基于协方差矩阵重构的稳健自适应波束形成算法综述

Capon波束形成器作为理论上最优的波束形成器具有良好的干扰抑制能力。然而Capon波束形成器对于模型失配误差非常敏感,尤其是针对协方差矩阵和期望信号导向矢量误差,波束形成器的性能会严重下降,这大大降低了波束形成器的稳健性。目前,一系列基于协方差矩阵重构的稳健自适应波束形成算法被提出,这些算法核心思想都是利用Capon功率谱一定的角度范围内积分来重构出协方差矩阵。本文首先介绍了波束形成的信号模型,然后在Capon波束形成器的基础上,介绍了4种基于协方差矩阵重构的稳健自适应波束形成技术,最后对未来波束形成技术的研究热点进行了展望。     

基于干扰噪声矩阵重构的自适应波束形成算法

针对在自适应波束形成中,当采样次数较少或期望信号导向矢量存在误差以及训练数据中含有期望信号成分时导致波束输出信干噪比(SINR)下降的问题,提出了一种重构干扰噪声协方差矩阵并且估计期望信号导向矢量的稳健自适应波束形成方法。在期望信号波达方向的角度范围已知的条件下,首先利用多重信号分类（MUSIC）空间谱在不含期望信号的区域重构出干扰噪声协方差矩阵;然后推导了避免期望信号的导向矢量的估计值收敛到任一干扰的导向矢量或它们的线性组合的约束条件;进而以此约束条件和阵列输出功率最大化条件建立了期望信号导向矢量估计的优化问题,并使用凸优化软件估计出最优的期望信号导向矢量。讨论了该方法的计算复杂度并通过仿真实验验证了其有效性和优越性。仿真结果表明,当期望信号和干扰源存在随机指向误差和局部散射的情况下,所提方法在很大的输入信噪比范围内的输出信干噪比仍接近理论值,优于其他自适应波束形成方法。     

基于干扰噪声矩阵重构的自适应波束形成算法

针对在自适应波束形成中,当采样次数较少或期望信号导向矢量存在误差以及训练数据中含有期望信号成分时导致波束输出信干噪比(SINR)下降的问题,提出了一种重构干扰噪声协方差矩阵并且估计期望信号导向矢量的稳健自适应波束形成方法。在期望信号波达方向的角度范围已知的条件下,首先利用多重信号分类(MUSIC)空间谱在不含期望信号的区域重构出干扰噪声协方差矩阵;然后推导了避免期望信号的导向矢量的估计值收敛到任一干扰的导向矢量或它们的线性组合的约束条件;进而以此约束条件和阵列输出功率最大化条件建立了期望信号导向矢量估计的优化问题,并使用凸优化软件估计出最优的期望信号导向矢量。讨论了该方法的计算复杂度并通过仿真实验验证了其有效性和优越性。仿真结果表明,当期望信号和干扰源存在随机指向误差和局部散射的情况下,所提方法在很大的输入信噪比范围内的输出信干噪比仍接近理论值,优于其他自适应波束形成方法。     

数据含期望信号的重构稳健波束形成

研究稳健波束形成问题.样本数据含期望信号时,若存在导向矢量误差,常规MVDR波束形成会在期望信号方向上产生期望信号对消,性能损失严重.针对上述问题,提出了一种在对称干扰环境下的稳健MVDR波束形成方法.首先消除数据协方差矩阵的实部得到期望信号分量,进而重构出期望信号协方差矩阵,然后从数据协方差矩阵中减去重构的期望信号协方差矩阵,得到仅含有干扰和噪声的协方差矩阵,并以此来实现MVDR的权向量设计.仿真结果表明,改进方法消除了期望信号分量的不良影响,提高了波束形成对系统误差的稳健性.     

