Knowledge-aided adaptive beamforming

In array processing, when the available snapshot number is comparable with or even smaller than the sensor number, the sample covariance matrix ^R is a poor estimate of the true covariance matrix R. To estimate R more accurately, prior environmental knowledge can be used, which is manifested as knowing an a priori covariance matrix R/sub 0/. In practice, R0 usually represents prior knowledge on dominant sources or interferences. Since the noise power level is unknown, and thus cannot be included into the a priori covariance matrix, R/sub 0/is often rank deficient. Both modified general linear combinations (MGLC) and modified convex combinations (MCC) of the a priori covariance matrix R/sub 0/, the sample covariance matrix ^R and an identity matrix I to obtain an enhanced estimate of R, denoted as ~R are considered. Both MGLC and MCC can choose the combination weights fully automatically. Moreover, both the MGLC and MCC methods can be extended to deal with linear combinations of an arbitrary number of positive semi-definite matrices. Both approaches can be formulated as convex optimisation problems that can be solved efficiently to obtain globally optimal solutions. Numerical examples are provided to demonstrate the type of achievable performance by using ~R instead of ^R in the standard Capon beamformer.     

Super-exponential blind adaptive beamforming

The objective of the beamforming with the exploitation of a sensor array is to enhance the signals of the sources from desired directions, suppress the noises and the interfering signals from other directions, and/or simultaneously provide the localization of the associated sources. In this paper, we present a higher order cumulant-based beamforming algorithm, namely, the super-exponential blind adaptive beamforming algorithm, which is extended from the super-exponential algorithm (SEA) and the inverse filter criteria (IFC). While both SEA and IFC assume noise-free conditions, this requirement is no longer needed, and all the noise components are taken into account in the proposed algorithm. Two special conditions are derived under which the proposed blind beamforming algorithm achieves the performance of the corresponding optimal nonblind beamformer in the sense of minimum mean square error (MMSE). Simulation results show that the proposed algorithm is effective and robust to diverse initial weight vectors; its performance with the use of the fourth-order cumulants is close to that of the nonblind optimal MMSE beamformer.     

顽健自适应波束形成算法

针对方向向量偏差会导致最小均方(LMS)算法的性能急剧下降这一问题,提出了一种基于可变对角载入的顽健自适应波束形成算法.采用最陡下降法对信号方向向量进行优化求解,并在每次迭代过程中更新对角载入值,进而求出最优的权重向量,避免了矩阵求逆运算和特征值分解运算,大大降低了计算复杂度.通过建立步长与输入信号的关系得到可变的步长因子,克服了收敛速度和稳态误差之间的矛盾.该算法收敛速度快,抗扰动性强,对信号方向向量偏差具有很强的顽健性,从而改善了阵列输出的信干噪比,使其更接近最优值.理论分析和仿真结果表明与传统自适应波束形成算法相比,所提顽健算法具有更好的性能.     

自适应波束形成算法的研究

自适应波束形成是智能天线的关键技术,其核心是通过一些自适应波束形成算法获得天线阵列的最佳权重,并最终最后调整主瓣专注于所需信号的到达方向,以及抑制干扰信号,通过这些方式,天线可以有效接收所需信号。在实际应用中,收敛性,复杂性和鲁棒性的速度是在选择自适应波束形成算法时要考虑的主要因素。本文聚焦于最小均方(LMS)算法和样本矩阵求逆(SMI)的算法,分析了它们的性能,并在Matlab的帮助下将这两个算法应用于自适应波束形成。     

均匀先验分布Bayesian自适应波束形成方法

针对UUV舷侧阵存在观测信号方向有误差的情况，提出了基于均匀先验分布的Bayesian自适应波束形成方法（UB）。该方法假设期望信号的到达方向是区间内服从均匀先验分布的一个变量，利用含有均匀先验分布信息的阵列接收数据和Bayesian后验分布来估计期望信号的到达方向，最后计算权矢量。仿真结果表明，该方法对观测信号方向误差具有较好的稳健性，其阵列方向图的主波束不受观测方向误差的影响，始终对准信号的到达方向，其输出信干噪比随着输入信噪比、快拍数的增加而稳定增加，随着观测方向误差的增大而保持稳定的恒定值。      

The PDF of adaptive beamforming weights

The author derives a closed-form expression for the marginal probability density function (PDF) for the weight vector coefficients in a minimum-variance distortionless response (MVDR) adaptive beamformer, when the snapshots are independently identically distributed (IID) normal and the weights are computed via sample matrix inversion. The marginal PDF allows one to determine the dynamic range required to avoid saturation (with a specified degree of probability) in digital and/or analog implementation of beamforming weights     

Robust adaptive beamforming for broadband arrays

It is very important in many applications to preserve a desired signal without distortion. This paper presents a robust adaptive beamforming method to extract a desired signal from the signals received by broadband arrays. The proposed method relaxes the requirement of approximate knowledge of the desired direction and the sensor gains and delays (phases). Also the method enhances the desired signal based on a focusing transform for that signal, requires less computation than the taped-delay-line beamforming method, and provides good results even in a multipath environment. Computer simulations are given to support the proposed method.On leave from the Department of Electronic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China.Nanjing 210016, People's Republic of China.     

