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A shaped beam pattern (SBP) synthesis algorithm, which obtains the desired SBP in an analytical way, is proposed. The new algorithm describes the SBP with the weighted superposition of a set of pencil beam patterns (PBPs). First, the array weight of the PBP is obtained via analytical algorithms, such as; Chebychev and Taylor, etc. Then, by computing the weights of the PBPs with the least‐square method, the synthesized SBP is expressed explicitly. Different from the state‐of‐the‐art algorithms, the proposed algorithm can obtain the desired SBP analytically, avoiding the time‐consuming iteration processes. Moreover, the proposed algorithm enables the array antenna to scan the beam in different directions. Simulations with linear and planar array antennas are provided to assess the superiority and effectiveness of the proposed algorithm.

The problem of optimised design of diversely polarised sparse array for joint synthesis of spatial and polarisation beampattern is addressed in this Letter. Two kinds of polarised array configurations, cocentred and non-cocentred crossed-dipole arrays, are considered. Minimum interelement spacing constraint along with non-cocentred constraint are involved in the design methods by using two discrete linear operators. The optimisation process can be formulated as a mixed-integer quadratically constrained programming problem which guarantees the optimal solution of the sparse array configuration. Comparison examples with state-of-the-art method validate the advantages of the proposed method in terms of the reduction of required element number and the enlargement of adjacent element spacing.

A hybrid approach to the synthesis of sparse arrays radiating shaped or focused beampattern is presented in this paper. Specifically, an iterative scheme is used where the prescribed pattern response in the mainlobe peak direction is cast as a multi-convex problem at each step that the non-convex lower bound constraint is relaxed while including a reweighted l(1)-norm minimisation based on the magnitudes of the elements. Numerical tests, referred to benchmark problems, show that the proposed method achieves improved radiation performance by using fewer number of radiating elements.

The pattern synthesis based on the spectral Green's functions for multi-layered perforated dielectric loaded patch antenna is presented. It is conducted by optimising the dielectric superstrate parameters, i.e. relative permittivity (e r) and thickness. To solve the problem of the optimised e r unavailable from market, perforated dielectric superstrate (PDS) is utilised. The equivalence between PDS and homogeneous dielectric superstrate (HDS) in spectral domain is investigated and the effective relative permittivity (e reff) of PDS is studied. Moreover, by introducing e reff, the general optimisation procedure for HDS loaded antenna is also applicable for PDS loaded antenna, which reduces the computational cost significantly. To validate their method, a two-layer PDS loaded patch antenna with E/H beamwidth equalisation was designed, fabricated and measured. Simulations and measurements show that the synthesised antenna has satisfactory performances over the ITU-RS.1068-1994 band from 13.75 to 14 GHz. The half 10 dB E/H beamwidths of 19°/20°, −27 dB cross polarisation and −15.5 dB side lobe level have been achieved.

Although particle swarm optimisation (PSO) algorithm is an effective tool to solve the real-number optimisation problem, it cannot be directly adopted to the discrete optimisation. Many discrete PSO versions focused on the different discrete strategies on particle position and speed update equation, but these attempts decreased the performance of the PSO on discrete problems (compared with other intelligent optimisation algorithms). In this study, binary inheritance learning PSO (BILPSO) is proposed and is used to solve thinned antenna array synthesis problems, such as the pattern synthesis of 100-element symmetrical thinned linear array and 20 × 10 symmetrical thinned planar array. The optimisation results show the BILPSO is superior to other discrete PSO versions and other discrete intelligent optimisation algorithms.

A novel pattern synthesis approach for circularly polarised (CP) four-dimensional (4D) antenna arrays with microstrip patch elements is presented. Sequential rotation method is used to reduce the cross-polarisation component of the CP antenna array and good circular polarisation purity is achieved. Moreover, the time modulation technique of 4D antenna arrays is adopted for the realisation of low sidelobe levels (SLLs), thus forming a CP 4D antenna array. The differential evolution (DE) algorithm is used to optimise the time sequences, and hence low SLLs and sideband levels (SBLs) are obtained. To achieve low SLLs and low SBLs simultaneously, both of the static amplitude excitations and time sequences are optimised by the DE algorithm. Simulation results show that the CP 4D patch arrays can be used to achieve lower SLLs, while the dynamic-range ratios of the amplitude excitations can be very small or even uniform.