基于改进加权空间平滑的凸优化协方差估计

针对相干信号受到非均匀噪声的干扰,在低信噪比环境中常规DOA估计存在估计效果较差甚至失效的情况,基于改进加权空间平滑,提出一种使用凸优化构造最优权重矩阵的方法。改进加权空间平滑算法解相干的同时构造权重矩阵,再用凸优化重构无噪声权重矩阵,将平滑过的协方差矩阵加权,并用MUSIC算法进行DOA估计。仿真结果证实,所提方法相对于空间平滑（spatial smoothing,SS）、基于特征空间MUSIC的空间平滑估计（spatial smoothing and eigen space based MUSIC,SS-ESMUSIC）以及接收信号协方差矩阵秩最小化（spatial smoothing based covariance rank minimization,SS-CRM）算法能更好地抑制非均匀噪声和解相干,且减少了低信噪比的干扰,展现出更优良的分辨力和准确性。     

基于对称谱的宽带相干信号快速DOA估计

针对聚焦类宽带信号方位估计算法运算量较大的问题,提出了一种快速算法。首先利用矩阵的Toeplitz化重构,不用对阵列进行子阵分割,就可实现宽带信号的解相干;然后根据接收数据协方差矩阵的厄尔米特特性,利用酉变换将复数矩阵映射为实数矩阵,通过在实数域特征分解,降低了特征分解的计算复杂度;最后通过投影子空间正交技术,利用噪声子空间和共轭噪声子空间重新构造空间谱,根据谱对称性,在半谱内搜索即可得到信号的角度,同时使谱峰搜索的运算量降低了一半。理论分析及仿真结果表明,新算法无需聚焦运算,精度较高,运算量小,对宽带相干信号有效。     

两种协方差估计方法的性能比较

干扰抑制合并(IRC)是一种能有效应对小区间同频干扰的算法。与最大比合并(MRC)不同,IRC能根据干扰的统计特性来抑制干扰。实现IRC算法的关键有两方面,而对干扰噪声的协方差矩阵的估计是其中之一。在接收信号的处理中加入对干扰噪声协方差的考虑,可以有效的抑制干扰,提高系统性能。干扰噪声的协方差估计有两种方法,一种是通过导频信号估计,另一种是接受信号协方差估计。在多数通信系统中,导频信号属于稀有资源,虽然可以通过求出导频位置的干扰加噪声协方差矩阵,进而使用插值获得每个时频位置的干扰加噪声协方差矩阵,但是参考信号太少,带来的估计误差难免对IRC算法的干扰抑制能力产生影响,再加上信道估计的误差,最终的性能难尽人意[1]。导频信号固然有限,但是能够利用的接收信号却绰绰有余,本文将通过理论证明和仿真验证,用两种协方差估计方法(接收信号协方差估计、干扰噪声协方差估计)恢复的信号存在一定的比例关系,基于这种关系,可以将接收信号的协方差矩阵替代干扰噪声协方差矩阵,获得较理想的译码性能。     

DOA估计算法的一种修正MUSIC算法的研究

传统改进 MUSIC 算法通过对接收信号协方差矩阵作预处理,使信号协方差矩阵分解得到信号子空间与噪声子空间正交,从而降低噪声的影响。但当信号间隔很小时,随着信噪比的降低,传统改进MUSIC算法已无法分辨出信号。基于此问题提出的修正MUSIC算法在使信号子空间与噪声子空间正交的基础上,充分利用了噪声子空间及其特征值对噪声子空间的修正,进而构造谱峰搜索函数估计出信号。通过仿真实验,证实了在信噪比很低的情况下,信号间隔很小且存在相关信号时,修正MUSIC算法能准确地估计出传统改进MUSIC算法不能估计的信号。     

基于干扰加噪声协方差矩阵重构的稳健自适应波束形成

在自适应波束形成中,由于期望信号(SOI)导向矢量(SV)的误差、采样点数较少、训练数据中存在期望信号成分等原因,造成波束形成的性能严重下降。针对以上问题,提出了一种稳健波束形成方法。首先利用MUSIC算法和参数估计来重构不包含SOI的干扰噪声协方差矩阵,再通过利用相关系数来估计出期望信号导向矢量。仿真结果表明,该算法可以处理较大的方向误差,并且信噪比(SNR)在较大的范围内都可以得到比传统方法更佳的性能。     

