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Given an antenna array and a digital beamformer, one can form individually steerable multi‐beams using adaptive beamforming algorithms, but this is achieved at the high cost of both analog and digital hardware, as well as energy consumption. This chapter addresses a number of array synthesis problems facing the design of 5G, 6G, and beyond arrays. These include the synthesis of thinned arrays to save cost; the synthesis of antenna arrays using element rotations to simplify the feed network; the synthesis of sum and difference patterns for communications with moving platforms; and the synthesis of single input multiple output multi‐beam arrays. Detailed synthesis algorithms are presented to illustrate the advantages of an array with rotated elements to meet such wireless communication system requirements. Two examples of synthesizing sum and difference patterns using rotated dipole array elements are examined to demonstrate the efficacy of the approach.

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.

Investigations on an enhanced adaptive genetic algorithm (EAGA) for pattern synthesis of a conformal array are presented. The proposed algorithm uses the advantages of the adaptive genetic algorithm (AGA) and the invasive weed optimization so that it improves the searching ability and the convergence speed. Convergence characteristics of the EAGA are compared with those of the AGA. Also, the pattern synthesis performance of the EAGA is compared with that of the AGA. A 4 × 16 conformal array operating as a 1 × 16 array in the azimuth direction is fabricated and measured to demonstrate the proposed algorithm. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1173–1176, 2015

Taguchi's method is a quality design technique recently expanded to multiobjective optimization and electromagnetic engineering problems. This novel technique is applied here to multibeam array synthesis and compared to a standard multiobjective genetic algorithm. Results indicate fast convergence, good spreading, and a good number of nondominated solutions. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:1836–1840, 2013

Genetic algorithms coupled with the Schelkunoff synthesis method are used to synthesize equispaced linear and planar arrays. The purpose is to find the different excitation amplitudes and phases to achieve good matching between the desired and calculated radiation patterns. Examples which demonstrate the versatility of the approach presented in this article are considered for various patterns including the steered pattern case. The planar array is treated as a set of two separate linear arrays upon which Schelkunoff method is applied separately. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1619–1623, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22510

We describe a method for the synthesis of sulfonamides through the combination of an organometallic reagent, a sulfur dioxide equivalent, and an aqueous solution of an amine under oxidative conditions (bleach). This simple reaction protocol avoids the need to employ sulfonyl chloride substrates, thus removing the limitation imposed by the commercial availability of these reagents. The resultant method allows access to new chemical space, and is also tolerant of the polar functional groups needed to impart favorable physiochemical properties required for medicinal chemistry and agrochemistry. The developed chemistry is employed in the synthesis of a targeted 70 compound array, prepared using automated methods. The array achieved a 93% success rate for compounds prepared. Calculated molecular weights, lipophilicities, and polar surface areas are presented, demonstrating the utility of the method for delivering sulfonamides with drug-like properties.

The application of spatially encoded principles in solid phase combinatorial synthesis requires no chemical or physical coding strategies. The resulting products are encoded by their position inside the array and their synthesis history. The advantages of microreactor arrays for solid phase synthesis as one of the embodiments in the field of microreaction technology are discussed. Here, we review the reactor design, necessary process steps, and a strategy for the diversity oriented array synthesis. In particular, the glass-made microreactor and its assembly for 1563 parallel solid phase reactions, which can be performed at temperatures up to 120 °C, are described. Bead loading and liquid handling steps were adapted to this array. The production of large libraries demands suitable synthesis protocols and building blocks. The optimization of appropriate synthesis conditions is a time-consuming process. A multiple core structure library approach for the efficient synthesis of diverse heterocyclic libraries is described. The aim of this work was to prove the feasibility of the glass-microreaction array for massive parallel library synthesis.

In certain antenna arrays (“switched-element” arrays), some of the radiating elements are turned on or off during operation to provide some desired reconfigurability at different times, or are effectively turned on or off at different frequencies, through the use of filters connected to groups of radiating elements, in order to retain the same performance over wide-frequency bands. In such circumstances, the excitations of the elements must be the same, irrespective of whether all or only some of the elements are being used. Thus, one may wish to synthesize an array (that is, determine its element excitations) so that the required performance is obtained under different sets of circumstances. In this paper, we indicate how the use of a parallel approach allows the method of generalized projections to be used for such synthesis problems, and demonstrate its use for a specific example. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 465–471, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20006

An array synthesis technique that straightforwardly extends an earlier quadratic-programming based method to the case of multifrequency arrays is described. The method is applied to a specific multifrequency array example. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 326–330, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20459

