一种基于协方差矩阵的MU-MIMO干扰消除算法研究

LTE-A(Long Term Evolution-Advanced)系统有高速率、低时延的需求。但是,系统中的干扰严重影响了终端接收信号质量,限制了系统性能的提升。对于小区间的同频干扰,重点研究了干扰消除性能较优的IRC(Interference Rejection Combining)算法。针对目前IRC算法的两种经典的协方差矩阵估计方案—基于数据信号和基于DM-RS参考信号的协方差矩阵估计方案的优点与不足,给出了一种基于样本点选取的协方差矩阵估计的改进方案。仿真结果表明,改进后的IRC算法较基于DM-RS参考信号的协方差矩阵估计的IRC算法有1 d B~2 d B的性能增益,因此更适用于受同频干扰比较严重的LTE-A系统中。     

An algorithm for calculation of the Jordan canonical form of a matrix

Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.     

基于修正后矩阵分解的最优协方差DOA估计

针对传统来波方向（direction-of-arrival,DOA）估计在信号相干、低信噪比与噪声非均匀环境下性能差的问题,基于修正后的矩阵分解,提出一种利用凸优化的协方差矩阵最优DOA估计方法。修正后的矩阵分解方法,解相干的同时克服了孔径损失;然后,利用凸优化,重构出无噪声的协方差矩阵;最后,利用最小化搜索计算出DOA。仿真结果表明,所提算法与矩阵分解（matrix decomposition,MD）算法、基于◢l▼1▽范数的奇异值分解（l◣▼1▽-norm singular vector decomposition,◢l◣▼1▽-SVD）算法以及基于空间平滑的协方差秩最小化估计（spatial smoothing based covariance rank minimization,SS-CRM）算法比较,能更好地抑制非均匀噪声,且在低信噪比条件下,依然性能良好。     

基于GPU的高效图像协方差矩阵算法与实现

为提高图像处理领域协方差矩阵的计算效率,满足其在实时要求下的应用,借助GPU通用计算技术,结合CUDA编程模型,对协方差矩阵的计算进行有针对性的并行化优化,设计并实现一种高效的并行图像协方差矩阵算法。为在通用PC平台上使用协方差矩阵并满足实时性需求的各种图像处理应用提供了一个可行的解决方法,对其它领域涉及到协方差矩阵的实时计算也有良好的借鉴作用。与原有的CPU实现方法相比,GPU的效率有了平均数千倍的提升。     

Maximum likelihood estimation via the extended covariance and combined square-root filters

The method of maximum likelihood is a general method for parameter estimation and is often used in system identification. To implement it, it is necessary to maximize the likelihood function, which is usually done using the gradient approach. It involves the computation of the likelihood gradient with respect to unknown system parameters. For linear stochastic system models this leads to the implementation of the Kalman filter, which is known to be numerically unstable. The aim of this work is to present new efficient algorithms for likelihood gradient evaluation. They are more reliable in practice and improve robustness of computations against roundoff errors. All algorithms are derived in measurement and time updates form. The comparison with the conventional Kalman filter approach and results of numerical experiments are given.     

An algorithm for computing functions of triangular matrices

Any function of a triangular matrix can be recursively calculated on the basis of simple properties stated in this paper.     

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。     

基于多特征协方差矩阵的图像匹配算法

针对灰度及红外图像的匹配过程中经常出现的一些问题,如缺乏丰富的目标特征、易遭受复杂背景及噪声等外界因素干扰、目标出现放大缩小或偏转等,抽取目标图像的梯度幅值与方向,腐蚀与膨胀以及信息熵等特征,通过协方差矩阵将其融合在一起,构成新的特征模型.通过全图遍历求取矩阵间相似度距离的方法找到最佳匹配重心,将新方法与其它3种已有的匹配方法进行了对比说明.实验结果表明:在灰度图像匹配时新方法准确率高、鲁棒性好,同时也可以应用于红外图像中,满足了在一些条件下提高匹配准确度的要求.     

Heterogeneous pipelined square-root Kalman Filter algorithm for the MMSE-OSIC problem

This paper describes a pipelined parallel algorithm for the MMSE-OSIC decoding procedure proposed in V-BLAST wireless MIMO systems, for heterogeneous networks of processors. It is based on a block version of the square-root Kalman Filter algorithm that was initially devised to solve the RLS problem. It has been parallelized in a pipelined way obtaining a good efficiency and scalability. The optimum load balancing for this parallel algorithm is dynamic, but we derive a static load balancing scheme with good performance.     

自适应区域协方差跟踪算法

协方差跟踪算法由于其优秀的特征描述能力在近年获得众多关注,但其全局遍历搜索策略使其仍不够高效。提出一个通用的、自适应的协方差跟踪算法,该算法利用了自适应积分区域计算策略和简单的遮挡检测处理方法,前者远快于积分图像计算并自适应于跟踪目标和跟踪环境,后者用于动态调整搜索窗口的大小。积分图像计算和全局协方差跟踪可以看作所提算法的一种特例。所提算法自然统一了局部搜索策略和全局搜索策略,并可根据跟踪环境(如遮挡、突然偏移)自然切换。所提算法既获得了在正常情况下局部搜索所带来的高效、偏离的健壮性和稳定的轨迹,又获得了在非正常情况下的由更大搜索窗口所带来的遮挡处理和重新识别定位目标的能力。通过在部分视频序列上的实验,所提算法展现出优秀的目标表达能力、更快的跟踪速度和更好的健壮性。     

