复杂度。文中基于CSVO算法，以ZC706套件和AD9361射频收发器为基础，实现了一套四天线阵元基带波束成形接收机设计方案。实验测试结果表明，实现的接收机波束成形增益接近理论值，验证了CSVO算法的可行性和有效性。实验结果进一步展示，与其他传统的几种波束成形算法相比，在达到同样性能的条件下，CSVO算法所需乘法次数更少，且收敛速度更快。     

基于GNSS多通道跟踪接收机的阵列反欺骗方法

近年来,基于阵列天线的空域处理方法被认为是最有效的欺骗检测和抑制手段之一。提出了一种基于卫星导航接收机多通道跟踪能力的阵列反欺骗方法。多通道跟踪接收机对每一个捕获到的导航信号在所有阵元通道后均进行跟踪处理并提取信号幅度和载波相位观测量,首先计算载波相位双差平方和进行欺骗检测,然后利用载波相位单差和信号幅度比估计信号导引矢量,从而进行基于子空间投影的欺骗信号抑制或基于波束形成的真实卫星信噪比提升。理论分析和仿真试验证明,该方法可有效检测并消除同一来向的欺骗信号且不影响真实卫星信号质量。由于前端非理想因素带来的幅度和相位偏移都已包含在接收机跟踪通道提取的观测量内,实际应用时对阵列天线校准和射频通道均衡的要求明显降低。     

Throughput-Optimal Precoding and Rate Allocation for MISO Systems With Noisy Feedback Channels

A throughput metric is considered for a multiple-input single-output (MISO) system with noisy feedback of channel state information (CSI). The goal is to optimize a precoding matrix with a medium-access control layer metric. The problem is a nonlinear multidimensional optimization. Results show that the optimal precoding turns into beamforming when the signal-to-noise ratio (SNR) of CSI feedback is sufficiently large. A necessary condition for the optimality of beamforming under the throughput metric is determined, and the necessary and sufficient condition is numerically found based on the Gauss-Chebyshev Quadrature method. Next, the rate allocation for beamforming and spatial diversity is analyzed. Then, a two-mode transmission scheme is proposed such that the transmitter is engaged in either the beamforming mode or the spatial diversity mode depending on the SNR of the CSI feedback. It is shown that at a fairly high SNR of CSI feedback, the rate allocation needs to be reduced, while at a low SNR of CSI feedback, the allocated rate should be increased. It is shown that when the SNR of CSI feedback is lower than a threshold, there always exists an SNR of the transmitted signal such that the CSI feedback can be viewed as the real CSI solely for the purpose of rate allocation. The result also shows that the throughput of two-mode transmission is almost the same as the throughput of the optimal precoding scheme, even with a low SNR and large feedback delay.     

Interpolation based transmit beamforming for MIMO-OFDM with limited feedback

Transmit beamforming and receive combining are simple methods for exploiting spatial diversity in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system. Optimal beamforming requires channel state information in the form of the beamforming vectors for each OFDM subcarrier. This paper proposes a limited feedback architecture that combines beamforming vector quantization and smart vector interpolation. In the proposed system, the receiver sends a fraction of information about the optimal beamforming vectors to the transmitter and the transmitter computes the beamforming vectors for all subcarriers through interpolation. A new spherical interpolator is developed that exploits parameters for phase rotation to satisfy the phase invariance and unit norm properties of the transmitted beamforming vectors. The beamforming vectors and phase parameters are quantized at the receiver and the quantized information is provided to the transmitter. The proposed quantization system provides only a moderate increase in complexity versus over comparable approaches. Numerical simulations show that the proposed scheme performs better than existing diversity techniques with the same feedback data rate.     

Adaptive Beamforming with Dimension Reduction in Spatially Correlated MISO Channels

In this paper, we propose an adaptive beamforming scheme that generates the beam weight using dominant eigenvectors of the spatial covariance matrix. The number of eigenvectors used for the generation of beam weight is determined to maximize the signal-to-noise ratio (SNR) for given feedback constraints (e.g., the amount of feedback information and feedback delay). It is shown that the conventional limited feedback beamforming and eigen-beamforming are special cases of the proposed scheme. Simulation results show that the proposed beamforming scheme can effectively be applied to spatially correlated channels.     

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

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.     

