宽带频率-方向不变恒定主瓣波束形成

常规波束形成主瓣随频率和指向变化,为了实现频率方向二维主瓣恒定,本文基于约束优化的方法,提出了一种宽带频率-方向不变恒定主瓣波束形成算法,并将之应用到宽带信号DOA估计中。首先在参考频率上约束方向不变主瓣恒定,然后在不同指向上约束频率不变主瓣恒定,并将约束问题表示为标准的二阶锥规划形式,运用SeDuMi求解最优权向量。仿真实验表明,本文提出的算法能够实现不同频率不同指向上波束主瓣恒定,与频率不变波束相比,采用频率-方向不变波束的DOA估计方法降低了信噪比分辨门限,提高了估计精度。     

一种稳健的宽带聚焦波束形成算法

将聚焦变换的思想与二阶锥规划方法相结合,提出了一种稳健的宽带聚焦波束形成算法。该算法首先将宽带信号划为多个窄带信号,再通过最佳聚焦矩阵,聚焦到最佳聚焦频率上,将宽带问题转换为窄带问题,最后利用二阶锥规划的方法实现窄带波束形成。计算机仿真验证了该算法的有效性。     

小型阵列宽带恒定束宽波束形成器仿真研究

关于优化宽带恒定束宽波束形成,是阵列小型化和对低频宽带信号探测的核心问题.为了研究阵元间距小于四分之一波长的线列阵的宽带恒定束宽波束形成器设计,提出了FIR滤波器的适用于小型传感器阵列的时域恒定束宽波束形成方法,分析了频域和时域宽带波束形成的特点,进行了时域宽带恒定束宽波束形成器的设计.根据最小均方准则,求出了频域子带波束形成加权向量,使工作频带内各子带波束主瓣趋近于期望波束,同时控制工作频带内波束旁瓣响应幅度,波束图主瓣形状设计与期望频率响应FIR滤波器的设计问题都转化为二阶锥规划方法,从而实现工作频带内的恒定主瓣束宽.通过仿真证明,改进方法可使密排阵列在2000Hz ～ 4000Hz工作频段范围内具有恒定束宽的方向特性.     

一种宽带恒定束宽自适应波束形成算法

在宽带恒定束宽波束形成中,强干扰信号是导致波束性能下降的一个重要原因.为了抑制强干扰信号特别是快速运动中的强干扰信号,提出了一种宽带恒定束宽自适应波束形成算法.首先采用一种具有零陷控制特性的自适应波束形成技术形成参考波束图,然后利用二阶锥规划的方法计算出其它子带上与参考波束图既有相同主瓣响应又有相同零陷响应的自适应权向量,同时通过对白噪声增益的限制来保证算法的稳健性.不仅具有恒定束宽波束的特性,而且具有自适应波束零陷控制的特性,从而保证对强干扰信号有较强的抑制能力.仿真结果验证了该算法的有效性.     

基于二次型约束的稳健宽带恒定束宽波束形成

针对期望信号导向矢量失配时传统宽带波束形成器性能恶化的问题,提出一种稳健的宽带恒定束宽波束形成算法。首先结合空间响应变化(Spatial response variation, SRV)约束,将算法在信号带宽内不同频点的阵列响应约束简化为对某一参考频点的约束,实现具有恒定束宽特性的宽带波束形成,再通过对权矢量模值施加二次不等式约束,抑制指向误差及传感器参数随机扰动误差,提高算法的稳健性,并通过拉格朗日乘子法,在约束边界上求得最优权矢量的解析解。实验结果表明算法可有效克服信号指向误差引起的波束形成器性能恶化问题,且具有良好的恒定束宽特性及较高的阵列输出性能。     

麦克风阵列鲁棒频率不变波束形成算法

在实际应用中,频率不变波束形成器通常受到麦克风阵列失配误差的影响,因此提高频率不变波束形成器的鲁棒性具有重要意义。针对上述问题提出了一种约束优化模型,可以在保持频率不变波束形成的同时提高阵列的鲁棒性。首先设计目标波束图,考虑到差分麦克风阵列本身具有频率不变的波束图,选用传统二阶超心型差分麦克风波束图做为目标波束图。上述模型以麦克风阵列权矢量的二范数作为目标函数来最大化鲁棒性,在无失真约束,目标波束主瓣逼近约束以及旁瓣增益精准控制约束下实现频率不变。然后在交替方向乘子法算法框架下,将优化问题分解为多个优化子问题求解,然后对每个优化子问题分别求解,通过仿真验证了在交替方向乘子法算法下上述模型的可行性与有效性,最终达到了麦克风阵列鲁棒频率不变波束响应的效果。     