低复杂度非相干分布源参数估计方法

提出了一种低复杂度的非相干分布源参数估计方法,证明了在小角度扩展下,无噪声协方差矩阵的元素能够被分离成幅度信息和相位信息两部分。基于此性质,利用样本协方差矩阵次对角线上元素的相位信息首先估计出分布源的中心波达方向。根据无噪声协方差矩阵列矢量和采样伪噪声子空间之间的近似正交性构造代价函数,并通过一维搜索估计出分布源的角度扩展参数。该方法避免了对样本协方差矩阵进行特征分解,不需要确定伪信号子空间的维数,而这是现有子空间方法的主要困难。此外,它估计分布源的两个角度参数时仅需要完成一次一维谱搜索,计算复杂度较低。仿真结果证实了所提方法的有效性。     

Robust adaptive beamforming using a novel signal power estimation algorithm

Recently, many robust adaptive beamforming (RAB) methods based on covariance matrix reconstruction have been proposed. Motivated by the idea, in this paper, a novel and efficient signal power estimator is devised to reconstruct the interference-plus-noise covariance (INC) matrix, with the corresponding RAB algorithm proposed. Firstly, the steering vectors of the incoming sources are derived using the Capon spatial spectrum and known array geometry. Secondly, a set of linear equations is established based on the signal subspace projection, from which the powers of the incoming sources are estimated. Based on the presumed angular sector of the signal-of-interest (SOI), the steering vectors and powers of the SOI and interferences are distinguished, and the INC matrix is then reconstructed. Finally, the beamformer is determined by the estimated INC matrix and SOI steering vector. The proposed algorithm is computationally more efficient than other reconstruction-based methods because there are closed-form solutions for the signal powers. Simulation results indicate that our proposed algorithm performs better than the existing methods at high signal-to-noise ratios (SNRs), and achieves nearly optimal performance across a wide range of SNR.     

Pulse-order recursive method for inverse covariance matrix computation applied to space-time adaptive processing

The conventional space-time adaptive processing(STAP) method such as the typical sample matrix inversion(SMI)-based STAP method is difficult to implement for a practical system because intense computational complexity arises in calculating the inversion of a space-time covariance matrix directly.According to the block Hermitian matrix property of space-time covariance matrix,a new pulse-order recursive method is proposed in this paper to calculate the inverse covariance matrix for the STAP adaptive weight,which can reduce the computational complexity significantly.The proposed method requires initially calculating the inverse covariance matrix of the first pulse-order recursively based on the block Hermitian matrix property.In the following,the inversion of space-time covariance matrix is obtained recursively based on the previous pulse-order inverse covariance matrix.Next,the STAP adaptive weight is calculated based on the inversion space-time covariance matrix previously obtained.Compared with the conventional SMI-based STAP algorithms,the computational complexity of the proposed method is reduced to more than 50% for the same clutter suppression performance.This method can be applied to practical systems benefiting from small computational complexity and stable clutter suppression performance.     

Robust adaptive beamforming method using principal eigenpairs with modification of PASTd

Adaptive arrays suffer from performance degradation in the presence of steering vector errors. The doubly constrained robust Capon beamformer (DCRCB) can deal with the problem, utilizing all the eigenvalues and eigenvectors of the covariance matrix, which leads to high computational complexity. This paper presents a robust beamforming method which is computationally efficient, exploiting principal eigenpairs only. The eigenpairs can be estimated based on the projection approximation subspace tracking with deflation (PASTd). The original PASTd algorithm, which does not provide orthonormal eigenvectors in general, is modified so that the orthonormalization of eigenvectors can be efficiently made using the structure of the modified algorithm. The proposed beamforming method significantly reduces the computational load, particularly when the number of the directional signals is much less than that of sensor elements, and substantially has the same performance as the conventional one utilizing all the eigenpairs.     

