【作者】 聂卫科；

【导师】 冯大政；

【作者基本信息】 西安电子科技大学 ， 信号与信息处理， 2008， 博士

【摘要】 空间信号自适应波束形成与参数估计是阵列信号处理中的两个主要研究内容。其在雷达、声纳、地震探测、电子侦察、射电天文等领域有广泛而重要的应用前景。本文研究了不同应用背景和实际环境中空间信号自适应波束形成和参数估计问题。给出了一些有效的算法,并通过理论分析和仿真实验进行了验证。主要工作包括以下几个方面:1.提出一种基于数据域的二维自适应波束形成算法,将标准的Capon波束形成(Standard Capon Beamforming, SCB)算法的高维权向量分解成两个低维权向量的Kronecker积的形式,通过双迭代算法求解两个低维权向量,再还原成所需的高维权向量。由于使用的数据矩阵维数比SCB算法的相关矩阵维数大大降低,相同情况下用较小的快拍可得到较优的采样数据矩阵的估计,使得所给算法在小快拍下性能优于标准的SCB波束形成算法。分解的两个权向量维数明显降低,使用数据矩阵也避免了大维数采样协方差矩阵的求逆,计算量显著减小。理论上详细分析并对比了所提算法和经典Capon法的计算量。仿真实验对所给算法的收敛速度、方向图、信噪比及快拍变化下的输出信干噪比、指向误差变化下的输出信干噪比等性能进行了研究。2.针对高斯白噪声环境,提出一种非酉联合对角化算法估计二维频率。利用二维数据的旋转不变性,构造四个具有对角结构的数据矩阵,在时域进一步扩展,形成一组对角结构的数据矩阵。通过数据矩阵组的联合对角化,实现二维频率的估计,所得二维频率能自动配对。相对最近提出的多阶段分解与重构算法,该方法每步迭代具有精确的最小二乘闭式解,消除了多阶段算法的累积误差,提高了估计精度。在理论上证明了所提算法的渐近收敛性。3.推广了上述非酉联合对角化算法,并将其应用到波达方向估计和谐波恢复中。利用平移不变阵列信号子空间的旋转不变性,构造一组具有对角结构的空时相关矩阵。为抑制噪声、减少计算量并加快收敛速度,对矩阵组降维处理,利用降维后相关矩阵组的结构信息,基于非线性最小二乘建立二次代价函数,提出一种新的三迭代算法(TIA)求解波达方向。谐波恢复中也有类似的结构信息,利用TIA算法同样可恢复谐波信号。所求的波达方向和恢复的谐波频率均不需要配对算法支持,能实现自动配对。仿真结果证实了所提算法的有效性。所提的TIA算法是上述非酉联合对角化算法的进一步推广,其右对角化因子矩阵具有多样性,可解决更广泛的一类问题。4.在任意平面阵列下提出一种二维波达方向跟踪算法。由于引入了辅助变量,使得该算法可用于色噪声下的波达方向跟踪。该方法采用秩1更新结构,构造两个无约束的代价函数,求其递归最小二乘解获得信号子空间。为了简化运算,将推导过程进行了两次近似,运算复杂度显著降低。最后对跟踪结果正交化,获得了良好的正交性。理论上计算并对比了本章算法和经典的EIV-PAST算法的计算量。仿真实验在快变化和慢变化两种情况下对所提算法和EIV-PAST算法的跟踪结果进行了观察。对两种算法跟踪的信号子空间的误差、子空间夹角、正交性误差进行了对比。更多还原

【Abstract】 The adaptive beamforming and parameters estimation of spatial signal are two important research fields of array signal processing. They finds wide applications in many fields such as radar, sonar, seismic exploration, electronic surveillance, radio astronomy, etc. this dissertation aims at the problems of adaptive beamforming and estimation of signal parameters in different practical environments, provide several useful algorithms and verifies them by computer simulations. The main contents of this dissertation can be summarized as follows:1. Based on the data matrix, a novel algorithm termed bi-iteration algorithm (BIA) is proposed to implement the two-dimension (2-D) adaptive beamforming. The long weight vector of the Standard Capon beamforming (SCB) can be written as a kronecker product of two short weight vectors. The proposed BIA is used to deduce the two short weight vectors. Then the long weight vector can be reconstructed through the two short weight vectors by Kronecker product. Since the dimension of data matrix we use is much lower than the dimension of correlation matrix in the standard capon beamforming, we can obtain a better estimation of data matrix than correlation matrix in the case of less snapshots. Hence our BIA shows a better performance in the case of small snapshots. Moreover, the inverse of the high-dimensional correlation matrix is avoided by using the data matrix, so the computational complexity of BIA is remarkably reduced. A set of experiments is presented to compare the proposed BIA with the well known Capon beamforming in the performance of convergence speed, the beampattern, the output SINR versus input SNR, input snapshots and so on.2. A non-unitary joint diagonalization algorithm is proposed to estimate the 2-D frequencies embedded in additive Gaussian white noise. By exploiting the rotational invariance property of the 2-D data matrix, we establish four matrices which possess diagonal structures. Moreover, we expand the data matrix in temporal domain and derive a set of diagonal structure matrices. Consequently the 2-D frequencies are estimated by accomplishing the joint diagonalization of the group of data matrices. It is worth mentioning that the estimated 2-D frequencies can be paired automatically. The proposed algorithm eliminates the error propagation of the multistage decomposition algorithm because each iteration poses a typical least square problem with a unique closed solution. Hence the estimation accuracy is increased. The asymptotical convergence of the proposed algorithm is also proved.3. We develop a generalized version of non-unitary joint diagonalization algorithm, and then propose an algorithm to resolve the problems of direction of arrival and harmonic retrieval. The underlying rotational invariance among signal subspace induced by an array of sensors with a displacement invariance structure is exploited, a set of spatio-temporal correlation matrices possessing diagonal structures are introduced. To make the computational complexity lower and the convergence speed faster, we deduce a dimension-reduction matrix dealing with the set of correlation matrices. Using the structure information of the dimension-reduction correlation matrices, a novel cost function is proposed based on nonlinear least squares. Afterwards, a new approach termed tri-iterative algorithm (TIA) is derived for solving the cost function and estimating the direction of arrival of sources and the harmonic frequencies. Simulation results demonstrate the effectiveness of the proposed algorithm.4. An algorithm is proposed to track the azimuth and elevation angle in the case of arbitrary plane antenna array. Introducing instrumental variable can make this algorithm used in colored noise environment. It makes use of the rank one update model to construct two unconstrained cost functions, then the signal subspace can be obtained through the recursive least square solutions of the cost functions. Two proper approximations are made in the deduction to reduce the computational complexity. The tracked signal subspace are orthonormalized to obtain better performance. The computational complexity between the proposed algorithm and the well known EIV-PAST algorithm is detailly analyzed and compared. Simulations are conducted to show the tracking performance of the proposed algorithm and the EIV-PAST algorithm. Specially, we compare the error of signal subspace, the subspace angle and the error of orthonormality.更多还原