基于稀疏表示的OFDM信号的DOA估计

针对正交频分复用（OFDM）, 宽带信号波达方向(DOA)估计问题, 提出一种基于宽带信号协方差矩阵稀疏表示的DOA估计方法。该方法是在协方差矩阵主对角线下对左下角三角形元素按各条对角线取平均值后形成一个新的向量, 然后将该向量写成冗余字典形式。在冗余字典下对信号进行稀疏性约束形成二阶锥约束优化问题, 再用工具箱SeDuMi来实现DOA估计。理论分析和仿真结果表明, 该方法在低信噪比和少快拍数下分辨率很高, 是一种有效的宽带信号DOA估计算法, 此方法优于基于高阶累积量算法和宽带聚焦算法的DOA估计方法。     

基于相位约束的低复杂度稳健宽带波束形成算法

针对传统空时结构宽带波束形成器结构复杂、计算量大和稳健性差的问题,提出低复杂度的稳健宽带波束形成算法。首先给出频率变化时阵列响应相位,分析频率变化与角度变化对阵列响应相位的影响。通过对期望信号不同频点施加阵列响应幅度和相位约束,补偿不同频率间的阵列响应相位差来实现无需延迟线或FIR/IIR滤波器结构的稳健宽带波束形成。然后分析频率和角度同时变化对阵列响应相位的影响,在期望信号来向附近引入辅助方位角,进一步提高期望信号来向趋于零度和相对带宽较小时算法的稳健性。理论分析与仿真实验表明,本文算法结构简单,计算复杂度较低且具有较好的稳健性。     

采用二阶锥规划和压缩感知的方向图综合算法

针对常规自适应方向图综合在求解最优权值向量时需经过复杂的广义矩阵求逆运算,计算过程繁琐,占用存储空间大的缺陷,提出一种采用二阶锥规划与压缩感知理论的改进自适应方向图综合算法。改进的算法将传统算法中的误差性能函数通过数学变换转换成标准二阶锥规划形式快速求解。同时应用压缩感知理论将大规模阵列权值稀疏化处理,从而得到最优天线阵列权值向量并减少训练时间。仿真结果表明,采用二阶锥规划与压缩感知的改进算法在大规模阵列天线方向图综合时求解速度快,运算精度高,且在应用压缩感知后形成的方向图有较低旁瓣,干扰方向零陷深,接近满阵时的波束性能。     

一种精确控制旁瓣的自适应波束形成算法

提出了一种精确控制旁瓣和抑制干扰的自适应波束形成算法。它是通常的最小方差无畸变（MVDR）波束形成算法的改进形式，使阵列输出信号功率最小的同时，保持目标信号方向的无失真响应，并且严格保证旁瓣低于某一给定值，抑制干扰。在仿真过程中，充分应用了二阶锥规划（second—order cone programming）算法，并与MVDR波束形成算法进行比较，验证了方法的正确性，同时研究了该算法的稳健性。     

Optimal design and verification of temporal and spatial filters using second-order cone programming approach

11 Introduction The filters are widely used in many applications of signal processing. Filter design is an important research problem in many diverse application areas. The filters we usually refer to are temporal filters, which pass the frequency components of interest and attenuate the others. A spatial filter passes the signal radiating from a specific location and attenuates signals from other locations. Beamformer that widely used in radar, sonar,and wireless communications is a kind of …     

Control applications of nonlinear convex programming

Since 1984 there has been a concentrated effort to develop efficient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interior-point methods (beyond their efficiency for LP): they extend gracefully to nonlinear convex optimization problems. New interior-point algorithms for problem classes such as semidefinite programming (SDP) or second-order cone programming (SOCP) are now approaching the extreme efficiency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to efficiently solve nonlinear convex optimization problems opens up new applications. In the first example we show how SOCP can be used to solve robust open-loop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the set-point and feedback gains for a controller, and compare this method with the more standard approach. Our final application concerns analysis and synthesis via linear matrix inequalities and SDP.     

