A modified likelihood function approach to DOA estimation in thepresence of unknown spatially correlated Gaussian noise using a uniformlinear array

The problem of modified ML estimation of DOAs of multiple source signals incident on a uniform linear array (ULA) in the presence of unknown spatially correlated Gaussian noise is addressed here. Unlike previous work, the proposed method does not impose any structural constraints or parameterization of the signal and noise covariances. It is shown that the characterization suggested here provides a very convenient framework for obtaining an intuitively appealing estimate of the unknown noise covariance matrix via a suitable projection of the observed covariance matrix onto a subspace that is orthogonal complement of the so-called signal subspace. This leads to a formulation of an expression for a so-called modified likelihood function, which can be maximized to obtain the unknown DOAs. For the case of an arbitrary array geometry, this function has explicit dependence on the unknown noise covariance matrix. This explicit dependence can be avoided for the special case of a uniform linear array by using a simple polynomial characterization of the latter. A simple approximate version of this function is then developed that can be maximized via the-well-known IQML algorithm or its variants. An exact estimate based on the maximization of the modified likelihood function is obtained by using nonlinear optimization techniques where the approximate estimates are used for initialization. The proposed estimator is shown to outperform the MAP estimator of Reilly et al. (1992). Extensive simulations have been carried out to show the validity of the proposed algorithm and to compare it with some previous solutions     

Synthesis of antenna arrays with spatial and excitation constraints

Synthesis of antenna arrays subject to spatial and excitation constraints to yield arbitrarily prescribed patterns in both the mean-squared and minimax sense are discussed. The spatial constraints may require that the interelement spacings be greater than a prescribed value or that the element locations lie within a specified region. The excitation constraints are of the form where the current-taper ratio is constrained to be less than or equal to a prescribed value. The technique employed consists of reducing the constrained optimization problem into an unconstrained one by the use of simple transformations of the independent variables. In such cases where explicit transformations are not available, a created response surface technique (CRST) has been used to convert the constrained optimization problem into a series of unconstrained optimizations. The optimization has been carried out using a nonlinear simplex algorithm. Numerical examples are given wherein both the linear and circular arrays are synthesized subject to constraints.     

圆柱面上的轴向偶极子阵的低副瓣方向图优化综合

本文利用新的非线性最优化方法讨论圆柱面上的轴向偶极子阵的低副瓣方向图优化综合问题，利用阵列的单元可实现增益方向图，我们把阵列综合问题表述为一个约束非线性规划问题，采用新直接法求解该问题即可得出一组使阵列的总方向图满足副瓣指标要求，同时具有尽可能高的方向性系数的激励系数，如果阵列的总方向图不能达到副瓣指标，则可得出一组使阵列方向图在可达到的副瓣方向图综合设计的模拟计算结果。     

Newton's method for nonparallel plane proximal classifier with unity norm hyperplanes

In our previous research we observed that the nonparallel plane proximal classifier (NPPC) obtained by minimizing two related regularized quadratic optimization problems performs equally with that of other support vector machine classifiers but with a very lower computational cost. NPPC classifies binary patterns by the proximity of it to one of the two nonparallel hyperplanes. Thus to calculate the distance of a pattern from any hyperplane we need the Euclidean norm of the normal vector of the hyperplane. Alternatively, this should be equal to unity. But in the formulation of NPPC these equality constraints were not considered. Without these constraints the solutions of the objective functions do not guarantee to satisfy the constraints. In this work we have reformulated NPPC by considering those equality constraints and solved it by Newton's method and the solution is updated by solving a system of linear equations by conjugate gradient method. The performance of the reformulated NPPC is verified experimentally on several bench mark and synthetic data sets for both linear and nonlinear classifiers. Apart from the technical improvement of adding those constraints in the NPPC formulation, the results indicate enhanced computational efficiency of nonlinear NPPC on large data sets with the proposed NPPC framework.     

