On beamforming with finite rate feedback in multiple-antenna systems

We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t-1)2/sup -B/t-1/, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.     

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.     

Design and analysis of transmit-beamforming based on limited-rate feedback

This paper deals with design and performance analysis of transmit beamformers for multiple-input multiple-output (MIMO) systems based on bandwidth-limited information that is fed back from the receiver to the transmitter. By casting the design of transmit beamforming based on limited-rate feedback as an equivalent sphere vector quantization (SVQ) problem, multiantenna beamformed transmissions through independent and identically distributed (i.i.d.) Rayleigh fading channels are first considered. The rate-distortion function of the vector source is upper-bounded, and the operational rate-distortion performance achieved by the generalized Lloyd's algorithm is lower-bounded. Although different in nature, the two bounds yield asymptotically equivalent performance analysis results. The average signal-to-noise ratio (SNR) performance is also quantified. Finally, beamformer codebook designs are studied for correlated Rayleigh fading channels, and a low-complexity codebook design that achieves near-optimal performance is derived.     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

Efficient implementation of robust adaptive beamforming based on worst-case performance optimisation

Traditional adaptive beamforming methods undergo serious performance degradation when a mismatch between the presumed and the actual array responses to the desired source occurs. Such a mismatch can be caused by desired look direction errors, distortion of antenna shape, scattering due to multipath, signal fading as well as other errors. This mismatch entails robust design of the adaptive beamforming methods. Here, the robust minimum variance distortionless response (MVDR) beamforming based on worst-case (WC) performance optimisation is efficiently implemented using a novel ad hoc adaptive technique. A new efficient implementation of the robust MVDR beamformer with a single WC constraint is developed. Additionally, the WC optimisation formulation is generalised to include multiple WC constraints which engender a robust linearly constrained minimum variance (LCMV) beamformer with multiple-beam WC (MBWC) constraints. Moreover, the developed LCMV beamformer with MBWC constraints is converted to a system of nonlinear equations and is efficiently solved using a Newton-like method. The first proposed implementation requires low computational complexity compared with the existing techniques. Furthermore, the weight vectors of the two developed adaptive beamformers are iteratively updated using iterative gradient minimisation algorithms which eliminate the estimation of the sample matrix inversion. Several scenarios including angle-of-incidence mismatch and multipath scattering with small and large angular spreads are simulated to study the robustness of the developed algorithms.     

Beamforming for inter‐relay interference reduction in MIMO‐aided two‐path successive relaying

To effectively reduce the inter‐relay interference (IRI) in two‐path successive relaying, two beamforming schemes are proposed in this paper, utilizing multiple‐antenna relay nodes. Specifically, the two cooperation nodes perform receive combining of the source signal and transmit beamforming of the relayed signal alternately in the successive relaying process. As a result, the IRI between them can be effectively suppressed, thanks to the additional degree of freedom provided by the multiple‐input multiple‐output inter‐relay channel. In the first beamforming scheme, the source‐to‐destination signal‐to‐interference‐plus‐noise ratios (SINR) of separate paths are maximized with approximation, leading to a minimum variance distortionless response beamformer under the high SINR condition. To further improve the system performance, noting that the received SINRs of the two paths have impact on each other due to the mutual coupling of the beamformers, the sum of mean squared errors from these two transmission paths is minimized in the second scheme. Based on this performance criterion, a suboptimal beamformer design is developed numerically through cyclic minimization of the sum of mean squared error cost function. Simulation results demonstrate the superiority of both proposed beamforming schemes in terms of symbol error rate and the achievable system rate, in particular, at high IRI levels. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

基于Laguerre滤波器等价设计的IIR宽带波束形成

常规IIR宽带波束形成器可以获得比FIR宽带波束形成器更好的性能,但其需要多极点的自适应调整过程,存在稳定性无法保证,计算复杂度较高等问题.本文提出一种新的基于IIR滤波器的宽带波束形成算法.该算法基于高阶Laguerre宽带波束形成器,利用双线性变换和函数束方法设计相应的低阶等价IIR宽带波束形成器.仿真实验及理论分析表明,该方法无需常规IIR宽带波束形成器的多极点自适应调整过程,在保证算法稳定性的同时,减少了计算复杂度,并提高了输出信干噪比(SINR).     