Range–angle-decoupled beampattern synthesis with subarray-based frequency diverse array

The beam steering of conventional phased array (PA) is fixed in one direction, thus its beampattern synthesis can only be performed in angle domain. Compared with the conventional PA, frequency diverse array (FDA), which applies an additional frequency shift across the array aperture, possesses degrees-of-freedom (DOFs) in not only angle domain but also range domain, thus providing great superiority and many potential applications. However, the range and angle information of the FDA cannot be exclusively determined at the output of the array due to the fact that its beam steering is coupled in range and angle domains. In this paper, we firstly propose a subarray-based FDA framework to obtain the range–angle-decoupled beampattern. Specifically, the array is divided into multiple non-overlapped subarrays with different frequency shifts and these subarrays with non-zero frequency shifts exist in pairs. With the devised subarray-based FDA framework, the DOFs in both range and angle domains can be obtained simultaneously. On this basis, a novel beampattern synthesis method based on semidefinite relaxation (SDR) is proposed to focus the transmit energy in the desired range–angle region. The aim of the constructed constrained optimization problem is to find an optimal transmit weight matrix such that the true transmit beampattern best approximates a desired beampattern. Numerical simulations are implemented to demonstrate the effectiveness of the proposed range–angle-decoupled beampattern synthesis approach.     

Mathematical methods to study the polling systems

Reviewed were the mathematical methods that are used to investigate the polling systems which found wide application in modeling and design of various transport and industrial processes. Emphasis was made on the models of polling systems used to investigate the wireless broadband networks. The polling systems were classified; presented were stochastic models and methods of investigating discrete-time and continuous-time systems, systems with cyclic, periodic, and random queue polling, as well as the methods of their optimization.     

Support vector regression with noisy data: a second order cone programming approach

A robust convex optimization approach is proposed for support vector regression (SVR) with noisy input data. The data points are assumed to be uncertain, but bounded within given hyper-spheres of radius η. The proposed Robust SVR model is equivalent to a Second Order Cone Programming (SOCP) problem. SOCP formulation with Gaussian noise models assumption is discussed. Computational results are presented both on real world and synthetic data sets. The robust SOCP approach is compared with several other regression algorithms such as SVR, least-square SVR, and artificial neural networks by injecting Gaussian noise to each of the data points. The proposed approach out performs the other regression algorithms for some data sets. Moreover, the generalization behavior of the SOCP method is better than the traditional SVR with increasing the uncertainty level η until a threshold value.     

一种基于二阶锥规划的浮点分数时延滤波器

宽带图像声纳通常采用分数时延滤波器来提高时延精度.传统的分数时延滤波器基本采用Farrow定点结构,但其动态范围窄并且需要占用较多的硬件资源.为克服上述不足,提出了一种采用二阶锥规划（SOCP）算法进行分数时延滤波器系数设计,并以分布式算法为基础的浮点分布式时延滤波器.该滤波器具有计算精度高、动态范围大等优点,适于在FPGA上进行规模化应用.     

Possibilities of using pattern recognition methods in research on mathematical models

The possibilities of research on mathematical models with a large number of parameters using pattern recognition methods are discussed in this paper. Research of models through construction of phase and parametric portraits is the basic approach, which makes it possible to solve state prediction and control problems for objects described by the mathematical models being investigated and also analyze and study the problems arising due to a particular model’s content. To illustrate the possibilities of research, three mathematical models are taken as examples.     

Restoration of matrix fields by second-order cone programming

Summary Wherever anisotropic behavior in physical measurements or models is encountered matrices provide adequate means to describe this anisotropy. Prominent examples are the diffusion tensor magnetic resonance imaging in medical imaging or the stress tensor in civil engineering. As most measured data these matrix-valued data are also polluted by noise and require restoration. The restoration of scalar images corrupted by noise via minimization of an energy functional is a well-established technique that offers many advantages. A convenient way to achieve this minimization is second-order cone programming (SOCP). The goal of this article is to transfer this method to the matrix-valued setting. It is shown how SOCP can be applied to minimize various energy functionals defined for matrix fields. These functionals couple the different matrix channels taking into account the relations between them. Furthermore, new functionals for the regularization of matrix data are proposed and the corresponding Euler–Lagrange equations are derived by means of matrix differential calculus. Numerical experiments substantiate the usefulness of the proposed methods for the restoration of matrix fields.      

Energy-efficient joint path-following for attitude-fixed space manipulators with bounds on completion time and motor voltage/current

This paper investigates the minimum-energy joint path-following problem for space manipulators whose base attitude is stabilized by reaction wheels. In the problem, manipulator joint path is specified for rest-to-rest motion and constraints are imposed as the upper bound on both motion completion time and the voltage/current limits of DC motors in manipulator joints and reaction wheels. We suggest a simple two-stage algorithm to address this problem. The algorithm first tries to find a global optimal solution by solving a relaxed convex problem. If the convex relaxation is not successful, then the algorithm solves subproblems iteratively to find a suboptimal solution. Since both problems are formulated as second-order cone programming (SOCP) form, they can be solved efficiently using dedicated SOCP solvers. The effectiveness of the proposed method is verified by numerical experiments.