Complex Chebyshev Optimization Using Conventional Linear Programming - A versatile and comprehensive solution

Document type: Researchreports
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Author(s): Mattias Dahl, Sven Nordebo, Ingvar Claesson
Title: Complex Chebyshev Optimization Using Conventional Linear Programming - A versatile and comprehensive solution
Series: Research Report
Year: 2000
Issue: 6
ISSN: 1103-1581
Organization: Blekinge Institute of Technology
Department: Department of Telecommunications and Signal Processing (Institutionen för telekommunikation och signalbehandling)
Department of Telecommunications and Signal Processing S-372 25 Ronneby
+46 455 780 00
Authors e-mail: Mattias.Dahl@its.hk-r.se
Language: English
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.
Summary in Swedish: Behandlar antennarray teknik för mobiltelefoni.
Subject: Signal Processing\Filter Design
Signal Processing\Beamforming
Signal Processing\General
URN: urn:nbn:se:bth-00150
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