一种基于特征空间的盲波束形成算法

绝大多数通信信号都具有周期平稳信号特性。利用信号的周期平稳特性可以进行真正的盲自适应波束形成,因而受到了广泛关注。ＣＡＢ类算法就是其中的一种。它的运算量较小,但鲁棒性不够强。本文针对其不足,提出了一种基于特征空间的盲波束形成算法。该算法将估计的导引矢量约束在信号子空间,降低了目标信号含于自相关估计矩阵和有限次快拍相关阵引起的子空间扰动的影响,提高了算法的收敛速度和鲁棒性。同时,目前用于进行子空间分解的新算法层出不穷,运算量不断降低。因此,本文提出的盲算法具有很强的实用性和广阔的应用前景。计算机仿真验证了理论分析。     

Compressive sampling optimization for user signal parameter estimation in massive MIMO systems

As the most promising technology in wireless communications, massive multiple-input multiple-output (MIMO) faces a significant challenge in practical implementation because of the high complexity and cost involved in deploying a separate front-end circuit for each antenna. In this paper, we apply the compressive sampling technique to reduce the number of required front-end circuits in the analog domain and the computational complexity in the digital domain. Unlike the commonly adopted random projections, we exploit the a priori probability distribution of the user positions to optimize the compressive sampling strategy, so as to maximize the mutual information between the compressed measurements and the direction-of-arrival (DOA) of user signals. With the optimized compressive sampling strategy, we further propose a compressive sampling Capon spatial spectrum estimator for DOA estimation. In addition, the user signal power is estimated by solving a compressed measurement covariance matrix fitting problem. Furthermore, the user signal waveforms are estimated from a robust adaptive beamformer through the reconstruction of an interference-plus-noise compressed covariance matrix. Simulation results clearly demonstrate the performance advantages of the proposed techniques for user signal parameter estimation as compared to existing techniques.     

Robust blind adaptive beamforming under double constraints

In practical complex communication environments, the performance of linearly constrained constant modulus algorithm (CMA) is known to degrade severely in the presence of even slight signal steering vector mismatches. To overcome the mismatches, a novel robust CMA is proposed for blind adaptive beamforming via the worst-case performance optimization and the oblique projection of signal steering vector, which is based on double constraints on explicit modeling of uncertainties in the desired signal array in this paper. To improve robustness, the weight vector is optimized to involve minimization of a constant modulus algorithm objective function with penalty for the worst-case signal steering vector. The theoretical analysis for our proposed algorithm in terms of SINR and convergence performance is presented in this paper. The proposed robust constrained CMA resolves the problem of interference capture, provides excellent robustness against the signal steering vector mismatches, and improves array output performance. Simulation results are presented to show the excellence of this technique and the main parameters of concern to evaluate the performance are analyzed.     

导向矢量存在匹配误差时Capon波束校正算法

针对信号导向矢量存在匹配误差时提出一种Capon波束校正算法.该算法利用噪声子空间与期望信号导向矢量正交的特点,首先通过构造代价函数估计来波信号的方向角;然后在约束最优的基础上对误差进行迭代估计;最后对导向矢量进行校正并进行波束形成.本文通过计算机仿真验证了该方法的有效性.     

导向矢量失配情况下基于稀疏表示的波达方向估计算法

提出了一种传感器阵列导向矢量失配情况下的基于稀疏表示的信号源波达方向DOA估计算法。针对一些实际环境中噪声重尾现象严重的特点,采用合成圆对称广义高斯噪声分布对其进行模拟。考虑到实际环境中传感器自身运动以及外界环境因素的改变可能会导致传感器导向矢量产生波动,利用加权最小二乘法对波动生成的增益值进行最优估计。然后,构建信号模型的分数低阶矩FLOM矩阵,进行矢量化处理,以提高其数组维数。最后,利用稀疏表示方法重构信号模型,将信号源DOA估计转化为二阶锥规划问题进行求解,并采用奇异值分解降低运算量。仿真结果表明,本算法的信号源DOA估计具有很高的分辨率,且有效地避免了导向矢量失配对DOA估计产生的影响。