Array Pattern Synthesis Problem Research Articles

Pattern Synthesis With Closed-Form Array Response Control Algorithms

In this letter, the problem of array pattern synthesis is considered by developing two array response control algorithms. The devised two algorithms build on the basis of the accurate array response control approach, and both of them have closed-form solutions and low computational complexities. More specifically, the first proposed algorithm realizes multipoint array response control from an any given weight vector, and the second algorithm modifies the first one by avoiding the possible beam axis shift. The proposed two algorithms are able to control array responses accurately under the conditions of independence on steering vectors. By applying the first and the second array response control algorithm, two effective pattern synthesis methods for focused patterns and shaped patterns are devised, respectively. Representative examples are presented to demonstrate the performance of the proposed algorithms in array response control and pattern synthesis.

Linear Arbitrary Array Pattern Synthesis With Shape Constraints and Excitation Range Control

This letter proposes a method based on primary-dual iteration to address the array pattern synthesis problem of minimizing the peak sidelobe level (PSL) under the constraints of controlled mainlobe ripples and dynamic range ratio (DRR) of current excitations. Especially, when DRR = 1, the phase-only beampattern synthesis problem is solved. Simulation examples are presented to verify the effectiveness of the proposed method in terms of PSL and DRR.

An ADMM-Based Approach to Robust Array Pattern Synthesis

In most existing robust array beam pattern synthesis studies, the bounded-sphere model is used to describe the steering vector (SV) uncertainties. In this letter, instead of bounding the norm of SV perturbations as a whole, we explore the amplitude and phase perturbations of each SV element separately, thereby obtaining a tighter SV uncertainty model. Based on this model, we formulate the robust array pattern synthesis problem from the perspective of the min-max optimization, which aims to minimize the maximum side lobe response, while preserving the main lobe response. However, this problem is difficult due to the infinitely many non-convex constraints. As a remedy, we employ the worst-case criterion and recast the problem as a convex second-order cone program (SOCP). To solve the SOCP, we further develop an alternating direction method of multipliers (ADMM)-based algorithm, which is computationally efficient with each step being computed in closed form. Numerical simulations demonstrate the efficacy and efficiency of the proposed algorithm.

Array pattern synthesis using semidefinite programming and a bisection method

In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as a ...

Joint Sparsity-Based Range-Angle-Dependent Beampattern Synthesis for Frequency Diverse Array

For frequency diverse array (FDA) range-angle-dependent beampattern synthesis, the objective is to obtain the desired beampattern performance using fewer antenna elements or smaller aperture. This paper proposes a FDA single-beam pattern synthesis by joint $\ell _{1}$ -norm minimization and convex optimization in the beginning. A virtual uniform FDA array with small element spacing and corresponding frequency increment is created first. Then, we formulate the array pattern synthesis (APS) problem as finding a joint sparse weight vector, which can be obtained by solving a convex optimization problem with the joint sparse constraint between angle dimension weight vector and range dimension weight vector, where some small entries of the vector can be regarded as zeros without significantly changing the array pattern performance. The antenna elements corresponding to the mapping positions of nonzero values of the joint sparse weight vector are placed to form a non-uniform FDA. Finally, convex optimization is further conducted to obtain the optimal weight vector of the non-uniform FDA. Besides, we expand the idea to FDA multi-beam pattern synthesis based on the convex optimization problem with joint sparse constraint between angle dimension weight matrix and range dimension weight matrix. Numerical examples are provided to verify the efficiency of achieving the desired radiation pattern with the fewer antenna elements, and better APS performance for given array elements.

A PATTERN SYNTHESIS METHOD FOR LARGE PLANAR ANTENNA ARRAY

The pattern synthesis for large antenna arrays is very important because of its wide applications. Several antenna array synthesis techniques for planar antenna array have been developed in the past years. In this paper, a hybrid method for solving antenna array pattern synthesis problem is introduced. The proposed method has three steps. Firstly, the iterative fast Fourier transforms (IFT) is used to generate a number of initial array excitations based on aim pattern. Then, the global optimization method differential evolution strategy (DES) is used to optimize these excitations based on initial excitations. After that, if the optimized pattern does not satisfy the goal, the simulated annealing (SA) method is applied to optimize the excitations until the goal is achieved or the maximum iteration is reached. Several simulation results show that the desired pattern can be effectively synthesized by using the proposed method.

