Extension of the Pisarenko method to sparse linear arrays

When applied to array processing, the Pisarenko harmonic decomposition (PHD) method is limited to linear equispaced arrays. We present an approach that allows us to extend it to general arrays, although for the ease of exposition, we consider only sparse linear arrays. We exploit the fact that the PHD can be seen as a deconvolution or model-fitting approach that minimizes an t₁ norm and can thus be implemented as a standard linear program. Looking at the PHD from this point of view has two advantages: it allows us to extend its applicability to arbitrary arrays, and by diverging slightly from the basic philosophy, it allows us to improve its performance, which is often quite poor in its original version     

一种平面稀疏阵列的快速综合方法

以快速综合出满足期望方向图以及阵元数最少的平面阵列为目标,提出一种基于迭代加权1范数的平面阵列综合方法。该方法将平面稀疏阵列综合问题转化为加权1范数最小化的稀疏信号重构过程,并利用拉格朗日乘数法求解每次迭代中的阵列加权向量的闭式解,由于二维平面的空间采样导致闭式解中存在大规模矩阵的求逆运算,进而引入共轭梯度法以促进算法加速收敛。当满足迭代终止条件时,由加权向量的非零值确定平面阵列的阵元位置及其激励。仿真结果表明,该方法能有效提高平面稀疏阵列综合的收敛速度。     

一种有阵元间距约束的稀布阵天线综合方法

提出了一种基于改进遗传算法的稀布阵综合新方法,用于优化设计有最小阵元间距约束的稀布线阵.该方法利用个体的实值编码提高了遗传算法的优化效率,通过设计遗传操作预处理和后处理,并采用一种广义的交叉算子和变异算子,有效地避免了基因重组和变异时出现不可行解.在给定阵列孔径和阵元数的条件下,高效地实现了任意最小阵元间距约束下抑制稀布线阵峰值旁瓣电平的稀布直线阵列综合.给出了应用该方法的具体步骤,并通过仿真实验证实了该方法的有效性和稳健性.     

A method for computing scattering by large arrays of narrow strips

The electromagnetic scattering characteristics of an array of narrow, conducting strips can he developed readily by extending the work of Butler and Wilton who show that Chebyshev polynomials augmented with the edge condition can be used to solve the narrow-strip/narrow-slot integral equations. The strips reside in a homogeneous medium of infinite extent and are considered narrow relative to wavelength in the medium at the frequency of excitation. The unknown current distributions on the strips are represented as linear combinations of certain basis functions that are exact solutions to the approximate equation for an isolated narrow strip subject to a special excitation. The resulting power-series treatment allows easy calculation of the coupling terms among the strips in the array in a simple matrix equation by which the unknown coefficients in the current distribution expansions may be readily computed. With these coefficients, one can obtain the distribution of current on each strip and the total scattered field. The method is particularly well suited for handling large arrays with more strips than could be accommodated by the usual moment method. Numerical data-currents and scattered fields-are presented for various cases of interest.     

A method for the optimal pattern synthesis of linear arrays withprescribed nulls

A new L_∞ optimal method for the synthesis of equispaced linear array functions with asymmetrical far-field pattern functions is proposed. This iterative method provides for the exact specification of the beam width, while at the same time allowing for the specification of the relative levels of individual sidelobes by index or as a function of bearing (e.g., angularly-extended nulls), as well as the realization of specified narrowband nulls. The resulting array factors are optimal in the weighted L_∞ sense and, in general, have complex coefficients. This new Remez-type method employs multiple objective functions to provide the degrees of freedom that are required for exact null placement. Examples which demonstrate the design flexibility offered by the method are included for various sum and difference patterns, including superdirective and shaped-beam arrays     

Reliable and fast reconfigurable hierarchical interconnectionnetworks for linear WSI arrays

A self-pruning binary tree (SPBT) interconnection network architecture that tolerate faults in a wafer scale integration (WSI) environment is proposed. The goal of the SPBT network is to provide a reliable and a quickly reconfigured interconnection network architecture for linear WSI arrays. The proposed architecture uses a bottom-up approach to reconfigure a linear pipelined array on a potentially defective WSI array using a binary tree interconnection scheme. The binary tree is generated by successive formation of hierarchical modules. For N processing elements (PEs) on the wafer, reconfiguration time is O(log N). The propagation delay is bounded by Θ(log N) and is independent of the number of faulty PEs. Faults in the switching network as well as faulty processing elements are tolerated     