A Fuzzy Optimization Approach for Variation Aware Power Minimization During Gate Sizing

Technology scaling in the nanometer era has increased the transistor's susceptibility to process variations. The effects of such variations are having a huge impact on the yield of the integrated circuits and need to be considered early in the design flow. Traditional corner based deterministic methods are no longer effective and circuit optimization methods require reinvention with a statistical perspective. In this paper, we propose a new gate sizing algorithm using fuzzy linear programming in which the uncertainty due to process variations is modeled using fuzzy numbers. The variations in gate delay which is a function of the gate sizes and the fan-outs of the gates are represented using triangular fuzzy numbers with linear membership functions. Initially, as a preprocessing step for fuzzy optimization, we perform deterministic optimizations by fixing the fuzzy parameters to the worst and the average case values, the results of which are used to convert the fuzzy optimization problem into a crisp nonlinear problem. The crisp problem with delay and power as constraints is then formulated to maximize the robustness, i.e., the variation resistance of the circuit. The fuzzy optimization approach was tested on ITC'99 benchmark circuits and the results were validated for timing yield using Monte Carlo simulations. The proposed approach is shown to achieve better power reduction than the worst case deterministic optimization as well as the stochastic programming based gate sizing methods, while having comparable runtimes.     

A new approach to the optimization of robust antenna arrayprocessors

The authors present a method for solving a class of optimization problems with nonsmooth constraints. In particular, they apply the method to the design of narrowband minimum-power antenna array processors which are robust in the presence of errors such as array element placement, look direction misalignment, and frequency offset. They first show that the constrained minimum power problem has a unique global minimum provided that the constraint set is nonempty. Then it is shown how the design problem derived directly from considerations of the sensitivity of the antenna array processor to errors can be transformed into a quadratic programming problem with linear inequality constraints which can be solved efficiently by the standard active set strategy. They also present numerical results for two types of nonsmooth constraints developed to provided robustness. These results confirm the effectiveness of the method     

Pattern Nulling in Coupled Oscillator Antenna Arrays

An optimization method is presented for constrained beam steering with null formation in linear coupled oscillator arrays. The method is based on a perturbation model of the far field of the array that includes both amplitude and phase perturbations, to accommodate prescribed nulls. Moreover, it takes into account the array nonlinear dynamics through a first-order approximation model of the array steady state. The optimization results are verified by harmonic balance simulations. Also, the stability of the optimized solutions is examined by perturbing the steady state solution and is verified with envelope transient. Design examples are used to demonstrate the validity and limitations of the proposed method     

An evolutionary algorithm for solving nonlinear bilevel programming based on a new constraint-handling scheme

In this paper, a special nonlinear bilevel programming problem (nonlinear BLPP) is transformed into an equivalent single objective nonlinear programming problem. To solve the equivalent problem effectively, we first construct a specific optimization problem with two objectives. By solving the specific problem, we can decrease the leader's objective value, identify the quality of any feasible solution from infeasible solutions and the quality of two feasible solutions for the equivalent single objective optimization problem, force the infeasible solutions moving toward the feasible region, and improve the feasible solutions gradually. We then propose a new constraint-handling scheme and a specific-design crossover operator. The new constraint-handling scheme can make the individuals satisfy all linear constraints exactly and the nonlinear constraints approximately. The crossover operator can generate high quality potential offspring. Based on the constraint-handling scheme and the crossover operator, we propose a new evolutionary algorithm and prove its global convergence. A distinguishing feature of the algorithm is that it can be used to handle nonlinear BLPPs with nondifferentiable leader's objective functions. Finally, simulations on 31 benchmark problems, 12 of which have nondifferentiable leader's objective functions, are made and the results demonstrate the effectiveness of the proposed algorithm.     

Timing-Aware Cell Layout De-Compaction for Yield Optimization by Critical Area Minimization

This paper proposes a yield optimization method for standard cells under timing constraints. Yield-aware logic synthesis and physical optimization require yield enhanced standard cells and the proposed method automatically creates yield enhanced cell layouts by decompacting the original cell layout using linear programming. We develop a novel accurate linear delay model which approximates the difference from the original delay and use this model to formulate the timing constraints into linear programming. Experimental results show that the proposed method can pick up the yield variants of a cell layout from the tradeoff curve of cell delay versus critical area and is used to create the yield enhanced cell library which is essential to realize yield-aware VLSI design flows.     

