一种新的二维MUSIC算法的研究

提出了一种新的基于垂直阵列结构的二维MUSIC方法来估计信号的DOA(direction of arrive)，此方法只需三个均匀直线阵就可估计用户的二维DOA。该方法利用其中的一个直线阵来组合两个线阵分别估计的一维DOA，大大改善了DOA的估计性能。仿真结果证明了该方法的有效性。     

基于约束MUSIC的二维DOA估计

本文首先分析了约束MUSIC算法的原理,然后采用这种方法,研究了均匀圆阵的二维到达波方向估计问题,并推广到平面任意阵的情况.研究结果表明,对于相关信号源的DOA估计,采用约束MUSIC法比MUSIC法具有更好的估计性能.     

Asymptotic properties of the least squares estimates of 2-D exponential signals

Recently Rao et al. [13] established the strong consistency and asymptotic normality of the maximum likelihood estimates of the 2-D superimposed exponential signal model under the assumption of normality of the error random variables. In this paper we investigate the theoretical properties of the least squares estimates of the same model under the assumption of general error distribution. The strong consistency and asymptotic distribution of the least squares estimates have been obtained. Further extension to the multidimensional case has been proposed.The work is partly supported by a Grant (No: SR/OY/M-06/93) of the Department of Science and Technology, Government of IndiaThe work is partly supported by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India     

一种解耦合二维MUSIC算法研究

针对目前多信号环境中信号的测频测向问题,利用非均匀时延,解开频率和信号到达角之间存在的耦合,在此基础上实现了解耦合的二维MUSIC算法。可同时测量信号频率和到达角,计算量小,并保持了MUSIC算法测量精度高的特点。仿真结果证明了该方法的有效性。     

Bias analysis of the MUSIC location estimator

The authors present a rigorous bias analysis of the MUSIC location estimator, and they derive an accurate and concise bias expression. The analysis is based on the second-order Taylor series expansion of the derivative of the null spectrum, properties of the null spectrum, and statistics of the estimated signal eigenvectors. It is proven that in the derivation the remainder term in the second-order Taylor series can be dropped but the second-order terms cannot be. Simulations verify that the bias expression is valid over a wide range of signal-to-noise ratios (SNRs) extending down into the resolution threshold region of MUSIC. Although asymptotic, this expression can be accurately applied to a limited number of snapshot cases. The utility of the expression is shown by using it in a study of MUSIC location estimator characteristics. Estimate bias and standard deviation are compared for variations in SNR, numbers of sensors and snapshots, and source correlation. MUSIC resolvability and estimator performance bounds are addressed, accounting for bias     

An Efficient FPGA Implementation for 2-D MUSIC Algorithm

Multiple signal classification (MUSIC) algorithm is widely used in measuring the direction of arrival. In VLSI implementation of a two-dimensional MUSIC algorithm, the two primary modules, eigenvalue decomposition and spatial spectrum search, generally consume a significant hardware and cause long processing delay. Two novel design techniques: serial rotation angle broadcasting and multi-scale peak searching are introduced in this paper to mitigate these problems. An FPGA implementation is presented to demonstrate the efficiency of the proposed techniques. It only takes 1 ms for one set of 2-D direction estimation, and the deviations in elevation angle and azimuthal angle are both less than \(0.1^{\circ }\). The whole design is implemented in Xilinx’s Virtex-6 LX130T, which consumes about 60 % of the total resources of a single device.     

一种用于二维MUSIC算法的谱峰识别方法研究

MUSIC测向技术是一种性能优异的测向方法,得到了广泛的应用.MUSIC算法中对谱峰的识别问题,一直是研究的热点.文中对MUSIC谱峰特征进行了分析,并提出了一种确定谱峰位置的方法,最后通过二维MUSIC算法的计算机仿真验证了方法的正确性.     

Asymptotic Bias and Variance of Conventional Bispectrum Estimates for 2-D Signals

In this paper, we derive the asymptotic bias and variance of conventional bispectrum estimates of 2-D signals. Two methods have been selected for the estimation: the first one – the indirect method – is the Fourier Transform of the weighted third order moment, while the second one – the direct method – is the expectation of the Fourier component product. Most of the developments are known for 1-D signals and the first contribution of this paper is the rigorous extension of the results to 2-D signals. The calculation of the bias of the direct method is a totally original contribution. Nevertheless, we did all calculations (bias and variance) for both method in order to be able to compare the results. The second contribution of this paper consists of the comparison of the theoretical bispectrum estimate bias and variance with the measured bias and variance for two 2-D signals. The first studied signal is the output of a non-minimal phase linear system driven by a non-symmetric noise. The second signal is the output of a non-linear system with Gaussian input data. In order to assess the results, we performed the comparison for both methods with different sets of parameters. We show that the maximum bias coefficient is the one of the 1-D case multiplied by the dimensionality of the signal for both methods. We also show that the estimate variance coefficient is the 1-D case coefficient with a power equal to the signal dimensionality.Received October 21, 2002; Revised December 2003; Accepted March 25, 2004; First Online Version published in December 2004     

