Introduction to linear and nonlinear programming

Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

With the demanding system requirements for the fifth-generation (5G) wireless communications and the severe spectrum shortage at conventional cellular frequencies, multibeam antenna systems operating in the millimeter-wave frequency bands have attracted a lot of research interest and have been actively investigated. They represent the key antenna technology for supporting a high data transmission rate, an improved signal-to-interference-plus-noise ratio, an increased spectral and energy efficiency, and versatile beam shaping, thereby holding a great promise in serving as the critical infrastructure for enabling beamforming and massive multiple-input multiple-output (MIMO) that boost the 5G. This paper provides an overview of the existing multibeam antenna technologies which include the passive multibeam antennas (MBAs) based on quasi-optical components and beamforming circuits, multibeam phased-array antennas enabled by various phase-shifting methods, and digital MBAs with different system architectures. Specifically, their principles of operation, design, and implementation, as well as a number of illustrative application examples are reviewed. Finally, the suitability of these MBAs for the future 5G massive MIMO wireless systems as well as the associated challenges is discussed.

Multibeam Antenna Technologies for 5G Wireless Communications

The proliferation of wireless services is driving innovative phased array solutions that are able to provide better cost/performance tradeoffs. In this context, the use of irregular array architectures provides a viable solution. This paper reviews and highlights some of the most recent advances in this field, including clustered, thinned, sparse, and time-modulated arrays, and their proposed design methodologies.

Unconventional Phased Array Architectures and Design Methodologies—A Review

From the material presented here, it is clear that the theory underlying the SNF approach is complex and involved to implement. However, it is also very elegant and provides one with many measurement options and powerful capabilities. The numerical implementation of the theory can be efficiently deployed through the use of the fast Fourier transform (FFT) enabling transforms of even electrically large antennas to be accomplished in a matter of a few seconds on a modern powerful digital computer. With the advent of commercially available SNF test systems, the user can exploit these techniques, largely unimpeded by the burden of the theory or the implementation thereof. The material presented here highlighted some of the fundamental concepts and limitations the user needs to be aware of in order to use these test systems with confidence.

/pdf/spherical-near-field-antenna-measurements-5bm37osur0.pdf

Spherical near-field antenna measurements

An iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented The algorithm consists in solving a sequence of weighted l1 convex optimization problems The method can thus be readily implemented and efficiently solved In the optimization procedure, the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements The method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns Numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach, whose computation time is several orders of magnitude below those of so-called global optimization algorithms

/pdf/synthesis-of-sparse-arrays-with-focused-or-shaped-mbqud2fe2v.pdf

Synthesis of Sparse Arrays With Focused or Shaped Beampattern via Sequential Convex Optimizations

The substrate integrated waveguide (SIW) technology allows to construct several types of commonly used antennas in a planar way. However, some practical constraints limit their performances when frequencies below 20 GHz are considered. In the case of SIW horn antennas, the available substrates are much thinner than the wavelength yielding to poor matching and undesired back radiation. In this paper, an innovative structure to overcome these limitations is presented. It consists of a transition printed on the same SIW substrate, which improves both the radiation and the matching performances of conventional SIW horns. The horn shape is also further optimized by reducing its dimensions required for a given directivity. This is obtained by modifying the horn profile in order to effectively combine different TE modes. Guidelines are provided to design this type of thin and compact SIW horn antenna. They were applied to manufacture a prototype in the Ku-band with a substrate thinner than λ0/10. Measurement results validate the proposed concepts showing excellent performances.

/pdf/novel-thin-and-compact-h-plane-siw-horn-antenna-50d33wak0g.pdf

Novel Thin and Compact H-Plane SIW Horn Antenna

The substrate integrated waveguide (SIW) technology allows to construct several types of commonly used antennas in a planar way. However, frequency limitations associated to commercial substrates appear in the implementation of certain types of antennas, e.g., SIW horn antennas are not well matched when the substrate thickness is much smaller than the wavelength. A printed transition is proposed to overcome this problem. Differently from current solutions, no bulky elements are required allowing to maintain the most important features of this technology namely its compactness and ease of manufacturing. In order to quickly analyze and design the transition, both a coupled resonator and a transmission line models are developed, together with design guidelines. The proposed transition is designed to match a H-plane SIW horn antenna built in a thin substrate $({\rm thickness} at different frequency bands at the Ku-band. Experimental results for 3 different transitions show that the matching characteristics are efficiently improved compared with the conventional SIW horn antenna and validates the proposed models.

A Printed Transition for Matching Improvement of SIW Horn Antennas

A general procedure to solve efficiently non convex array synthesis problems is presented. It is based on the SemiDefinite Relaxation (SDR) technique. The way to properly relax the constraints in order to formulate the synthesis of shaped beams, phase-only arrays and reconfigurable arrays as semidefinite programming problems is detailed. These so-approximated array synthesis problems are then convex, easy to implement and can be efficiently solved using off-the-shelf numerical routines. The conditions under which the relaxed problems provide the optimal solution to the original non convex synthesis problems are specified. Various representative numerical comparisons with arrays designed by other approaches show the validity of the proposed method and illustrate its potentialities.

Application of Convex Relaxation to Array Synthesis Problems

This work presents the analysis of the influence of insulation on implanted antennas for biotelemetry applications in the Medical Device Radiocommunications Service band. Our goal is finding the insulation properties that facilitate power transmission, thus enhancing the communication between the implanted antenna and an external receiver. For this purpose, it has been found that a simplified model of human tissues based on spherical geometries excited by ideal sources (electric dipole, magnetic dipole and Huygens source) provides reasonable accuracy while remaining very tractable due to its analytical formulation. Our results show that a proper choice of the biocompatible internal insulation material can improve the radiation efficiency of the implanted antenna (up to six times for the investigated cases). External insulation facilitates the electromagnetic transition from the biological tissue to the outer free space, reducing the power absorbed by the human body. Summarizing, this work gives insights on the enhancement of power transmission, obtained with the use of both internal, biocompatible and external, flexible insulations. Therefore, it provides useful information for the design of implanted antennas.

/pdf/the-effect-of-insulating-layers-on-the-performance-of-517gknu6sm.pdf

Benjamin Fuchs

Papers

Synthesis of Sparse Arrays With Focused or Shaped Beampattern via Sequential Convex Optimizations

Novel Thin and Compact H-Plane SIW Horn Antenna

A Printed Transition for Matching Improvement of SIW Horn Antennas

Application of Convex Relaxation to Array Synthesis Problems

The Effect of Insulating Layers on the Performance of Implanted Antennas