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- Dahl, Mattias, et al.
(författare)
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A New General Front-End Technique for Complex Quadratic Programming : Applications to Array Pattern Synthesis
- 2000
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents a new practical approach to complex quadratic programming which solves the broad class of complex approximation problems employing finitization of semi-infinite formulations. The approximation problem may be general with arbitrarily complex basis functions. By using a new technique, the associated semi-infinite quadratic programming problem can be solved taking advantage of the numerical stability and efficiency of conventional quadratic programming software packages. Furthermore, the optimization procedure is simple to describe theoretically and straightforward to implement in computer coding. The new design technique is therefore highly accessible. The complex approximation algorithm is versatile and can be applied to a variety of applications such as narrow-band as well as broad-band beamformers with any geometry, conventional FIR filters, digital Laguerre networks, and digital FIR equalizers. The new algorithm is formally introduced as the quadratic Dual Nested Complex Approximation (DNCA) algorithm. The essence of the new technique, justified by the Caratheodory's dimensionality theorem, is to exploit the finiteness of the related Lagrange multipliers by adapting conventional finite-dimensional quadratic programming to the semi-infinite quadratic programming re-formulation of complex approximation problems. The design criterion in our application is to minimize the side-lobe energy of an antenna array when subjected to a specified bound on the peak side-lobe level. Additional linear constraints are used to form the main-lobe. The design problem is formulated as a semi-infinite quadratic program and solved by using the new front-end applied on top of a software package for conventional finite-dimensional quadratic programming. The proposed optimization technique is applied to several numerical examples dealing with the design of a narrow-band base-station antenna array for mobile communication. The flexibility and numerical efficiency of the proposed design technique are illustrated with these examples where even hundreds of antenna elements are optimized without numerical difficulties.
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| 3. |
- Dahl, Mattias, et al.
(författare)
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Antenna Array Design using Dual Nested Complex Approximation
- 2003
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Konferensbidrag (refereegranskat)abstract
- This paper presents a new practical approach to complex Chebyshev approximation by semi-infinite linear programming. The approximation problem may be general with arbitrary complex basis functions. By the new front-end technique, the associated semi-infinite linear programming problem is solved exploiting the finiteness of the related Lagrange multipliers by adapting finite--dimensional linear programming to the dual semi--infinite problem, and thereby taking advantage of the numerical stability and efficiency of conventional linear programming software packages. Furthermore, the optimization procedure is simple to describe theoretically and straightforward to implement in computer coding. The new design technique is therefore highly accessible. The new algorithm is formally introduced as the linear Dual Nested Complex Approximation (DNCA) algorithm. The DNCA algorithm is versatile and can be applied to a variety of applications such as narrow-band as well as broad-band beamformers with any geometry, conventional Finite Impulse Response (FIR) filters, analog and digital Laguerre networks, and digital FIR equalizers. The proposed optimization technique is applied to several numerical examples dealing with the design of a narrow-band base-station antenna array for mobile communication. The flexibility and numerical efficiency of the proposed design technique are illustrated with these examples where hundreds of antenna elements are optimized without numerical difficulties.
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| 5. |
- Dahl, Mattias, et al.
(författare)
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Complex Chebyshev Optimization Using Conventional Linear Programming : A versatile and comprehensive solution
- 2000
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents a new practical approach to semi-infinite complex Chebyshev approximation. By using a new technique, the general complex Chebyshev approximation problem can be solved with arbitrary base functions taking advantage of the numerical stability and efficiency of conventional linear programming software packages. Furthermore, the optimization procedure is simple to describe theoretically and straightforward to implement in computer coding. The new design technique is therefore highly accessible. The complex approximation algorithm is general and can be applied to a variety of applications such as conventional FIR filters, narrow-band as well as broad-band beamformers with any geometry, the digital Laguerre networks, and digital FIR equalizers. The new algorithm is formally introduced as the Dual Nested Complex Approximation (DNCA) linear programming algorithm. The design example in limelight is array pattern synthesis of a mobile base-station antenna array. The corresponding design formulation is general and facilitates treatment of the solution of problems with arbitrary array geometry and side-lobe weighting. The complex approximation problem is formulated as a semi-infinite linear program and solved by using a front-end applied on top of a software package for conventional finite-dimensional linear programming. The essence of the new technique, justified by the Caratheodory dimensionality theorem, is to exploit the finiteness of the related Lagrange multipliers by adapting conventional finite-dimensional linear programming to the semi-infinite linear programming problem. The proposed optimization technique is applied to several numerical examples dealing with the design of a narrow-band base-station antenna array for mobile communication. The flexibility and numerical efficiency of the proposed design technique are illustrated with these examples where even hundreds of antenna elements are optimized without numerical difficulties.
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