基于数据共轭重排的修正二维MUSIC算法分析

在阐述二维MUSIC算法基本原理的基础上,通过将接收数据共轭重排的再利用、构造相关矩阵,提出一种基于正交阵列的修正二维MUSIC算法。在快拍次数有限时,此算法可以明显改善信号的波达方向估计性能,特别是相干信号波达方向(DOA)的估计性能,计算机仿真结果证明了该改进算法的有效性和可行性。     

一种改进的2×1-D维纳滤波器OFDM信道估计器

本文对OFDM系统中广泛应用的一种导频辅助的信道估计器-2×1-D维纳滤波器进行了改进,以ML信道估计代替了其中的频域滤波,并将改进的估计器与2×1-D维纳滤波器在IEEE 802.16e OFDM系统中的BER、MSE性能及计算复杂度进行了比较.仿真结果表明,在802.16e OFDM系统下,改进的估计器能够以较低的复杂度达到优于2×1-D维纳滤波器的性能.此估计器也可以应用于其他基于导频估计的OFDM系统.     

The Asymptotic Cramér-Rao Bound for 2-D Superimposed Exponential Signals

The problem of estimating the parameters of complex-valued two-dimensional (2-D) exponential signals corrupted by noise occurs in many signal processing applications. In this paper we derive a simple and easily interpretable expression for the asymptotic Cramér-Rao bound (CRB) matrix associated with this problem. The Maximum Likelihood (ML) method attains the performance corresponding to the asymptotic CRB as the dimensions of the observed field increase. Furthermore, the Nonlinear Least Squares (NLS) method, which ignores the possible correlation of the noise, achieves the same performance as the ML method in large samples.     

Performance comparison of subspace rotation and MUSIC methods fordirection estimation

The statistical performance of subspace rotation (SR) methods (such as the Toeplitz approximation method and a variant of ESPRIT) for direction estimation using arrays composed of matched sensor doublets is studied. The distributional properties of these methods are established, and a compact explicit formula for the covariance matrix of their estimation error is provided. Next, using this formula and a similar formula for MUSIC covariance matrix, it is shown that the SR methods are statistically less efficient than MUSIC, at least for a sufficiently large number of snapshots. The difference in statistical performance between the commonly used SR method and MUSIC may be substantial if the number of sensors in the array is large. An optimally weighted SR method which may approach the MUSIC level of statistical performance for one direction parameter (specified by the user) is introduced     

On the Asymptotic Stability of Positive 2-D Systems Described by the Roesser Model

This brief investigates the asymptotic stability of positive 2D systems described by the Roesser model. A necessary and sufficient condition is derived for the asymptotic stability, which amounts to checking the spectrum radius of the system matrix. Furthermore, it can be shown that the asymptotic stability of positive 2D systems is equivalent to that of the traditional 1D systems. This observation would greatly facilitate the analysis and synthesis of positive 2D systems.     

一种改进的2×1-D维纳滤波器OFDM信道估计器

本文对OFDM系统中广泛应用的一种导频辅助的信道估计器-2×1-D维纳滤波器进行了改进,以ML信道估计代替了其中的频域滤波,并将改进的估计器与2×1-D维纳滤波器在IEEE 802.16e OFDM系统中的BER、MSE性能及计算复杂度进行了比较。仿真结果表明,在802.16e OFDM系统下,改进的估计器能够以较低的复杂度达到优于2×1-D维纳滤波器的性能。此估计器也可以应用于其他基于导频估计的OFDM系统。     

Multistatic Response Matrix of a 3-D Inclusion in Half Space and MUSIC Imaging

Recent work on the retrieval of 3-D bounded dielectric and/or magnetic inclusions in free space is extended to burial in a half-space. Though emphasis is on the case of a single inclusion, enabling the derivation of closed-form mathematical results in illuminating fashion, the approach extends to the case of (an unknown number of) well-separated inclusions. Within an asymptotic field formulation derived from exact contrast-source vector integral formulations satisfied by the time-harmonic fields and using proper reciprocity relationships of the dyadic Green's functions, the multistatic response matrix of the inclusion is constructed from the leading-order term of the fields. Its singular value structure is analyzed in detail for a dielectric or a magnetic contrast, or both contrasts. This is performed in the case of a unique electric dipole array operated in the transmit/receive mode at a single frequency. A multiple signal classification-type algorithm follows from the decomposition, yielding a cost functional the magnitude of which peaks at the inclusion center. Numerical results illustrate the above as a function of the geometric and electromagnetic parameters of the configuration. Imaging of a spherical inclusion is in particular investigated from severely noisy synthetic data, as well as of two inclusions embedded within a non-conductive or conductive half space.     