波束空时分组编码的ICA盲检测方案

理论研究已经证明,结合波束形成和空时分组编码的混合系统与传统的单纯使用波束发射或空时编码的方案相比具有很大的性能提高;传统的译码方案是借助接收端的信道估计来实现的,它需要知道准确的信道状态信息(CSI)。但如果信道估计不易实现,则系统性能将受很大影响。独立分量分析(ICA)作为一种经典的盲信号分离技术可以在不进行信道估计的情况下对发射信号实现有效检测。本文针对接收端的信号结构提出了一种基于ICA的正交检测方案;并通过仿真将新方案与传统方案进行了性能比较。仿真结果表明,新方案具有较好的系统适应性和误码率特性。     

A broadband MVDR beamforming core for ultrasound imaging

The Minimum Variance Distortion less Response (MVDR) beamformer is an attractive alternative to conventional delay and sum (DAS) beamformers in medical ultrasound imaging. However, it is not widely employed in medical ultrasound imaging due to its computational complexity. In this paper, we intend to present a novel broadband MVDR beamformer architecture and its implementation for up to 32 channel ultrasound imaging system. The proposed architecture is based on the subarray MVDR and Dichotomous Coordinate Descent (DCD) iteration based adaptive weight computation. A Field Programmable Gate Array (FPGA) based ultrasound system prototype set up is designed, and the proposed MVDR beamforming Core is emulated on the FPGA. The proposed beamforming core could achieve up to 65.5 fps for a 640 x 480 ultrasound frame. The ultrasound system prototype operates at 20 MHz sampling frequency, and the FPGA implementation resulted in approximately 35% of FPGA resources (Xilinx Kintex-7 410T). Image quality comparisons in terms of Contrast Ration (CR) and Contrast to Noise Ratio (CNR) were performed with MATLAB™ MVDR model ported on the Verasonics™ Vantage-64 ultrasound research platform.     

Broadband beamforming using Laguerre filters

Space-time processing is a well-substantiated method for designing broadband beamformers. In the conventional Frost space-time beamformer, tapped delay line (TDL) filters are used in each branch of the array to create a wideband response for interference suppression. In this article a new space-time beamforming method is introduced in which Laguerre filters replace the traditional TDL filters in the Frost beamformer. The Laguerre filters are fundamentally IIR filters but with only one pole in their structure. Unlike other IIR-based space-time beamforming methods, the proposed method does not need an adaptive procedure for the pole adjustment and is inherently stable. Simulation results show superior performance of the proposed method compared to the Frost beamformer and comparable results against other IIR-based beamformers with much less computational complexity and guaranteed stability.     

脉冲噪声环境中鲁棒的自适应波束形成方法

本文提出一种脉冲噪声环境中的自适应波束形成方法.方法假定噪声服从对称 α 稳定(S α S:Symmetric α -stable)分布,首先定义分数低阶阵列响应,然后根据最小方差无畸变响应波束形成器(MVDR)提出分数低阶最小方差无畸变响应波束形成器(FrMVDR).理论上证明了当阶数小于噪声特征指数的一半时,分数低阶阵列输出功率有界.计算机仿真实验证明了本文提出的FrMVDR波束形成器在高斯噪声和非高斯脉冲噪声环境中性能都优于MVDR和其他有关的基于分数低阶矩的波束形成器,是一种鲁棒的自适应波束形成器.     

Robust Adaptive Beamformers Based on Worst-Case Optimization and Constraints on Magnitude Response

In this paper, novel robust adaptive beamformers are proposed with constraints on array magnitude response. With the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight, the optimization of an adaptive beamformer, which is often described as a quadratic optimization problem in conventional beamforming methods, is then reformulated as a linear programming (LP) problem. Unlike conventional robust beamformers, the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple. In practice, an array has many imperfections besides steering direction error. In order to make the adaptive beamformer robust against all kinds of imperfections, worst-case optimization is exploited to reconstruct the robust beamformer. By minimizing array output power with the existence of the worst-case array imperfections, the robust beamforming can be expressed as a second-order cone programming (SOCP) problem. The resultant beamformer possesses superior robustness against arbitrary array imperfections. With the proposed methods, a large robust response region and a high signal-to-interference-plus-noise ratio (SINR) enhancement can be achieved readily. Simple implementation, flexible performance control, as well as significant SINR enhancement, support the practicability of the proposed methods.     