一种基于协方差矩阵重构和EMP的宽带波束形成算法

在宽带波束形成中,若干扰信号从主瓣方向进入,会引起主瓣畸变、旁瓣电平抬高,从而使波束性能严重恶化。为了解决波束形成中的这些问题,研究了一种基于协方差矩阵重构和特征投影预处理（EMP）的宽带波束形成算法。该算法首先通过EMP算法求取阻塞矩阵,对接收信号进行干扰相消预处理阻塞掉主瓣干扰;然后通过相干信号子空间（CSM）方法、协方差矩阵重构求取合理的协方差矩阵;最后进行波束形成。在主瓣干扰、旁瓣干扰同时存在的情况下,该算法能够自适应地阻塞主瓣干扰、抑制旁瓣干扰,解决了存在主瓣干扰情况下宽带波束形成的波形畸变问题。计算机仿真验证了该算法有效性。     

基于简化群优化算法和协方差矩阵学习的差分进化算法

把SSO算法的交叉策略、协方差矩阵学习策略与传统的DE算法结合,提出一个新的DE算法的变种,我们把它称作SCDE算法。正如我们所知,DE算法的变异策略在DE算法中占据了非常重要的位置,然而,传统的DE算法的变异策略都是用相对位置来产生候选解,本文尝试利用个体历史最优解来诱导变异产生候选解,这将大大提高种群跳出局部最优的能力。此外,将算法的变异和交叉操作放在由种群的协方差矩阵的所有特征向量组成的坐标系中执行,这将使算法的交叉和变异操作具有旋转不变性。实验结果表明,本文提出的新的交叉和变异策略可以大大提高DE算法在CEC 2013中28个测试函数的全局寻优能力。     

An efficient algorithm for characteristic tracking on two-dimensional triangular meshes

Tracking characteristics on unstructured meshes is an important part of many numerical methods in computational fluid mechanics. In this paper, we propose an efficient algorithm for characteristic tracking on two-dimensional unstructured triangular meshes. Numerical experiments, including an example for applying this algorithm with the Eulerian-Lagrangian localized adjoint method (ELLAM) to solve a convection-dominated convection-diffusion problem, are presented to demonstrate the efficiency of this algorithm.     

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。     

An improved algorithm for Boolean matrix multiplication

A new algorithm for computing the product of two arbitraryN×N Boolean matrices is presented. The algorithm requiresO (N ³/logN) bit operations and onlyO(N logN) bits of additional storage. This represents an improvement on the Four Russians' method which requires the same number of operations but usesO(N ³/logN) bits of additional storage.     

An algorithm for polynomial matrix factor extraction

An algorithm is described for extracting a polynomial matrix factor featuring any subset of the zeros of a given non-singular polynomial matrix. It is assumed that the zeros to be extracted are given as input data. Complex or repeated zeros are allowed. The algorithm is based on interpolation and relies upon numerically reliable subroutines only. It makes use of a procedure that computes the generalized characteristic vectors of a polynomial matrix at a given point. The extracted factor is provided in column- and row-reduced Popov form. Applications of the algorithm include polynomial matrix interpolation, plus/minus factorization, column- and row-reduction, or computation of the Smith form of a polynomial matrix. The numerical routines described in this paper are implemented in the new release 2.0 of the Polynomial Toolbox for MATLAB.     

集成协方差矩阵自适应进化策略与差分进化的优化算法

不同智能优化算法在求解优化问题时通常表现出显著的性能差异.差分进化(DE)算法具备较好的全局搜索能力,但存在收敛慢、效率低的不足,协方差矩阵自适应进化策略(CMA–ES)局部搜索能力强,具备旋转不变性,但容易陷入局部最优,因此, DE和CMA–ES之间具有潜在的协同互补能力.针对上述问题,提出了一种集成协方差矩阵自适应进化策略与差分进化的优化算法(CMADE).在CMADE框架中, DE算法负责全局搜索, CMA–ES算法进行局部搜索.通过周期性解交换机制实现CMA–ES和DE两个算法间协同交互和反馈控制.在解交换时,从DE种群中选择优秀个体,利用CMA–ES算法在优秀个体周围进行局部搜索.同时在DE和CMA–ES的混合种群中,综合考虑解的多样性和最优性,选取一定比例的解作为DE算法的新种群进行全局搜索,实现全局搜索与局部搜索的动态平衡.将CMADE算法与CMA–ES, DE, SaDE, jDE, EPSDE, ACODE和SHADE算法在CEC2014标准测试集上进行比较实验.结果表明, CMADE整体性能显著优于其它比较算法.     

An improved algorithm for computing local fractal dimension using the triangular prism method

Despite the many applications of fractals in geosciences, the problem of inconsistent results derived from different fractal calculation algorithms remains. Previous research found that the modified triangular prism method was the most accurate for calculating the fractal dimension of complex surfaces such as remote sensing images. However, when extending the application of the technique into local measurements, new problems arise. Hence, adjustment to the existing technique is needed. This paper introduces a new algorithm for calculating the fractal dimension within a local window based on the triangular prism method. Instead of using arbitrary geometric steps, the new algorithm computes the number of steps needed for fractal calculation according to the window size. The new algorithm, called the divisor-step method, was tested using 4000 simulated surfaces and found to be more robust and accurate than the conventional geometric-step method. The new divisor-step method is recommended especially for local measurements.     

An efficient algorithm for calculation of the Luenberger canonical form

A new algorithm is presented to obtain the Luenberger canonical form for multivariable systems. A distinct feature of the method is that the canonical form is obtained directly and, if necessary, the similarity transformation can be computed. There is a substantial reduction in the amount of computation compared to Luenberger's method. The reduced computations along with Gaussian techniques lend greater inherent accuracy and the ability to refine the solution with additional computations. An example is presented to illustrate the technique.