How to reduce 3-D gray-scale mathematical morphology to 2-D

A planar encoding of three-dimensional (3-D) images, which is commutative with respect to set and gray-scale morphological operations, is proposed. Such an encoding indicates a way to reduce 3-D set and mathematical morphology operations to two-dimensional (2-D) ones     

Asymptotic properties of subband identification

The purpose of the paper is to study the asymptotic properties (i.e., strong convergence and asymptotic convergence rate) of the subband identification method in every subband and in the overall method. The study of strong convergence aims to answer the question whether the "best possible" model is retrieved, on the limit, with probability one. The study of the asymptotic convergence rate aims to give an expression that quantifies how fast the model approaches the "best possible" value as the number of samples goes to infinity. To do this, we need to generalize existing results for fullband identification. In the process of doing so, we come up with a new notion of ergodicity, which we call strong ergodicity. Strongly ergodic signals not only satisfy the assumptions required for our analysis but also enjoy an interesting property, which is that strong ergodicity is invariant under a number of transformations. In particular, the subband components of a strongly ergodic signal are guaranteed to be strongly ergodic, therefore, ergodic, which is not true for an ergodic signal in general.     

2维超晶格结构光子晶体传输特性研究

为了研究超晶格结构对光子晶体禁带的影响,应用时域有限差分法对圆/椭圆、圆/复合柱超晶格结构光子晶体的传输特性进行了计算,得到了相应的透射谱.结果表明,对圆/椭圆超晶格,禁带宽度随椭圆柱截面积的增大而变宽,中心频率变大;对于圆/复合柱超晶格结构,椭圆柱内接于圆孔时,禁带宽度随截面积的增大而变窄,中心频率变小;当长轴垂直入射波方向时,高频段出现较宽禁带,低频禁带完全消失;而椭圆孔中内嵌圆柱时,禁带宽度变化与前者相反.该研究为光子晶体器件的制作提供了理论依据.     

3-D/2-D registration of CT and MR to X-ray images

A crucial part of image-guided therapy is registration of preoperative and intraoperative images, by which the precise position and orientation of the patient's anatomy is determined in three dimensions. This paper presents a novel approach to register three-dimensional (3-D) computed tomography (CT) or magnetic resonance (MR) images to one or more two-dimensional (2-D) X-ray images. The registration is based solely on the information present in 2-D and 3-D images. It does not require fiducial markers, intraoperative X-ray image segmentation, or timely construction of digitally reconstructed radiographs. The originality of the approach is in using normals to bone surfaces, preoperatively defined in 3-D MR or CT data, and gradients of intraoperative X-ray images at locations defined by the X-ray source and 3-D surface points. The registration is concerned with finding the rigid transformation of a CT or MR volume, which provides the best match between surface normals and back projected gradients, considering their amplitudes and orientations. We have thoroughly validated our registration method by using MR, CT, and X-ray images of a cadaveric lumbar spine phantom for which "gold standard" registration was established by means of fiducial markers, and its accuracy assessed by target registration error. Volumes of interest, containing single vertebrae L1-L5, were registered to different pairs of X-ray images from different starting positions, chosen randomly and uniformly around the "gold standard" position. CT/X-ray (MR/ X-ray) registration, which is fast, was successful in more than 91% (82% except for L1) of trials if started from the "gold standard" translated or rotated for less than 6 mm or 17 degrees (3 mm or 8.6 degrees), respectively. Root-mean-square target registration errors were below 0.5 mm for the CT to X-ray registration and below 1.4 mm for MR to X-ray registration.     

Asymptotic properties of data compression and suffix trees

Recently, Wyner and Ziv (see ibid., vol.35, p.1250-8, 1989) have proved that the typical length of a repeated subword found within the first n positions of a stationary ergodic sequence is (1/h) log n in probability where h is the entropy of the alphabet. This finding was used to obtain several insights into certain universal data compression schemes, most notably the Lempel-Ziv data compression algorithm. Wyner and Ziv have also conjectured that their result can be extended to a stronger almost sure convergence. In this paper, we settle this conjecture in the negative in the so called right domain asymptotic, that is, during a dynamic phase of expanding the data base. We prove-under an additional assumption involving mixing conditions-that the length of a typical repeated subword oscillates almost surely (a.s.) between (1/h₁)log n and (1/h₂)log n where D21<∞. We also show that the length of the nth block in the Lempel-Ziv parsing algorithm reveals a similar behavior. We relate our findings to some problems on digital trees, namely the asymptotic behavior of a (noncompact) suffix tree built from suffixes of a random sequence. We prove that the height and the shortest feasible path in a suffix tree are typically (1/h₂ )log n (a.s.) and (1/h₁)log n (a.s.) respectively