Radiation pattern synthesis for arrays of conformal antennas mounted on arbitrarily-shaped three-dimensional platforms using genetic algorithms

A domain-decomposition/reciprocity procedure is presented which allows the radiation patterns of microstrip patch antennas mounted on arbitrarily-shaped three-dimensional perfectly electric conducting (PEC) platforms to be computed accurately as well as efficiently. The utility of this technique is demonstrated by considering an example consisting of a nine-element conformal array of microstrip patch antennas mounted axially along a finite-length PEC circular cylinder. It is shown that the elements close to the ends of the cylinder have significantly different patterns than those close to the center of the cylinder. The results from this example suggest that the common practice where all the individual element patterns are assumed identical is not always valid and, in fact, can lead to significant performance degradation in the design of conformal phased arrays. This observation is supported by the fact that an attempt to steer the main beam of the nine-element conformal array to an angle /spl theta//sub 0/=60/spl deg/ using a standard uniform progressive phase shifting technique proves unsuccessful. Next a genetic algorithm (GA) synthesis procedure is introduced that is capable of determining the optimal set of element excitation phases required to yield a desired or specified far-field radiation pattern. The results of this GA phase-only optimization are shown to yield the desired main beam steered to the correct angle for this nine-element linear array mounted on a circularly cylindrical platform. The GA radiation pattern synthesis procedure introduced appears to be a highly effective means of correcting for platform effects on the individual element patterns of a conformal phased array.     

A new low-side-lobe pattern synthesis technique for conformalarrays

The application of the new nonlinear optimization algorithms to array design is demonstrated by the low-side-lobe pattern synthesis of conformal arrays. By adopting the information of array element realized gain patterns the authors formulate synthesis problems as nonlinearly constrained optimization problems, and propose a direct method to solve them. The technique allows them to find a set of array coefficients that yield a pattern meeting a specified side-lobe level and achieving the maximum directivity, if such a set of array coefficients exists. If the side-lobe specifications cannot be met with the given array, the technique will result in a set of coefficients that yield a pattern meeting the best attainable side-lobe level and having directivity as high as possible. Simplified synthesis problems for an axial dipole array in an infinite, perfectly conducting cylinder are discussed, and numerical results are given. The synthesis technique works for general array patterns     

Phase optimization of antenna array gain with constrained amplitude excitation

The formulation of antenna array optimization with variable phase and constant amplitude excitation is presented. The method shown using steepest ascents is general in that a nonlinear performance index expressible as a ratio of Hermitian quadratic forms can be optimized. Directive gain optimization of a linear array of isotropic elements is illustrated and compared with gain optimization using variable excitation. Endfire gain is emphasized and compared to the Hansen-Woodyard condition showing that the Hansen-Woodyard condition is not optimum in the directive gain sense for a discrete endfire array. In addition a0.4lambdaspaced linear array is optimized using phase only for scanning from endfire to broadside.     

考虑互耦修正的机会阵雷达波束方向图综合优化

机会阵雷达大量天线单元在空间随机分布,波束方向图综合时考虑阵元间的互耦影响十分必要。该文基于子阵思想,提出交叉划分子阵,利用子阵的互阻抗矩阵构建任意阵的互阻抗矩阵,并结合自适应算法实现了互耦情况下的机会阵雷达的波束综合优化。该方法利用矩量法计算子阵的广义互阻抗矩阵,应用最大输出信噪比准则,在方向图区域施加干扰信号自适应地调整阵因子,综合了非均匀偶极子线阵和面阵,结果与FEKO软件仿真结果吻合良好。     

Theory and design of signal-adapted FIR paraunitary filter banks

We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks     

稀布圆阵的降维优化方法

针对有阵列孔径,阵元数目和最小阵元间距3种约束下的稀布圆形阵列综合问题,该文提出了一种基于修正遗传算法的降维优化方法。为了充分利用阵元布阵的自由度,同时使稀布阵列满足多个设计约束,在阵元排布时将2维平面阵列优化设计降维成1维的稀布直线阵列,计算阵列性能时再还原为平面阵列。该方法改进了现有圆阵综合方法中轨迹圆半径和轨迹圆上阵元数分布优化的不足,实现了全部阵元的联合优化,降低了算法的复杂性,同时保证了阵列的旁瓣性能,仿真结果证明了该方法的有效性。     