A fast computation method for MUSIC spectrum function based on circular arrays

The large computation amount of multiple signal classification (MUSIC) spectrum function seriously affects the timeliness of direction finding system using MUSIC algorithm, especially in the two-dimensional directions of arrival (DOA) estimation of azimuth and elevation with a large antenna array. This paper proposes a fast computation method for MUSIC spectrum. It is suitable for any circular array. First, the circular array is transformed into a virtual uniform circular array, in the process of calculating MUSIC spectrum, for the cyclic characteristics of steering vector, the inner product in the calculation of spatial spectrum is realised by cyclic convolution. The computational amount of MUSIC spectrum is obviously less than that of the conventional method. It is a very practical way for MUSIC spectrum computation in circular arrays.     

A fast algorithm for computing the response of a linear system to a large number of inputs

A method is presented which saves computation time when determining the response of an arbitrary linear time-invariant system, where several input-output responses are desired. The method is based on an assumption that the system input is band-limited.     

改进的快速稳健任意阵列天线方向图综合方法

针对任意阵列天线的方向图综合问题,提出了改进的基于线性约束最小方差准则方向图综合方法.该方法充分考虑综合方向图和参考方向图之间的相对幅度对方向图综合的影响,通过对迭代公式增加一比例常数,使得两者之间的相对幅度对干扰功率变化率的影响增强,不仅提高了干扰功率的迭代效率,即降低了迭代的次数,提高了方向图的综合效率,而且使得迭代系数的取值范围得到了扩展,即降低了迭代系数对方向图综合的影响,增强了方向图综合方法的应用范围和适用性.仿真分析验证了理论分析的正确性和所提方法的有效性.     

Very fast method to synthesise conformal arrays

Avery fast technique that allows the synthesising of arbitrary footprint patterns by using conformal arrays with many radiating elements is described. This method is based on a combination of Woodward-Lawson and Elliott-Stern techniques, and it was applied to the synthesis of a triangular footprint generated by 657 axial dipoles placed on a cylindrical surface, obtaining acceptable ripple and sidelobe levels.     

平面稀布天线阵列的优化算法

基于一种改进的实数遗传算法,以降低平面稀布阵旁瓣电平为优化目标,提出了一种综合有阵元数约束、孔径约束和最小阵元间距约束的稀布面阵的新方法。与稀疏布阵相比,该方法利用了阵元在布阵时更大的自由度,因而在阵元数、孔径和最小阵元间距相同的条件下可以获得更优的峰值旁瓣性能,仿真试验显示了改进的实数遗传算法应用到该多约束稀布平面阵优化问题中是稳健和高效的。     

A flexible optimization method for the pattern synthesis ofequispaced linear arrays with equiphase excitation

A synthesis method is proposed for linear arrays having equiphase excitation currents. In addition to allowing for the exact specification of the beamwidth and for the specification of individual sidelobe levels by index or as a function of bearing (e.g., angularly extended nulls), multiple deep narrow nulls can be specified at arbitrary bearing angles. The method is suitable for the design of broadside or endfire arrays with sum or difference patterns and can also be used for the design of superdirective arrays with good radiation efficiencies and sensitivity properties. For computational efficiency, the method uses a new constrained multivariable Remez-type L_∞ approximation technique     

圆形口径平面天线阵列的多约束稀布优化方法

针对圆形口径平面稀布阵列的多约束优化设计问题,以均匀同心圆环阵列的阵元位置分布特性为基础,构造了稀布圆阵的满足多个优化约束的可行初始解.提出了一种个体元素的间接表示法,设计了一种新的交叉算子和变异算子,运用改进的实数遗传算法优化设计天线阵的阵元位置.优化约束包括阵元数约束、口径约束和最小阵元间距约束,优化目标是使阵列响应的峰值旁瓣电平最小.运用这种改进实数遗传算法可以充分利用阵元布阵的自由度,同时能减小搜索空间,提高计算效率。仿真试验证实了算法的稳健性和有效性.     