用于MIMO-OFDM无线通信系统的一种新的自适应半盲波束形成算法

该文根据MIMO-OFDM物理层结构和无线移动矩阵信道的特性,从神经网络和信息论观点详细推导了一种新的多天线阵列自适应半盲波束形成器算法。与常规的盲估计和导频辅助信道估计算法不同的是,本文提出的新的半盲算法在权矢量自适应更新时,不断地用基于导频估计的权矢量进行修正。最后,用实际的HIPERLAN2协议进行了计算机仿真。结果表明这种算法不增加发射信号功率和不占用额外带宽,能提高天线增益性能和有效地提取出期望的发射信号,在收敛速度和BER性能方面优于常规的导频辅助信道估计算法。该波束形成器能自适应调整权矢量,其更新方式与TDMA和CDMA相似,所以本算法可直接用于有天线阵列的基于OFDM的第三代(3G)和三代后(3G beyond)的无线通信系统。     

A User Parameter-Free Robust Adaptive Beamformer Based on General Linear Combination in Tandem with Steering Vector Estimation

If there is a mismatch between the assumed steering vector (SV) and the real value, the performance of adaptive beamforming methods is degraded. When the signal SV is known exactly but the sample size is small, the performance degradation can also occur. The second kind of degradation is mainly due to the mismatch between the sample covariance matrix and the real one. Almost all existing robust adaptive beamformers are proposed to improve the robustness against these two types of mismatch. Indeed, most of them are user parameter dependent, and the user parameter-free robust beamformers are scarce. As one of the shrinkage methods, the general linear combination (GLC) based beamformer is a good user parameter-free robust beamformer. However, it is only suitable for the scenarios with low sample size and/or small SV mismatch. In this paper, we propose a new robust beamformer, and it is based on general linear combination in tandem with SV estimation (GLCSVE). The proposed approach is superior to GLC in two aspects. One is that the GLCSVE beamformer performs well not only with small but also with large sample size. The other is that the GLCSVE can effectively deal with a large range of SV mismatch. Moreover, the proposed GLCSVE approach is a user parameter-free robust beamformer, and is more suitable for application than the parameter dependent approaches. The idea of our method can also be used to enhance other shrinkage based beamformers.     

PSO Assisted DD-ESB Beamforming with Robust Capabilities

This paper deals with adaptive array beamforming based on the decision-directed eigenspace-based (DD-ESB) technique with robust capabilities. It has been shown that DD-ESB adaptive beamformer demonstrates the advantages of better output signal-to-interference plus noise ratio performance and less sensitivity to pointing error over conventional ESB beamformers without any specific training bits. In conjugation with particle swam optimization assisted scheme to obtain more correct desired user’s transmitted bits from the output of the ESB, the more correct steering vector of the desired user can be reconstructed for DD-ESB adaptive beamforming in the presence of larger pointing error and relatively low interference-to-noise ratio. Computer simulations are provided to illustrate the effectiveness of the proposed approach.     

Modified constant modulus algorithm for digital signal processingadaptive antennas with microwave analog beamforming

This paper proposes a novel algorithm, called modified constant modulus algorithm (M-CMA), which is able to give adaptability to microwave beamforming phased array antennas. Since microwave analog beamformers basically require much fewer RF devices than digital beamformers, microwave analog beamformers based on M-CMA, that is, adaptive microwave beamformers, can be cheaply fabricated. Therefore, they are very suitable for mobile communication systems where both miniaturization and low cost are required for the mobile terminals. M-CMA obtains a gradient vector by a combination of analytical calculation and perturbation of the microwave beamforming control voltage. Though M-CMA is implemented with a digital signal processor, M-CMA controls the microwave analog beamformer by utilizing the gradient vector. The microwave analog beamformer based on M-CMA is analyzed to have the following characteristics: (1) the beamformer can point its main beam to the desired direction in additive white Gaussian noise (AWGN) channels; (2) although the beamformer may possibly fail in ill solutions in cochannel interference (CCI) channels, M-CMA can converge to the optimum solution when the desired direction is roughly a priori known     

Widely linear generalized sidelobe canceling beamforming with variable diagonal loading

We propose a robust widely linear (WL) beamformer for noncircular (NC) signals in the presence of angle of arrival (AOA) errors or array random perturbations. In our beamformer, the block conjugate structure of covariance matrix is exploited to avoid updating the full weight vector, which reduces the computational loads. We add a variable diagonal loading term in the weight vector to improve the robustness of the WL beamformer. Moreover, the orthogonality constraint of block matrix is not required to calculate the amount of diagonal loading. Computer-simulation results show that the proposed WL beamforming provides improved performance over the conventional linear beamformers for NC signals in the presence of AOA errors and array random perturbations.