Pattern Synthesis Problem Research Articles

Synthesis of antenna arrays with an efficient multiobjective differential evolution algorithm

An efficient multiobjective differential evolution algorithm for array synthesis is proposed in this article. By introducing novel strategies in the generalized differential evolution GDE3, the proposed algorithm can generate a better converged and distributed Pareto front than the standard GDE3. Five typical benchmark functions are optimized by the proposed improved GDE3 IGDE to verify its effectiveness. Furthermore, the proposed algorithm is applied in two-pattern synthesis problems, including an unequal spaced linear array and a conformal array. The superior performance of the proposed IGDE demonstrates that it is an efficient and competitive algorithm in the function optimization, pattern synthesis, and other electromagnetic problems. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:161-169, 2014.

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.

Sum, Difference and Shaped Beam Pattern Synthesis by Non-Uniform Spacing and Phase Control

A design procedure for the synthesis of non-uniformly spaced linear arrays is presented, which uses the Poisson sum expansion of the array factor introduced in the literature. By considering the nonzero phase term in the existent formula and using the appropriate line source pattern synthesis methods, a general design procedure is obtained to synthesize any type of pattern, such as sum, difference and shaped beams. This approach converts the nonlinear complex problem of pattern synthesis for non-uniformly spaced linear arrays to a simple problem, which makes it fast and easy to implement. Moreover, an extra optimization process is added to the synthesis procedure to improve final pattern and provide control on computed parameters.

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.

Pattern Synthesis of Narrowband Conformal Arrays Using Iterative Second-Order Cone Programming

A new design method is proposed for the power or shaped beam pattern synthesis problem of narrowband conformal arrays, where only the magnitude response is specified. The proposed method iteratively linearizes the non-convex power pattern function to obtain a convex subproblem in the design variables, which can be solved optimally using second-order cone programming (SOCP). In addition, a wide variety of magnitude constraints such as non-convex lower bound magnitude constraints can be incorporated. An efficient technique for determining a reasonably good initial guess to the problem is also proposed to further improve the reliability of the method. Computer simulations show that the initial guesses so obtained converge to satisfactory solutions while satisfying various prescribed magnitude constraints. Design results show that the performance of the proposed method is comparable to the optimal solution previously obtained for uniform linear arrays with isotropic elements. Moreover, we show by means of examples that the proposed method is also applicable to general non-convex power pattern synthesis problems involving arbitrary array geometries, arbitrary polarization characteristics and mutual coupling effect.

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.

Analysis and synthesis of fractal antenna radiation patterns

A problem of fractal antenna radiation pattern synthesis is considered. The problem of synthesis of fractal antenna radiation patterns is solved for two kinds of antennas (discrete and linear) in one- and two- dimensional cases. With the use of the theory of fractal synthesis, new modes with new properties are obtained in fractal electrodynamics. Fractal radiation pattern synthesis was conducted by means of the Weierstrass function.

선형 위상 배열 안테나의 비대칭 Sidelobe 레벨 제어 및 다중 Nulling에 관한 연구

본 논문에서는 선형 위상 배열 안테나 패턴 합성 문제에서, 주 빔 패턴 양쪽에 임의로 설정한 비대칭 sidelobe 레벨(SLL)들을 만족시키는 안테나 소자 가중치들을 계산하는 방법을 새로이 제안한다. 소자 가중치들을 배열인자로부터 직접 최적화하는 기존의 방법들과는 달리, 이 방법은 배열 인자를 표현하는 Schelkunoff 다항식에 내재된 복소근의 최적 섭동에 기본을 둔다. 제안한 방법으로부터 여러 개의 jammer들의 방향으로 다중 nulling도 가능하며, 이는 각 jamming 방향에 대응하는 복소근들만의 독립적인 섭동에 의해 이루어진다. 따라서 해 공간차원의 적절한 감소에 의해 수치적 절차가 간소화될 수 있다. 또한 배열 소자들의 복소 가중치들은 최적 섭동된 복소근들을 Schelkunoff 다항식에 대입함으로써 쉽게 계산된다. 몇 가지 예를 들어 검토하고, 도출된 가중치들을 배열 인자 방정식에 대입함으로써 타당성을 수치적으로 검증한다. This paper newly proposes a methodology towards computing antenna element weights which are satisfying asymmetric sidelobe levels(SLLs) specified arbitrarily on both sides of the main beam pattern, in the linear phased array antenna pattern synthesis problem. Opposite to the conventional methods in which the element weights are directly optimized from the array factor, this method is based on the optimum perturbations of complex roots inherent to the Schelkunoff's polynomial form which is described for the array factor. From the proposed methodology, the capability of nulling the directions of multiple jammers is also possible by independently perturbing only the complex roots corresponding to each jamming direction, hence allowing an enhancement of the simplicity of the numerical procedure by means of a proper reduction of the dimension of the solution space. The complex weights over the array are then easily computed by substituting the optimally perturbed complex roots to the Schelkunoff's polynomial. Some examples are examined and numerically verified by substituting the extracted weights into the array factor equation.