A MULTI-BEAM MODEL OF ANTENNA ARRAY PATTERN SYNTHESIS BASED ON CONIC TRUST REGION METHOD

In this paper, we propose a multi-beam model for antenna array pattern synthesis (AAPS) problem. The model uses a conic trust region algorithm (CTRA) similarly proposed in this paper to optimize its cost function. Undoubtedly, whole algorithm e-ciency ultimately lies on the CTRA, thereof, we propose a method to improve the iterative algorithm's e-ciency. Unlike traditional trust region methods that resolve sub-problems, the CTRA e-ciently searches a region via solving a inequation, by which it identifles new iteration points when a trial step is rejected. Thus, the proposed algorithm improves computational e-ciency. Moreover, the CTRA has strong convergence properties with the local superlinear and quadratic convergence rate under mild conditions, and exhibits high e-ciency and robustness. Finally, we apply the combinative algorithm to AAPS. Numerical results show that the method is highly robust, and computer simulations indicate that the algorithm excellently performs AAPS problem.

Optimisation of channel capacity for multiple-input multiple-output smart antenna using a particle swarm optimiser

In this study, the channel capacity of indoor multiple-input multiple-output ultra-wide band (MIMO-UWB) transmission for a smart antenna is described. A particle swarm optimiser (PSO) is used to synthesise the radiation pattern of the directional circular arc array to maximise the capacity performance in an indoor MIMO-UWB communication system. The UWB impulse responses of the indoor channel for any transmitter-receiver location are computed by applying shooting and bouncing ray/image techniques, inverse fast Fourier transform and Hermitian processing. By using the calculated frequency response, the capacity performance of the synthesised antenna pattern on an MIMO-UWB system can be computed. Based on the topography of the circular antenna array and the capacity formula, the array pattern synthesis problem can be reformulated into an optimisation problem and solved by the PSO algorithm. PSO optimisation is applied to a high-order non-linear optimisation problem. The novelties of our approach are not only choosing capacity as the cost function instead of the sidelobe level of the antenna pattern, but also considering the antenna feed length effect of each array element. The cost function for the problem is non-smooth and discontinuous with respect to the antenna pattern. It is difficult to solve by gradient methods, since the derivative is hard to derive. The strong point of the PSO algorithm is that it can find out the solution even if the performance index cannot be formulated by simple equations. The simulation results show that the synthesised antenna array pattern is effective to focus maximum gain on the line-of-sight path which scales as the number of array elements.

MIMO-UWB smart antenna communication characteristics for different antenna arrays of transmitters

The channel capacity of indoor multiple-input multiple-output ultra-wide band (MIMO-UWB) transmission for smart antenna is presented. The genetic algorithm (GA) is used to synthesize the radiation pattern of the directional antenna array to maximize the capacity performance in indoor MIMO-UWB communication system. Three types of antenna arrays such as circular shape, L shape and Y shape arrays are used in the transmitter and their corresponding capacity on several paths in the indoor environment are calculated. The UWB impulse responses of the indoor channel for any transmitter-receiver location are computed by applying shooting and bouncing ray/image (SBR/image) techniques, inverse fast Fourier transform and Hermitian processing. By using the calculated frequency response, the capacity performance of the synthesized antenna pattern on MIMO-UWB system can be computed. Based on the topography of the antenna array and the capacity formula, the array pattern synthesis problem can be reformulated into an optimization problem and solved by the GA algorithm. The GA algorithm optimization is applied to a high order nonlinear optimization problem. The novelties of our approach is not only choosing capacity as the cost function instead of sidelobe level of the antenna pattern, but also considering the antenna feed length effect of each array element. The cost function for the problem is nonsmooth and discontinuous with respect to the antenna pattern. It is difficult to solve by gradient methods, since the derivative is hard to derive. The GA algorithm is employed to optimize the excitation voltages and feed lengths for these antenna arrays to increase the capacity. The strong point of the GA is that it can find out the solution even if the performance index cannot be formulated by simple equations. Numerical results show that the synthesized antenna array pattern is effective to focus maximum gain to the LOS path for these antenna arrays. In other words, the receiver can increase the received signal energy to noise ratio. The synthesized array pattern also can mitigate severe multipath fading in complex propagation environment. As a result, the capacity can be increased substantially in indoor MIMO-UWB communication system. The investigated results can help communication engineers improve their planning and design of indoor wireless communication. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.