Statistical Channel State Information Aided Proportional Fair Scheduling Scheme for Highly Transmit Correlated Channels

In this paper, we consider the downlink heterogeneous scenario with highly transmit correlated channels, and propose two kinds of the statistical channel state information (SCSI) aided proportional fair scheduling (PFS) schemes: (1) signal-to-noise ratio based PFS (SNR PFS) scheme and (2) SNR PFS scheme with threshold, which determine the preferred beamforming vector and proportional fair index by exploiting the SCSI and only send back the instantaneous channel quality indicator (CQI) without the corresponding precoding matrix index at each timeslot. Although the SNR PFS scheme only requires little feedback overhead and low computational complexity, the performance of the SNR PFS scheme is nearly the same as the conventional scheme (i.e., codebook-based PFS scheme). However, with the increasing number of users, a large number of CQI feedbacks will increase the signaling burden. To overcome this obstacle, the proposed SNR PFS scheme with threshold which sets an appropriate feedback threshold to limit the CQI feedbacks with poor channel quality would hardly affect the performance of the scheme. We further derive the approximate rate expressions of the SNR PFS scheme by using probability statistics and the theory of order statistics, whose result is nearly approximated to that of the Monte Carlo simulation. Finally, our simulation results show that the performance of the SNR PFS scheme with β _th =  ln(K/5) is close to that of the SNR PFS scheme, while it has less limited feedback capacity than the SNR PFS scheme.     

Channel quality-to-interference ratio quantization criterion for limited feedback beamforming in MIMO systems

The discrete Fourier transform (DFT)-based codebook is employed in this paper to quantize channel state information so that the amount of feedback can be reduced in the multiple input multiple output (MIMO) downlink of long term evolution (LTE) system. And a novel beamforming (BF) scheme based on the proposed channel quality-to-interference (QIR) quantizing criteria is developed, which uses only the index of the optimal codebook for the beamforming at the base station (BS), and dramatically reduces the amount of feedback. The proposed BF scheme jointly considers the influences of the quality of the quantized channels and the mutual interference among the sub-channels. The extensive simulation results verify that throughput of the proposed BF scheme is better than that of the random BF with a little feedback, and that of the eigen-beamforming even under low signal noise ratio (SNR) scenario.     

A Simple and Efficient User-Scheduling Strategy for RUB-Based Multiuser MIMO Systems and Its Sum-Rate Analysis

We present a user-scheduling scheme for multiuser multiple-input–multiple-output (MIMO) systems with random unitary beamforming (RUB) in this paper. The new scheme, which is termed as adaptive beam activation based on the conditional best beam index feedback (ABA-CBBI), requires low average feedback load by imposing a feedback threshold on the users' signal-to-interference-plus-noise ratio (SINR) and suffers less multiuser interference by only activating those beams requested by at least one user. We derive the exact analytical expression for the sum-rate capacity of the resulting multiuser MIMO systems, based on which we examine the optimal selection of the feedback threshold in terms of sum-rate maximization. We demonstrate through selected numerical examples that the proposed ABA-CBBI scheme with optimal thresholds can achieve better sum-rate performance than existing schemes over high-signal-to-noise-ratio (SNR) regions.      

On the Optimality of Beamforming with Quantized Feedback

The ergodic capacity of a fading vector channel with multiple transmit antennas and a single receive antenna is explored. Perfect channel information is assumed to be available at the receiver while the transmitter has only partial knowledge of the direction of the user's channel vector based on quantized feedback. We present necessary and sufficient conditions for the optimality of beamforming in such systems. The conditions are applicable to all quantized feedback scenarios regardless of the channel distribution, number of transmit antennas, number of quantization vectors or transmit power. The optimality conditions are closely related to the iteration conditions of the Lloyd algorithm, revealing an interesting link between the optimality of beamforming and the optimality of the vector quantizers. Using the conditions, we prove the capacity optimality of beamforming for several quantized feedback scenarios such as the antenna-selection scheme. We also point out examples of quantized feedback scenarios where beamforming is not optimal. We find that for the independent identically distributed Rayleigh fading channel with more than a single bit of quantized feedback, there is no capacity benefit from increasing the number of antennas beyond the number of quantization vectors. Extensions of the necessary and sufficient optimality condition to the multiple-input multiple-output case are also provided.     

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.