A New General Front-End Technique for Complex Quadratic Programming - Applications to Array Pattern Synthesis

Document type: Researchreports
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Author(s): Mattias Dahl, Sven Nordebo, Ingvar Claesson
Title: A New General Front-End Technique for Complex Quadratic Programming - Applications to Array Pattern Synthesis
Translated title: A New General Front-End Technique for Complex Quadratic Programming - Applications to Array Pattern Synthesis
Series: Research Report
Year: 2000
Issue: 7
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 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.
Summary in Swedish: Behandlar antennarrayteknik för mobiltelefoni.
Subject: Signal Processing\Filter Design
Signal Processing\Beamforming
Signal Processing\General
URN: urn:nbn:se:bth-00163
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