Bit error rate reduction for circular ultrawideband antenna by dynamic differential evolution

The dynamic differential evolution (DDE) is used to synthesize the radiation pattern of the directional circular arc array to minimize the bit error rate (BER) performance in indoor ultrawideband (UWB) communication system. Using the impulse response of multipath channel, the BER performance of the synthesized antenna pattern on binary pulse amplitude modulation system can be calculated. Based on the topography of the circular antenna array and the BER formula, the array pattern synthesis problem can be reformulated into an optimization problem and solved by the DDE algorithm. The novelties of our approach are not only choosing BER as the object function instead of sidelobe level of the antenna pattern but also considering the antenna feed length effect of each array element. The strong point of the DDE algorithm is that it can find out the solution even if the performance index cannot be formulated by simple equations. Simulation results show that the synthesized antenna array pattern is effective to focus maximum gain to the line of site path which scales as the number of array elements. In other words, the receiver can increase the received signal energy to noise ratio. The synthesized array pattern also can mitigate severe multipath fading in complex propagation environment. As a result, the BER can be reduced substantially in indoor UWB communication system. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.

A comparative analysis of numerical optimization algorithm for array pattern synthesis

The problem of array pattern synthesis with desired shapes has received much attention over years. There is a number of intelligent optimization methods that were adopted for pattern synthesis, and to some content, several successful design cases are reported. In this paper, based on a special sensor array, a comparative study of those methods is given. Those methods include simulated annealing, genetic technique, and adaptive searching procedures. The effectiveness of the algorithms is demonstrated by the sidelobe level and the width of the main beam. For a given array, those techniques are investigated on their convergence speed and residue error energy. A set of design results are given in details and conclusions are included.

Comparison of different antenna arrays for the BER reduction in indoor wireless communication

In this paper, we use the ultra wideband antenna array combined with particle swarm optimization PSO to minimize the BER for indoor communication systems. Three types of antenna arrays, namely the circular shape, L shape, and Y shape arrays, are used in the transmitter and their corresponding BER on several paths in the indoor environment are calculated. On the basis of the topography of the antenna array and the BER formula, the array pattern synthesis problem can be reformulated into an optimization problem and solved by the PSO. The novelties of our approach is not only choosing BER as the object function instead of the sidelobe level of the antenna pattern, but also considering the antenna feed length effect of each array element. The particle swarm optimization algorithm is employed to optimize the excitation voltages and feed lengths for these antenna arrays to reduce the BER. The strong point of the PSO is that it can find the solution even if the performance index cannot be formulated by simple equations. By the obtained antenna patterns, we can know the route with the lowest BER; meanwhile, transmission power using this route can be reduced. Numerical results show that the synthesized antenna array pattern is effective in focusing maximum gain to the line-of-sight path for these antenna arrays. The synthesized array pattern also can mitigate severe multipath fading in complex propagation environments. As a result, the BER can be reduced substantially in indoor ultra wideband communication systems. The investigated results can help communication engineers improve their planning and design of indoor wireless communication.Copyright © 2011 John Wiley & Sons, Ltd.

Impacts of Genetic Algorithm Parameters on the Solution Performance for the Uniform Circular Antenna Array Pattern Synthesis Problem

In this paper, the uniform circular antenna array pattern synthesis problem is solved by means of the real coded genetic algorithm (GA). At the same time, the impacts of the mutation rate and the crossover position on the GAperformance are also investigated. For this purpose, a circular antenna array with uniformly spaced isotropic elements having identical excitation amplitudes is used as a model. Unlike the conventional GA (with fixed mutation rate and random crossover positions), typical GA implementations with variable mutation rate and restricted crossover position are considered for performance improvement. In conclusion, for the specific problem, decreasing mutation rate with negative derivative is observed to be outperforming the implementations with different mutation rate behaviors. Moreover, regarding the crossover technique, it is observed that imposing some restrictions on the crossover positions (rather than fully random position selection) yields better solutions.

BIT ERROR RATE REDUCTION FOR MULTIUSERS BY SMART UWB ANTENNA ARRAY

In this paper, a new ultra wideband circular antenna array (UCAA) combining genetic algorithm (GA) to minimize the bit error rate (BER) is proposed. The ultra wideband (UWB) impulse responses of the indoor channel for any transmitter-receiver location are computed by SBR/Image techniques, inverse fast Fourier transform and Hermitian processing. By using the impulse response of multipath channel, the BER performance of the binary pulse amplitude modulation (B-PAM) impulse radio (IR) UWB system with circular antenna array can be calculated. Based on the topography of the antenna and the BER formula, the array pattern synthesis problem can be reformulated into an optimization problem and solved by the genetic algorithm. The novelties of our approach is not only choosing BER as the object function instead of sidelobe level of the antenna pattern, but also considering the antenna feed length efiect of each array element. The strong point of the genetic algorithm is that, it can flnd out the solution even if the performance index cannot be formulated by simple equations. Simulation results show that the synthesized antenna array pattern is efiective to focus maximum gain to the multiusers.