Multicriterion optimized QMF Bank design

The quadrature mirror filter (QMF) bank with multicriterion constraints such as minimal aliasing and/or minimal error coding is among the most important problems in filterbank design, for solving which linear algebra-based methods are still heuristic and do not always work, especially for large filter length. It is shown in this paper that this problem can be reduced either to convex linear matrix inequality (LMI) optimization (when filters are of nonlinear phase) or to semi-infinite linear (SIP) programming (when filters are of linear phase), which can be very efficiently solved either by the standard LMI solvers or our previously developed SIP solver. The proposed computationally tractable optimization formulations are confirmed by several simulations.     

Constrained nonlinear optimization approaches to color-signalseparation

Separating a color signal into illumination and surface reflectance components is a fundamental issue in color reproduction and constancy. This can be carried out by minimizing the error in the least squares (LS) fit of the product of the illumination and the surface spectral reflectance to the actual color signal. When taking in account the physical realizability constraints on the surface reflectance and illumination, the feasible solutions to the nonlinear LS problem should satisfy a number of linear inequalities. Four distinct novel optimization algorithms are presented to employ these constraints to minimize the nonlinear LS fitting error. The first approach, which is based on Ritter's superlinear convergent method (Luengerger, 1980), provides a computationally superior algorithm to find the minimum solution to the nonlinear LS error problem subject to linear inequality constraints. Unfortunately, this gradient-like algorithm may sometimes be trapped at a local minimum or become unstable when the parameters involved in the algorithm are not tuned properly. The remaining three methods are based on the stable and promising global minimizer called simulated annealing. The annealing algorithm can always find the global minimum solution with probability one, but its convergence is slow. To tackle this, a cost-effective variable-separable formulation based on the concept of Golub and Pereyra (1973) is adopted to reduce the nonlinear LS problem to be a small-scale nonlinear LS problem. The computational efficiency can be further improved when the original Boltzman generating distribution of the classical annealing is replaced by the Cauchy distribution.     

Pattern characteristics of linear arrays using the constrained least squares distribution

The constrained least squares (CLS) distribution is a method for obtaining distribution functions that yield low sidelobe patterns with specified constraints on the aperture efficiency, and are especially useful for the transmit patterns of active array antennas. The widely used Taylor distribution optimizes only pattern performance while the CLS distribution optimizes pattern performance while taking into account the constraints on both the peak element amplitude and the total effective radiated voltage (ERV) of the aperture distribution. The paper compares the pattern characteristics of linear arrays with CLS and Taylor distributions. The results help to establish guidelines on when a CLS distribution would be preferable over a Taylor distribution when a specified aperture efficiency is important.     

Synthesis of nonuniformly spaced arrays using a general nonlinear minimax optimisation method

Antenna patterns can be synthesized using a new nonlinear minimax optimization method with sure convergence properties. Not requiring derivatives, the proposed method is general and easy to use so that it might be applied to a wide variety of nonlinear synthesis problems for which analytical solutions are not known. To test the algorithm a group of test problems for which exact analytical solutions are known has been considered, namely, optimization of Dolph-Chebyshev arrays by spacing variation. The method is further applied to find the element positions in nonuniformly spaced linear arrays with uniform excitation that produce minimized (equal) sidelobe levels, and comparisons are made with conventional Dolph-Chebyshev arrays.     

On the design of maximally sparse beamforming arrays

The problem of designing nonuniformly spaced arrays is formulated as one of constrained optimization in which the cost function is chosen to select the array with the minimum number of elements. The response of the array is controlled by a set of inequality point response constraints. It is shown that a suitable cost function for this problem is the l_p quasi-norm for 0<p<1 and that there exists a number p₁ such that for all 0<p<p₁ the resulting array is maximally sparse. Furthermore it is shown that a solution to the problem lies at an extreme point of the simplex formed by the point constraints. A simplex search algorithm is described which will converge to a local minimum of the cost function on this simplex. The algorithm is applied to the design of sparse linear and planar arrays