An amplitude approaching algorithm (AAA) for the pattern synthesis of adaptive arrays is presented in this paper. Furthermore, the algorithm is amended by the Newton downhill method. Simulations show that the main lobe and side lobe can be controlled efficiently, and the algorithm converges more quickly and steadily. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 503–507, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10804

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 article presents a new procedure for the synthesis of array antennas mounted over complex vehicular platforms, where an accurate control of the electromagnetic interference and disturbances (EMI) between systems is required. This is done by including into the overall optimization procedure near-field restrictions over those regions of the platform where sensitive devices are installed. The electromagnetic coupling between the radiating systems and with the platform is modeled by an accurate three-dimensional method-of-moments formulation. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 188–191, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10413

A new approach to the Orchard–Elliott pattern synthesis algorithm based on the least mean-square (LMS) technique and the pseudoinverse technique is described. The new algorithm offers better initial conditions and avoids possible divergence problems throughout the iteration process. The array current distribution obtained is optimized using a genetic algorithm. The effectiveness of the new approach is demonstrated on a linear array with a symmetric flat-topped radiation pattern. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 12–15, 2001.

The multibeam antenna for the 22-GHz band satellite broadcasting has been studied. The aim of this study is to meet future satellite broadcasting demands and advanced services such as high definition television (HDTV), digital broadcasting, and regional satellite broadcasting. The breadboard model of the 22-GHz band multibeam antenna has been developed. Here, a new type of primary feed and a pattern synthesis method are proposed to achieve high gain and low sidelobe antenna performance which is required for the 22-GHz band satellite broadcasting. The feasibility of the proposed antenna system and the design method have been verified numerically and experimentally.

All butterfly and moth scales and bristles are made of non-living insect cuticle. Each is the product of a single epithelial cell, and all share the same basic architecture. However, some are highly specialized, and their cuticle is further elaborated into stacks of thin-films, lattices, or other minute structures, many of which first came to our attention because they interact, with light to produce structural colors. The scale cell forms the scale by extruding a projection of itself and secreting around it the outer epicuticle, a thin cuticular envelope which will form the outermost layer of the scale. The inner layers of cuticle, collectively called the procuticle, are secreted thereafter and go on to form the lattices, pillars, or other internal structures of the scale. We believe that the pattern-forming mechanisms used by the cell to shape the cuticle into its finished form include elastic buckling of the outer epicuticle to produce external folds, and “masking” of certain areas of the original epicuticular envelope to produce thin spots which will break through to become windows. Varied though they be, all insect cuticular patterns have common basic elements, which suggests that our findings may be generalized to other highly patterned insect cuticles, particularly those formed by single cells. © 1994 Wiley-Liss, Inc.

A genetic algorithm (GA) finds complex weights that yield low-sidelobe levels for spherical arrays. The first example is a spherical–planar array with an initial high sidelobe of −13 dB, and which has an optimized pattern with a maximum sidelobe level of −27 dB. The second example is a spherical–circular array with an initial high sidelobe of −16 dB, and which has an optimized pattern with a maximum sidelobe level of −34 dB. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 32: 412–414, 2002.

New non-steroidal chemotypes are required for the development of drugs targeting the steroid hormone receptors. The parallel array synthesis of 3-aryl-1,2-diazepines employing solid-supported reagents is described. The resulting compounds demonstrated high affinity binding to the progesterone receptor.

The purpose of this communication is to discuss the effect of the mutual coupling between element arrays on the radiation pattern, and to compensate for this effect in introducing them into a power far-field pattern synthesis array. The synthesized pattern is an optimum approximation to the prescribed power pattern in the minmax sense. A study is realized for shaped sectarian and cosecant beams. © 1996 John Wiley & Sons, Inc.

This article proposes a unified method for |J1(u)/u| distribution synthesis in an equispaced circular ring array. The |J1(u)/u| distribution has much lower side lobes than that in the J0(u) distribution. The simulation results using the proposed method have shown this possibility. Hence, the |J1(u)/u| distribution can be utilized to control the side-lobe levels in most applications.

Designed as a new group of planar molecule containing the proposed 2-phenylnaphthalene-type structure, a number of 11H-indolo[3.2-c]quinoline derivatives were synthesized and evaluated biologically. Several compounds were found to possess cytotoxic activity against the growth of human promyelocytic leukemia cells (HL-60), against the small cell lung cancer (SCLC), and showed good response in the National Cancer Institute preclinical antitumor drug discovery 60-cell line panel.

Circular apertures are synthesized for maximization of the minimum gain over the coverage area. This study develops the gain-coverage area product limitation for circular apertures. Two conclusions are: (i) The gain-coverage area product is not directly proportional to the aperture diameter, (ii) The in-phase field is the proper field to use in small aperture.