一种稀布矩形平面阵的多约束优化方法

针对矩形孔径平面稀布阵的多约束优化问题(包括阵元数、阵列孔径和最小阵元间距约束), 提出了一种基于矩阵映射的差分进化算法.该方法把差分进化算法的优化变量与阵元位置坐标按照特定的关系进行矩阵映射, 使含有多约束的阵元分布优化问题转换为仅含差分进化算法优化变量上、下限约束的优化问题, 从根本上避免了进化过程中的不可行解.通过抑制阵列峰值副瓣电平进行仿真实验, 结果显示了该算法的高效性和稳健性, 且能获得比现有方法更好的优化结果.     

A fast algorithm for the linear canonical transform

In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal processing. The well-known integral transforms: Fourier, fractional Fourier, bilateral Laplace and Fresnel transforms are special cases of the LCT. In this paper we obtain an O(NlogN) algorithm to compute the LCT by using a chirp-FFT-chirp transformation yielded by a convergent quadrature formula for the fractional Fourier transform. This formula gives a unitary discrete LCT in closed form. In the case of the fractional Fourier transform the algorithm computes this transform for arbitrary complex values inside the unitary circle and not only at the boundary. This chirp-FFT-chirp transform approximates the ordinary Fourier transform more precisely than just the FFT, since it comes from a convergent procedure for non-periodic functions.     

Synthesis of sparse planar arrays

A synthesis method is proposed that is aimed at designing a planar, sparse, and aperiodic array to be used in a beamforming processor. This method minimises the number of elements able to generate a beam pattern that fulfils various a priori fixed constraints. The obtained results are better than those proposed in related literature     

A fast algorithm for computing distance spectrum of convolutionalcodes

A fast algorithm for searching a tree (FAST) is presented for computing the distance spectrum of convolutional codes. The distance profile of a code is used to limit substantially the error patterns that have to be searched. The algorithm can easily be modified to determine the number of nonzero information bits of an incorrect path as well as the length of an error event. For testing systematic codes, a faster version of the algorithm is given. FAST is much faster than the standard bidirectional search. On a microVAX, d_∞=27 was verified for a rate R=1/2, memory M=25 code in 37 s of CPU time. Extensive tables of rate R=1/2 encoders are given. Several of the listed encoders have distance spectra superior to those of any previously known codes of the same rate and memory. A conjecture than an R=1/2 systematic convolutional code of memory 2M will perform as well as a nonsystematic convolutional code of memory M is given strong support     

A fast algorithm for computing minimum cross-entropy positivetime-frequency distributions

An algorithm for obtaining nonnegative, joint time-frequency distributions Q(t, f) satisfying the univariate marginals |s(t)|² and |S(f)|² is presented and applied. The advantage of the algorithm is that large time series records can be processed without the need for large random access memory (RAM) and central processing unit (CPU) time. This algorithm is based on the Loughlin et al. (1992) method for synthesizing positive distributions using the principle of minimum cross-entropy. The nonnegative distributions with the correct marginals that are obtained using this approach are density functions as proposed by Cohen and Zaparovanny (1980) and Cohen and Posch (1985). Three examples are presented: the first is a nonlinear frequency modulation (FM) sweep signal (simulated data); the second and third are of physical systems (real data). The second example is the signal for the acoustic scattering response of an elastic cylindrical shell structure. The third example is of an acoustic transient signal from an underwater vehicle. Example one contains 7500 data points, example two contains 256 data points, and example three contains in excess of 30000 data points. The RAM requirements using the original Loughlin et al. algorithm for a 7500 data point signal is 240 mega bytes and for a 30000 data point signal is 3.5 billion bytes. The new algorithm reduces the 240 mega byte requirement to 1 mega byte and the 3.5 billion byte requirement to 4 million bytes. Furthermore, the fast algorithm runs 240 times faster for the 7500 data point signal and 3000 times faster for the 30000 data point signal as compared with the original Loughlin et al. algorithm     

A fast algorithm for optimal linear interpolation

A fast algorithm for computing the optimal linear interpolation filter is developed. The algorithm is based on the Sherman-Morrison inversion formula for symmetric matrices. The relationship between the derived algorithm and the Levinson algorithm is illustrated. It is shown that the new algorithm, in comparison with the well-known algorithms, requires fewer multiplications and hence is of lower complexity