Method of least squares is employed for synthesis of non-uniform spherical arrays using Euler rotation of coordinate axes for reduction of side-lobe levels, controllability of 3-db beam-width of main-lobe etc. It is useful for synthesis of conformal arrays, where pattern multiplication is not applicable and array synthesis is involved. This method for synthesis of spherical arrays is general that determines radius of sphere, longitude and latitude angles of elements and their current excitations (amplitudes and phases). The authors investigate several examples to demonstrate its capability. Studies on conformal arrays deal with non-uniform excitation currents, leading to complicated input networks. Therefore the authors suggest non-uniform spacing, which shows that array synthesis by variable element spacing will realise any specifications, same as non-uniform excitations. An error function is constructed for pattern synthesis, which is a function of element spacing and excitations. The authors use combination of global and local minimisation algorithms. In examples of spherical array synthesis, 2.5 and 5.5 dB reduction of side-lobe levels have been achieved in the E- and H-plane patterns, respectively, relative to the available design data. In addition, reduction of beam-width of main-beams in E- and H-planes has been obtained by 39% and 34%, respectively.

This work presents the design, simulation and implementation of a linear array antenna with a fully constrained cosecant squared radiation pattern and a novel wideband feeding network. This antenna is constructed of wideband printed dipole antennas as the array elements in which the mutual coupling effect is properly compensated. For this purpose, a constrained particle swarm optimisation (PSO) algorithm is used as the synthesis method which is able to deal with multiple constraints in the desired radiation pattern. The excitations obtained from the PSO algorithm are applied to the design of a wideband feeding network which is able to deliver stable phase shifts and output powers to the array elements over the desired bandwidth. Finally, the simulation results are confirmed by the measurement results.

An off-grid (OG) pattern synthesis algorithm for sparse non-uniform linear arrays is presented. It is based on Bayesian compressive sampling (BCS), and the design of maximally sparse linear arrays for the given reference patterns can be obtained. The proposed algorithm novelly introduces the OG model into the pattern synthesis problem, and it makes the synthesis more accurate than the conventional BCS algorithm. Moreover, the proposed algorithm has the advantage of high computational efficiency, since the BCS-based algorithms can be realised by the fast relevance vector machine. Numerical experiments show that the proposed algorithm has improved accuracy in terms of normalised mean square error.

A power pattern synthesis technique for a wideband array including mutual coupling (MC) is proposed. A frequency-dependent MC (FDMC) matrix is obtained accurately via the complex curve fitting technique. With the FDMC matrix the mutual coupling effect is included in the synthesis procedure automatically, resulting in an MC-compensated frequency-invariant power pattern.

A new array pattern synthesis method is proposed by using the concept of a sparse representation of beampattern, in which array pattern synthesis is achieved by evaluating the sparsity of beampattern and combining with a set of constraints on magnitude response. The proposed method can not only achieve a low sidelobe level, but also flexibly control the robust response region with specified beamwidth and response ripple.

An iterative method has been proposed for optimising element excitations in linear phased arrays for synthesising a cosecant-squared pattern (CSP). Compared with the other methods, this weighted alternating reverse projection (WARP) method allows having fewer ripples in the shaped region and lower sidelobe level (SLL). Some detailed examples are presented and results show that the WARP method has better performance in terms of SLL and ripple.

A frequency invariant power pattern is synthesised, based on the weighted least-squares criterion. An auxiliary function is introduced to transform the nonlinear synthesis problem into a linear one. The phases of the desired pattern are calculated by the simulated annealing technique, and the weighting function is iteratively modified to achieve a desired power pattern.

A method for non-uniformly spaced series-fed rectangular microstrip array synthesis is given. By this approach the problem of patch array design turns out to be slot array synthesis. The resulting equivalent configuration gives the necessary parameters for the microstrip array geometry. Applications on Taylor, Bayliss and shaped-beam patterns show the validity of the method.