基于投影对消处理技术的稳健自适应波束形成

针对传统自适应波束形成算法中目标波达方向(Direction of Arrival,DOA)估计不准确引起的波束形成性能下降问题,提出了一种采用投影对消矩阵的稳健自适应波束形成算法.首先,寻找与估计波达方向有最大相关性的特征矢量作为目标信号特征矢量,然后构建对消矩阵消除协方差矩阵中的信号分量,最后通过增加零点约束实现干...     

Partially adaptive beamforming for correlated interferencerejection

Conventional linearly constrained adaptive beamformers often suffer from severe signal cancellation in the presence of interferers correlated with the signal. We propose a partially adaptive beamforming technique for correlated interference rejection in broadband signal environments. The beamformer output mean squared error is decomposed into an interference mean squared error term and an additional signal cancellation term that is due to the presence of correlated interference. Both mean squared errors depend on the adaptation space. The partially adaptive beamforming technique proposed here chooses an adaptation space which results in little signal cancellation while maintaining satisfactory interference cancellation. It is shown that, for a given interference scenario, a partially adaptive beamformer can be designed such that maximum interference cancellation is achieved without any signal cancellation. In practice, an approximate design procedure is provided to accommodate a set of likely interference scenarios. Analysis of the feasibility of this approach is presented. The effectiveness of the technique is demonstrated through examples     

Non-sensitive adaptive beamforming against mutual coupling

The standard Capon beamformer (SCB) is known to suffer from severe performance degradation when there is a mismatch between the presumed signal steering vector and the actual one. There may be several reasons leading to this result such as mutual coupling between array elements. The problem of adaptive beamforming in the presence of mutual coupling is studied based on a uniform linear array (ULA). By setting a group of auxiliary elements on each side of the ULA, the authors prove that the proposed method can inherently compensate the effect caused by the mutual coupling and greatly decrease the sensitivity of the SCB against mutual coupling. This technique can also be applied to most of the existing robust beamforming methods to further improve their performances. Theoretical analysis and simulation results demonstrate the robustness and effectiveness of this technique.     

Blind adaptive beamforming for cyclostationary signals

In order to increase the capacity and to suppress co-channel interference in digital communication systems such as mobile cellular and mobile satellite communication systems, the employment of array beamforming techniques has been proposed. However, conventional beamforming methods are not suitable for such cases since these methods were mainly developed for signal detection and direction-of-arrival (DOA) estimation in radar and sonar. In this paper, utilizing the cyclostationary properties of communication signals, we propose three blind cyclic adaptive beamforming (CAB) algorithms and their fast implementation schemes. Several numerical examples are included. These results demonstrate that the CAB algorithms are good candidates for spatial reuse of frequency spectrum in digital mobile communication systems of the next generation     

Improved LMS algorithm for adaptive beamforming

Two adaptive algorithms which make use of all the available samples to estimate the required gradient are proposed and studied. The first algorithm is referred to as the recursive LMS (least mean squares) and is applicable for a general array. The second algorithm is referred to as the improved LMS algorithm and exploits the Toeplitz structure of the array correlation matrix and can be used only for an equispaced linear array     

On adaptive beamforming in correlated noise

This paper deals with the problem of adaptive beamforming in the presence of fully coherent (correlated) noise sources. Two different techniques are developed for minimizing the effects of coherent interference. The first method employs spatial interpolation of the array aperture, followed by spatial smoothing in order to decorrelate the desired signal and the interference. The second technique is based on a simple algebraic transformation for restoring the rank of the array signal correlation matrix, which is normally rank deficient in such situations. This technique is shown to work for nonuniform adaptive arrays as well. Extensive computer simulation results are presented to illustrate the effectiveness of the proposed techniques.This week was supported by the N.R.C., Resident Research Associateship Programme.     