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.

모노펄스 추적용 선형 배열 안테나 빔 패턴 및 여기 전류 가중치들의 최적 합성에 관한 연구

등간격 안테나 소자들로 구성된 모노펄스 추적용 선형 배열 안테나의 합 및 차 패턴 합성 문제에서 원하는 패턴을 만족시키도록 하는 개별 안테나 급전 여기 전류의 상대적인 가중치들을 도출하는 효율적인 수치적 방법을 제안한다. 이 방법은 패턴 배열 인자를 표현하는 Schelkunoff 다항식에 내재된 패턴 null 점들의 최적 섭동에 기본을 둔다. 따라서 여기 전류 가중치들을 직접 최적화하는 기존의 방식과는 달리, 이 방법은 null 점 제어에 의해 원하는 개별 sidelobe 레벨(SLL)들을 갖는 패턴과 해당 여기 전류 가중치들을 쉽게 합성할 수 있는 장점을 가진다. 또한, 최적화 과정에서 null 점 초기값에 따라 두 가지 형태의 차 패턴들을 합성할 수 있음을 보인다. 임의의 SLL들을 갖는 패턴들을 합성하고, 도출된 결과들을 배열 인자 식에 대입함으로써 제안한 방법의 타당성을 수치적으로 검증한다. In the sum and difference pattern synthesis problem of the equi-spaced monopulse tracking linear array antennas, an efficient numerical approach to deriving the relative excitation current weights of antenna elements is presented for the desired patterns. This method is based on the optimum perturbation of null points which are inherent to the Schelkunoffs polynomial representing the pattern array factor. Accordingly, opposite to the conventional method in which the excitation weights are directly optimized, this method is advantageous in that the patterns with the desired individual sidelobe levels(SLLs) and the corresponding excitation weights are easily synthesized by the control of null points. Furthermore, it is showed that two types of difference patterns can be synthesized as imposing the different initial values of null points in the optimization process. The proposed method is numerically validated by synthesizing the patterns with the arbitrary SLLs and substituting the extracted results into the array factor equation.

Low-Dimensional SDP Formulation for Large Antenna Array Synthesis

Bounding the sidelobe and mainlobe levels of an array with complex weights is attractive in that it allows direct control of the radiation pattern. In this paper we propose an efficient beamforming technique for synthesizing the patterns of large arrays with bound constraints on the sidelobe and mainlobe levels. It is shown that the pattern synthesis problem can be posed as a convex semi-infinite program (SIP) which is then turned into a semi-definite program (SDP) via a novel linear matrix inequality (LMI) characterization of semi-infinite trigonometric polynomial constraints. In contrast to existing SDP formulations which require a large number of additional variables, our SDP representation only uses a minimal number of additional variables. This subsequently enables the design of patterns for arrays with several hundred elements to be efficiently achieved on a standard personal computer using existing SDP solvers.

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.

Antenna pattern synthesis: a new general approach

The antenna pattern synthesis problem is of the utmost importance in almost every kind of antenna applications. Therefore, a very large number of contributions have appeared on this subject. But virtually all of them deal with simplified versions of the complete synthesis problem, wherein the degrees of freedom available in principle are strongly reduced, and/or idealized design criteria or requirements are considered. In this paper we present a formulation which allows us to overcome this fragmentation of the synthesis problem. A clear and direct description of the performance actually required by the antenna and a representation of the radiating properties of the antenna as a system allows us to formulate the synthesis problem as an intersections finding problem, i.e., to find a common element between a number of sets, each one containing elements fulfilling part of the requirements. This allows a completely general and flexible formulation of the problem, independent of the actual structure of the antenna. Then the practical implementation of this formulation is widely discussed, showing how an efficient solution procedure can be devised. The implications of the well-known ill-conditioning of the synthesis problem are also discussed. In order to show how the approach works and to assess its flexibility and power, a couple of significant examples are included, namely, a phase-only reconfigurable array and a shaped reflector synthesis. These examples are unconventional since no a priori choice of the intensity distribution (for the array case) or of the feed cluster (for the reflector case) is required. The method presented is able to exploit all the available degrees of freedom in order to fulfill the design requirements. >