A simple and novel structure of a tapered slotline antenna with a synthesised radiation pattern is proposed. By means of a non-symmetric taper profile with corrugated edges and a backed plate, a special vertical pattern for a base station of mobile communication is performed. The measurement pattern of a scaled sample at 10 GHz possesses 4° beam tilting, suppressed sidelobe (−19.9 dB) in the upper side and null filling in the lower side of the vertical pattern;65° HPBW in the horizontal pattern; and 11.7 dBi of gain.The frequency coverage for VSWR

In the paper a neural network algorithm is presented for the synthesis of array patterns in the presence of mutual coupling. The algorithm is based on wavelet activation functions and is tested on a linear dipole array with a shaped pattern. The excitations and the lengths of the dipoles in the array are determined. The architecture of the neural network is discussed and simulation results are presented. The proposed algorithm makes the synthesis procedure more practical and accurate compared to the synthesis technique without mutual coupling considerations.

A multi-stage optimisation method for solving the nonlinear least square error problem in flat-top power pattern synthesis using non-uniform linear arrays is presented. The optimisations are conducted from low to high order in eigenspace, and without the requirement of multidimensional initial value. Simulations show the robustness of the method over a conventional method dependent on initialisation.

A novel method for the minimax pattern synthesis of FIR filter based wideband beamformers is presented. Emphasis is placed on frequency invariant beamforming, although intentional frequency variant patterns may be synthesised as well. The method is based on the algorithm originally developed for the compressive FIR filter design in pulse compression radars.

A numerical pattern synthesis technique for low and shaped sidelobe difference beams is described. The approach is based on adaptive array theory and is a modification of a technique developed for sum beam synthesis. The method has been applied to a conformal array and the results of synthesising low sidelobe (-40 and -50 dB) difference beams are presented.

A pattern synthesis method for arbitrary arrays based on the linearly constrained minimum variance (LCMV) criterion is presented. Given mainlobe regions and an arbitrary sidelobe envelope, this algorithm searches the pattern with the lowest sidelobe levels. Its iteration coefficient is robust to synthesis conditions, and patterns with a flat top mainlobe can be obtained using phase-independent derivative constraints.

A pattern synthesis method, which incorporates deterministic nulls in the radiative near-field of an array is presented. The problem is formulated as a constrained least-mean-square approximation and an exact solution is given. Both linear and planar arrays are considered.

In several array synthesis problems the lack of a common element pattern among different antennas makes the use of classical synthesis methods based on the array factor questionable. A recently introduced approach to array synthesis is exploited to take account in an exact fashion of the mutual coupling between patches for the synthesis of pencil beams by microstrip arrays. Optimality of the approach allows quantifying the advantages of the method with respect to common approaches, which largely compensates in several cases for its additional computational burden.

A pattern synthesis technique for a conformal array antenna on a cylinder is presented using the method of alternate projections. Both the sidelobe region and the shape of the main beam are controlled. The method includes the effect of the mutual coupling in the synthesis. It is shown that if mutual coupling is neglected, then poor results are obtained, especially in the shaped beam region.

A numerical pattern synthesis and optimisation technique for shaped and low sidelobe beams adhering to desired array element excitations are described. The synthesis approach is a modification of the Woodward synthesis method with an additional sidelobe minimisation, and the final element excitation optimisation is based on array polynome complex root swapping and genetic algorithms. These methods have been applied to an equispaced linear planar array. Results of the synthesis and genetic algorithms are presented.

A pattern synthesis technique for low sidelobe arbitrarily scanned difference beams in small planar phased arrays is presented. The approach is based on adaptive array theory and is the development of a technique used for radiation pattern synthesis in linear arrays. The method has been applied to measured element pattern data from a small planar array, which includes the effects of pattern corruption by mutual coupling. The successful synthesis of low sidelobe difference beams is demonstrated, with arbitrary difference plane and scan angle.

A design method previously developed for the synthesis of antenna patterns of circular arc arrays is shown to also be applicable to the synthesis of conformal arrays in the 3D case. This method uses the flexibility of the simulated annealing technique to achieve the excitations of the elements for a desired radiation pattern. The algorithm allows the inclusion of constraints in the variability of the excitations in the synthesis procedure, as well the control of the sidelobe level, the beamwidth and any desired design specification.

A novel method for the synthesis of arrays in the presence of conducting scatterers is presented. This method includes and takes advantage of the radiation of the scatterer by using the generalised multipole technique. Thus, the optimum solution can be obtained for an array in the presence of a conducting obstacle.