一种改进的盲自适应波束形成算法

本文在最小二乘恒模（LSCMA）和梯度下降法（SDCMA）的基础上，提出了一种基于预解扩的判决反馈盲自适应波束形成算法，称为LS—SDCMA。本文分别在加性白高斯和多径衰落信道的环境中进行了仿真，仿真结果表明，本文提出的LS—SDCMA算法比传统的LSCMA、OCMA和SDCMA算法具有较强的抗多址干扰能力。     

Robust adaptive beamforming for large-scale arrays

For a large-scale adaptive array, heavy computational load and high-rate data transmission are two challenges in the implementation of an adaptive digital beamforming system. Moreover, the large-scale array becomes extremely sensitive to array imperfections. First, based on a restructured recursive linearly constrained minimum variance algorithm and a gradient-based optimization method, a new robust recursive linearly constrained minimum variance (RRLCMV) algorithm is proposed in this paper. The computational load of the RRLCMV algorithm is on the order of o(N), which is less than that of the conventional gradient-based robust adaptive algorithm. Then, a new efficient parallel robust recursive linearly constrained minimum variance (PRRLCMV) adaptive algorithm is proposed by appropriately partitioning the RRLCMV algorithm into a number of operational modules. It can be easily executed in a distributed-parallel-processing fashion, sequentially and in parallel. As a result, the PRRLCMV algorithm provides an effective solution that can alleviate the bottleneck of high-rate data transmission and reduce the computational cost. Finally, an implementation scheme of the PRRLCMV algorithm based on a distributed-parallel-processing system is also proposed. The simulation results demonstrate that the new PRRLCMV algorithm can significantly reduce the degradation due to various array errors.     

Eigenspace-based adaptive array beamforming with robustcapabilities

This paper deals with adaptive array beamforming based on eigenspace-based (ESB) techniques with robust capabilities. It has been shown that ESB adaptive beamformers demonstrate the advantages of fast convergence speed and less sensitivity to steering angle error over conventional beamformers. In conjunction with a signal subspace construction method, we present an efficient technique to achieve the advantages of ESB adaptive beamforming with less computing cost and more robust capabilities over existing ESB techniques. Several computer simulation examples are provided for illustrating the effectiveness of the proposed technique     

多普勒信号的稳健盲自适应波束形成

针对假设的多普勒频率和真实的多普勒频率之间的误差会导致盲波束形成的性能急剧的下降这一事实. 首先分析了存在多普勒误差时的最小均方误差准则意义下的盲自适应波束形成的性能, 然后提出了一种有效的算法来对抗多普勒误差, 该算法是一迭代过程, 可以在线估计出真实的多普勒频率. 计算机仿真验证了提出算法的有效性.     

基于谱分析的稳健自适应波束形成算法

针对在导向矢量存在误差情况下,自适应波束形成算法性能下降问题,提出一种基于谱分析的稳健自适应波束形成(SA-RAB)算法。算法利用空域与频域的对称性,根据真实导向矢量与理想导向矢量之间的误差,运用谱分析(SA)技术确定波束主瓣宽度,最后利用二阶锥规划(SOCP)技术在主瓣宽度内形成平顶响应,并在副瓣区域内进行干扰抑制。仿真结果表明:该算法可有效地抑制干扰,并输出理想的信号干扰噪声比(SINR),且提高了波束形成针对导向矢量误差的稳健性,验证了算法的有效性和优越性。     

A projection approach for robust adaptive beamforming

It is well known that calibration errors can seriously degrade performance in adaptive arrays, particularly when the input signal-to-noise ratio is large. The effect is caused by the perturbation of the presumed steering vector from its optimal value. Although it is not as widely known, similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data. Under these conditions, performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly. In the paper, a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors. The method involves projection of the presumed steering vector onto the observed signal-plus-interference subspace. An analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots. Both analytical and experimental results are presented that illustrate the advantages of the proposed method     

Efficient robust adaptive beamforming for cyclostationary signals

This paper deals with the problem of robust adaptive array beamforming for cyclostationary signals. By exploiting the signal cyclostationarity, the LS-SCORE algorithm presented in a paper by Agee et al. (1990) has been shown to be effective in performing adaptive beamforming without requiring the direction vector of the desired signal. However, this algorithm suffers from severe performance degradation even if there is a small mismatch in the cycle frequency of the desired signal. In this paper, we first evaluate the performance of the LS-SCORE algorithm in the presence of cycle frequency error (CFE). An analytical formula is derived to show the behavior of the performance degradation due to CFE. An efficient method is then developed based on the fact that the array output power approaches its maximum as the CFE is reduced. We formulate the problem as an optimization problem for reducing the CFE iteratively to achieve robust adaptive beamforming against the CFE. Simulation examples for confirming the theoretical analysis and showing the effectiveness of the proposed method are provided