Linear array pattern synthesis with multiple broad nulls

A fast algorithm is given for computing the optimal weight vector in antenna array pattern synthesis having a set of null constraints. The algorithm requires only a UDUT decomposition of an m + 1 × m + 1 real positive definite matrix and the computation of the first row of the inverse of a triangular matrix of the same dimension, where m is the number of null constraints.

It is shown that the radiation pattern of a hexagonal planar array with triangular arrangement of elements can be synthesized by using a pattern of a linear array. The resulting pattern has the same sidelobe level as the corresponding linear array pattern. The current amplitude of the array element is represented by a linear combination of the current amplitudes of linear array elements with constant coefficients.

Radiation pattern of linear arrays of microstrip rectangular antennas, on uniaxial anisotropic substrate is presented with Galerkin method. An optimization procedure based on the genetic algorithm (GA) method is introduced to reduce the side lobe level (SLL), by acting on the law of current amplitude of feed, spacing and phase of a linear array antennas. The results of optimisation are verified shows of narrow beamwidth are achieved.

This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array’s element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to −33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is −42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to −187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as −98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as −63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is −22.8766 dB, which is 0.1998 dB lower than the lowest SLL of −22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is −20.1012 dB, and the null depth is −125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms.

The pattern synthesis technique of antenna arrays has a wide range of applications in radar and communication systems, which is an important research direction in the field of smart antennas. In order to improve the optimization performance of pattern synthesis of linear antenna arrays, an optimization method based on the Modified RIME Optimization Algorithm (MRIME) is proposed. RIME is a new heuristic algorithm inspired by the condensation process of frost ice in nature, which has a unique update mechanism with strong convergence as well as randomization. In the present work, MRIME is used for optimal pattern synthesis of a linear antenna array (LAA). One part of the present study is to optimize the side lobe level by optimizing the antenna current amplitude while maintaining a uniform spacing; the other part is to optimize the antenna position while assuming a uniform excitation in the synthesis of a sparse LAA, where constraints are imposed on the spacing of the array elements and aperture length, and suppression of the side lobe level with the position of the zeros in the specified direction is also achieved. In this article, simulation experiments for uniform linear arrays as well as sparse linear arrays are presented in detail, and the results show that the MRIME optimization algorithm outperforms most of the existing evolutionary classes of optimization algorithms in optimizing the side lobe level. This illustrates the potential of utilizing the MRIME optimization algorithm for antenna arrays and various other electromagnetism-related challenges.

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 an SDP problem, it is known that an additional rank‐one constraint is generated inevitably and relaxed via semidefinite relaxation. If the solution to the relaxed SDP problem is not of rank one, then conventional SDP‐based array pattern synthesis approaches fail to obtain optimal solutions because the additional rank‐one constraint is not handled appropriately. To overcome this drawback, we adopted a bisection technique combined with a penalty function method. Numerical applications are presented to demonstrate the validity of the proposed scheme.

This work is concerned with the methodology for improvement of the radiation pattern performance and eliminating the effect of unwanted interference of symmetric time modulated linear antenna array (STMLAA) in the predefined direction. This is achieved using evolutionary technique called Novel Particle Swarm Optimization with Wavelet Mutation (NPSOWM) for various application specific optimization like SLL only reduction, dual broad null and multiple broad null optimization. The optimized results obtained by using NPSOWM are validated by CST-MWS by captivating practical elements of dipole antenna and its array configuration. The numerical results show the effect of the particular (practical) antenna on the array. Various examples have taken for this purpose. A set of 16-element antenna array have designed for SLL only reduction. 16-, 32-, and 64-element STMLAA for incorporating the dual broad nulls in the angular range from 400 to 700 over the elevation plane. A set of 24-, 30-, and 32-element antenna array have occupied for multiple broad nulls. The strength of the adopted algorithm is tested for different number of array antenna configuration, which establish the efficacy of the optimization technique NPSOWM adopted for achieving the interference cancellation in the predefined direction and performance improvement of the antenna array such as simultaneous improvements of broad nulls (BNs), sidelobe level (SLL), sideband level (SBL), and the directivity. From the simulated results it is clear that NPSOWM can perform better than that of un-optimized linear antenna array with respect to BNs, SLL, and SBLs and Directivity.