A pencil-beam pattern is synthesised, based on maximisation of the signal-to-interference-plus-noise ratio (SINR). Artificial interference is introduced and is iteratively adjusted to approximate the desired pattern. In particular, a set of linear equations is derived to find an efficient adjustment for the artificial interference which makes the iterations converge quickly.

Array pattern nulling by operating on the roots of the array polynomial in the complex plane using a genetic algorithm (GA) is demonstrated. A pattern envelope constraint and an array efficiency criterion are applied. The algorithm is much faster than a similar GA operating on the complex weights of the array factor.

A technique has been developed for the synthesis of fractal radiation patterns from concentric-ring arrays. A family of functions known as generalised Weierstrass functions, have been shown to play a key role in the theory of fractal radiation pattern synthesis. The authors examine the self-similarity relation of the array patterns.

A new technique for controlling the sidelobe level for general array pattern synthesis is presented. The basic idea is to introduce a weighting function to the performance index based on the integral of the power response over the sidelobe regions. This function more heavily weights the array power response further away from the mainlobe, so that in the minimisation of the integral of the weighted power response over the sidelobe regions, very low sidelobes can be achieved. The resulting beam pattern is highly directional. Numerical results show that the proposed technique is very effective for general array geometry sidelobe control design.

The Zolotarev polynomial distribution is optimum for difference pattern synthesis in the same sense as the Dolph-Chebyshev distribution is for sum synthesis. In this paper the results of a comprehensive numerical evaluation of Zolotarev arrays are used to summarise the principal features of the distribution. It is demonstrated that many of these characteristics parallel those of its sum counterpart. A tapered-sidelobe difference pattern synthesis technique is then outlined, which parallels the generalised Villeneuve n distribution approach of sum patterns. Just as the Villeneuve procedure provides the array excitations for a discrete 'Taylor-like' distribution directly, so the present procedure allows direct synthesis of discrete 'Bayliss-like' distributions. In addition the approach is extended to incorporate a parameter which controls the sidelobe envelope taper rate.

A general method of antenna pattern synthesis using weighted least squares is presented. The special case of linear equal spaced arrays is analysed, and three design examples are given. This design technique is compared with Woodward synthesis and with the method of Orchard, Elliott and Stern. An example using unequal spacing is also presented. The method can also be used on nonlinear arrays, for arrays with different element patterns on each element, and for near-field pattern synthesis.

A power pattern synthesis technique for mesh reflector antennas using the method of successive projections is described. The technique is computationally more efficient than the quasi-Newton technique and has applications across a wide variety of antennas.

A new simple method for accurate radiation pattern synthesis of parallel dipole arrays is described and its applications to low-sidelobe arrays with equal and unequal elements are presented.

A general technique for the synthesis of antenna power patterns is presented which does not require the calculation of derivatives. Based on the method of successive projections, it leads to a fast and simple algorithm. An example is presented for a satellite antenna giving hemispheric coverage from a directly radiating horn array.

A noniterative synthesis technique for planar arrays with arbitrary triangular lattice is described. The method, using a convolution process, synthesises the pattern nulls which may be completely arbitrary. An example of a 36-element diamond array synthesis is presented.

Increasingly stringent requirements are evolving for selective illumination of irregularly shaped geographical areas by communication-satellite antennas. The desirability of minimising spillover illumination near borders, and the technical requirement to conserve transmitter power, constrains the shape of the main beam of the antenna and the sidelobe levels. We describe a minimax optimisation algorithm for designing the required shaped-beam antennas. A 1-dimensional example is given to demonstrate the features of the method.

An iterative method is presented to find the reflector profile which minimises the mean-square error between a scattered and a desired field, thereby achieving pattern synthesis. This technique is applied to 3-dimensional circulary symmetric systems for either field- or power-pattern synthesis. Theoretical and experimental results are given for the problem of synthesising a uniform-amplitude sector beam between 20° and 66°.

Recent theoretical and experimental investigations have established the phase-mode technique for directional pattern synthesis in circular arrays of nonisotropic sources. For non-isotropic sources the possibility of phase-mode stability has emerged, indicating wideband directional patterns. In the letter a further examination analysing the shape of the element pattern for phase-mode stability is presented.