A NOVEL SMART UWB ANTENNA ARRAY DESIGN BY PSO

In this paper, a new ultra wideband circular antenna array (UCAA) combining particle swarm optimizer (PSO) to minimize the bit error rate (BER) is proposed. The ultra wideband (UWB) impulse responses of the indoor channel for any transmitter-receiver location are computed by applying shooting and bouncing ray/image (SBR/Image) techniques, inverse fast Fourier transform and Hermitian processing. By using the impulse response of multipath channel, the BER performance of the binary pulse amplitude modulation (B- PAM) impulse radio (IR) UWB system can be calculated. Based on the topography of the circular antenna array, and the BER formula, the array pattern synthesis problem can be reformulated into an optimization problem and solved by the PSO. The novelties of our approach is not only choosing BER as the object function instead of sidelobe level of the antenna pattern, but also consider the antenna feed length efiect of each array element. The strong point of the PSO is that it can flnd out the solution even if the performance index cannot be formulated by simple equations. Simulation results show that the synthesized antenna array pattern is efiective to focus maximum gain to the LOS path which scales as the number of array elements. In other words, the receiver can increase the received signal energy to noise ratio. The synthesized array pattern also can mitigate severe multipath fading in complex propagation environment. As a result, the BER can be reduced substantially in indoor UWB communication system.

The Application of a Modified Differential Evolution Strategy to Some Array Pattern Synthesis Problems

A high convergence rate and a robust exploration ability constitute a contradiction in modern heuristic optimization techniques. This paper describes a modified differential evolution strategy (MDES) that builds up a balanced relationship between the two contradictive elements by introducing several modifications into the conventional differential evolution strategy (DES). The novel MDES opens up an effective and robust approach for global optimization problems. Several representative mathematical functions are minimized using various optimization methods and the convergence rates are compared to evaluate the performance of MDES. Moreover, array synthesis examples which can be formulated as non-convex problems are presented, including the optimal synthesis of sum and difference patterns and the synthesis of unequally spaced arrays. Numerical results demonstrate that the proposed approach improves the performance of the algorithm significantly, in terms of both the convergence rate and the exploration ability.

Antenna array pattern synthesis via convex optimization

We show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems, which can be (numerically) solved with great efficiency by recently developed interior-point methods. The synthesis problems involve arrays with arbitrary geometry and element directivity, constraints on far- and near-field patterns over narrow or broad frequency bandwidth, and some important robustness constraints. We show several numerical simulations for the particular problem of constraining the beampattern level of a simple array for adaptive and broadband arrays.

Optimal beamforming via interior point methods

We show that two antenna array pattern synthesis problems can be expressed as convex optimization problems. The first one deals with a symmetric planar array with real weights, which can be expressed as a linear program. The second one concerns a broadband acoustic array, which becomes a convex quadratically constrained quadratic program. Because these two problems are convex, they can be (numerically) solved with great efficiency by recently developed interior-point methods. Thanks to the efficiency of the interior point methods, we also built a computer-aided design tool for the first problem.

Linear antenna array pattern synthesis with prescribed broad nulls

A technique of synthesizing an antenna array pattern with prescribed broad nulls is presented. The array pattern synthesis problem is formulated as a least-square null constrained optimization problem. Numerical techniques based on the matrix factorization method are developed for reducing the computational complexity of determining the optimal weight vector. Subsequently, a set of eigenvector constraints are used to approximate the effect of the quadratic constraint. Numerical results are presented to illustrate the performance achievable. >

Array pattern synthesis by the method of alternating orthogonal projections: the general case

In the paper, the method of alternating orthogonal projections is derived for the problem of array pattern synthesis with multiple null constraints. The required complex weight vector is obtained via an iterative algorithm starting from the known ‘look direction’. The projection operators required in the algorithm are shown to be easily computed from the ‘look direction’ vector and the null-constraint vectors. A lower bound on the rate of convergence of the algorithm is also established.