Pattern Synthesis for Arbitrary Arrays via Weight Vector Orthogonal Decomposition

This paper presents a new pattern synthesis algorithm with high radiation efficiency for the transmission antenna array. The synthesis algorithm uses adaptive array theory. By incorporating a quadratic constraint, the desired pattern characteristics, such as low sidelobe level, with high radiation efficiency can be achieved. With the sidelobe level fixed, a different value of Lagrangian multiplier corresponds to a different radiation efficiency.

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.

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.

An improved technique is presented for synthesizing a linear antenna array pattern with multiple prescribed broad nulls. The array pattern synthesis problem is formulated as a least-squares optimization problem. A computation method based on matrix factorization is developed for reducing the computational complexity of determining the optimal weight vector. In order to use this technique in HF radar systems in real time mode, a formula is derived to reduce the storage and computational complexity of the algorithm. Finally, simulation results demonstrate the capability of this technique in forming nulls in the prescribed directions.

Low sidelobe array pattern synthesis is achieved by finding appropriate phase shifter settings and amplitude weights for each element. The array pattern synthesis using a genetic algorithm (GA) has been shown in many references, and the various array types are used for the pattern synthesis. The performance of GAs using various types of chromosomes for low sidelobe spherical-circular array pattern synthesis are compared. The spherical-circular array layout consists of eight circular arrays on the surface of a sphere. The GAs control the phase shifters and the amplitude weights of array elements, and minimize the peak sidelobe level while they maintain the mainbeam direction and gain. Three methods are simulated. The first method is a GA with varied binary chromosome lengths (GA-VBCL), and the second method is a GA with a fixed binary chromosome length (GA-FBCL). In addition, the last method is a GA with real continuous chromosomes (GARCC). The convergence speeds and the adapted peak sidelobe levels of these three methods are compared when a good seed (-30 dB amplitude taper) is included/not included in the population.

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.

By comparing the disadvantages and advantages of conventional algorithms of adaptive beamformer, we put forward an adaptive beamformer based on weight iterative algorithm for suppressing RFI according to the distributing properties of radio frequency interference (RFI) in different range cell. We get the initial weight vector of the adaptive beamformer by using the algorithm of minimum variance distortionless response (MVDR). The other weight vectors are computed by the algorithm of linearly constrained minimum variance (LCMV) based on the last time weight vector. The covariance matrix of the two algorithms, i.e. MVDV and LCMV, are constructed with the array snapshots in the far range cells which have not useful radar echo. Thus the free degree of antenna array is increased. The feasibility of the adaptive beamformer is proved by using it to process the actual radar data.

Beam synthesis remains one of the most difficult problems for an antenna array designer, this task being made more difficult when one limits the number of elements to a handful. Pattern synthesis in planar arrays is often achieved by the sampling of a continuous aperture distribution at the element locations. In the case of arrays of limited numbers of elements this produces errors that can unacceptably distort the radiation pattern. When one also then considers the effects of mutual coupling between the antenna elements, the application of ideal element weights derived in this way are no longer valid. In the paper a technique is presented, using the concept of retrodirective beams, that can achieve a low sidelobe beam from a continuous distribution on a circular aperture. The theory is then extended to include a planar array of antenna elements. This is achieved by the addition of retrodirective beams to the uniform beam pattern of the array. Measured data is presented for a small planar array antenna using the derived method. A method for correction of the element weights, to minimise the effects of mutual coupling, producing low sidelobe radiation patterns is then applied. No knowledge of the antenna array's coupling coefficients are required.

A method of forming a pattern with a deep null by a couple of phases is proposed. The proposed method yields a pattern with a null at a prescribed direction by modifying phases of elements. It has been found that, in order to steer the nulls or deep nulls, it is necessary to adjust a couple of phases. It is pointed out that the pattern modified by a couple of phases cannot form deep nulls in some directions. In that case, the pattern with deep nulls can be steered by adjusting more couples of phases. >

The 3GPP Release-13 has recently introduced full-dimension multiple-input multiple-output (FD-MIMO) technology as a practical way to deploy massive MIMO arrays within feasible base station (BS) form factors through the use of active antenna systems with two-dimensional (2D) planar array structures. The 2D arrangement of antenna elements, where the elements in each antenna port are fed with downtilt weights, allows for adaptive electronic beamforming in the elevation as well as the conventional azimuth dimensions. This work focuses on the previously unaddressed problem of determining the optimal downtilt weight vectors for the antenna ports in each cell of a multi-cell multi-user system. The optimization criterion is to maximize the minimum signal to intra-cell interference ratio within a cell while constraining the inter-cell interference leakage. The quasi-optimal weight vectors are obtained through the application of semi-definite relaxation and Dinkelbach's method. The proposed algorithm performs better than the existing approximate schemes even under the effects of pilot contamination.

Robust adaptive beamforming using an iterative FFT algorithm

This chapter delves into the techniques of pattern synthesis through array response control, introducing several distinct methods: the accurate array response control (A2RC) algorithm, the multipoint accurate array response control (MA2RC) algorithm, optimal and precise array response control (OPARC) algorithm, the weight vector orthogonal decomposition (WORD) algorithm, and flexible array response control via oblique projection (FARCOP) algorithm. These algorithms are rooted in the adaptive array theory, aiming to provide precise, optimal, flexible, and robust control over array response levels. Collectively, these methods present a comprehensive and effective framework for pattern synthesis through precise array response control. They offer promising solutions for wireless communications, radar systems, and beyond, enabling fine-tuned control of array responses and pattern synthesis in a wide range of applications.

This correspondence proposes a method for array pattern synthesis of a concentric ring array that yields invariant array pattern over a certain frequency band for beamforming in three dimensions. The proposed method uses the Fourier-Bessel series to determine the weights from different rings to form the overall array pattern. Simulation examples are given to illustrate the proposed 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 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 paper presents a flexible and accurate wideband beam pattern synthesis algorithm utilizing oblique projection. The modified flexible array response control via oblique projection (MFARCOP) is firstly proposed with a novel weight vector construction manner, which is more computationally efficient for adjusting multi-points accurate array responses. Then, the wideband pattern synthesis utilizing the proposed MFARCOP algorithm is developed via the space-frequency scheme. Hence, the space-frequency response can be flexibly and accurately synthesized. Numerical simulations demonstrate the performance of the proposed algorithm.