Array pattern synthesis (APS) aims to create the desired array pattern as closely as possible to the prescribed mask template by varying the element excitations of the array. Herein, an efficient approach for the APS to control the sidelobe level is proposed. After designing the mask template to meet the prescribed sidelobe requirements and the waveform pattern, a set of element excitations is calculated through the Fourier transform performed on the projection the waveform pattern onto the mask template. Then, a desired array pattern can be synthesized from this updated set of excitation coefficients. The proposed APS approach directly presents a mathematical formulation of the exact set of excitations without any iterative optimization process. The proposed method is particularly suited for many array elements in linear antenna array. Thus, the proposed APS achieves substantial improvements in terms of computation complexity, performance, and ease of implementation in the algorithm when compared with conventional methods. Several simulation results are provided to verify the efficacy and effectiveness of the proposed method.

A flexible search technique based on a tabu search algorithm is presented for the shaped‐beam pattern synthesis of linear antenna arrays. To synthesize a desired pattern, element excitations and/or positions are optimally determined. Examples of cosecant, flat‐topped, and pencil beam patterns are given to illustrate the achievable performance. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 16–20, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10657

This paper deals with the problem of array pattern synthesis in the case of large element spacing. Particularly, the simultaneous excitation of two radiation modes (a classical broadside pattern and a monopole pattern) is used to increase the number of pattern synthesis degrees-of-freedom, and it is shown that this is a valid approach for the reduction of arising grating lobes which severely degrade the achievable sidelobe level, especially for increasing steering angles. A pattern optimization function is formulated for symmetric arrays, and numerical results reveal that a 18 dual-mode element one wavelength-spaced linear patch antenna array can offer a grating lobe reduction larger than 16 dB within the steering angle range 10°-40° with respect to a mono-mode antenna array.

This paper presents an efficient method for the pattern synthesis of linear antenna array based on the differential evolution algorithm. A number of examples are presented to demonstrate the various capabilities of the this method for different number of elements. The main objective of this paper is to achieve a set of current weights in order to steer the nulls in undesired directions (nulling the undesired signals) and steering the main beam towards the desired direction(direction of desired signal) by changing the phase excitation currents. The fitness function is obtained from maximization of error between actual pattern and desired pattern.

This communication introduces a new approach to achieve symmetrical array patterns using only phase adjustments in a Chebyshev-phase framework, employing a particle swarm optimization (PSO) technique known as PC-PSO. The initial phase setup, taken from the Catenary function, acts as the fundamental phase for adjusting phases. This helps in stopping the optimization process from getting stuck in local best solutions. Afterward, the phase adjustments are made in a lower-dimensional space using even-order Chebyshev polynomials, focusing on the coefficients of these polynomials for optimization. This method not only reduces the number of factors involved and speeds up the optimization but also achieves precise pattern shaping. To showcase its effectiveness, three examples involving linear and circular planar arrays were examined, confirming the advantages of this approach.

Basic antenna array theory is outlined with major emphasis on pattern analysis and synthesis for periodic linear and planar arrays, phased arrays, and conformal arrays. Extension is made to synthesis techniques which use computer algorithms. These include arbitrary sidelobe control, shaped beams, and phase-only null steering. The subjects of random errors and phased array quantization errors are outlined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Pattern synthesis of sparse linear arrays based on the atomic norm minimization and alternating direction method of multipliers approach

An efficient method based on the sequential quadratic programming (SQP) algorithm for the linear antenna arrays pattern synthesis with prescribed nulls in the interference direction and minimum side lobe levels by the complex weights of each array element is presented. In general, the pattern synthesis technique that generates a desired pattern is a greatly nonlinear optimization problem. SQP method is a versatile method to solve the general nonlinear constrained optimization problems and is much simpler to implement. It transforms the nonlinear minimization problem to a sequence of quadratic subproblem that is easier to solve, based on a quadratic approximation of the Lagrangian function. Several numerical results of Chebyshev pattern with the imposed single, multiple, and broad nulls sectors are provided and compared with published results to illustrate the performance of the proposed method. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.