Calculation the infinite norm ball of constant modulus receivers by D-K iterations

Tenqchen Shing; Ying Haw Shu; Ming Chang Sun; Wu Shiung Feng

doi:10.1109/SIPS.2003.1235656

Calculation the infinite norm ball of constant modulus receivers by D-K iterations

Tenqchen Shing
, Ying Haw Shu
, Ming Chang Sun
, Wu Shiung Feng

Department of Electronic Engineering

National Taiwan University
Chunghwa Telecom Co. Ltd.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We propose a method to calculate the infinite norm ball for the geometrical characterization of the constant modulus algorithm (CMA) and O. Shalvi and E. Weinstein's blind estimation of linear receivers (IEEE Trans. Inform. Theory, vol.36, no.2, p.312-20, 1990). The constant modulus algorithm uses the second and fourth order moments of a pre-whitened chip-rate received signal. The approach provides a framework within which various blind and non-blind Wiener receivers can find an ellipsoid by infinite norm balls of different types. A necessary and sufficient condition for equivalence among constant modulus, Shalvi-Weinstein, zero-forcing, and Wiener receivers is obtained. Their locations and their relationship with Wiener receivers are provided for the special orthogonal channel and general two-dimensional (2D) channel-receiver impulse response. It is also shown from the calculation of the infinite norm ball via D-K iterations in 2D, that each CM or SW receiver can be obtained associated with one and only one Wiener receiver for a QAM system. Some design examples are simulated to verify our results.

Original language	English
Title of host publication	2003 IEEE Workshop on Signal Processing Systems
Subtitle of host publication	Design and Implementation, SIPS 2003
Editors	Wonyong Sung, Myung Hoon Sunwoo
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	126-132
Number of pages	7
ISBN (Electronic)	0780377958
DOIs	https://doi.org/10.1109/SIPS.2003.1235656
State	Published - 2003
Event	2003 IEEE Workshop on Signal Processing Systems, SIPS 2003 - Seoul, Korea, Republic of Duration: 27 08 2003 → 29 08 2003

Publication series

Name	IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation
Volume	2003-January
ISSN (Print)	1520-6130

Conference

Conference	2003 IEEE Workshop on Signal Processing Systems, SIPS 2003
Country/Territory	Korea, Republic of
City	Seoul
Period	27/08/03 → 29/08/03

Bibliographical note

Publisher Copyright:
© 2003 IEEE.

Keywords

Blind equalizers
Cost function
Ellipsoids
Quadrature amplitude modulation
Random variables
Stochastic processes
Sufficient conditions
Sun
Two dimensional displays
Vectors

Access to Document

10.1109/SIPS.2003.1235656

Cite this

Shing, T., Shu, Y. H., Sun, M. C., & Feng, W. S. (2003). Calculation the infinite norm ball of constant modulus receivers by D-K iterations. In W. Sung, & M. H. Sunwoo (Eds.), 2003 IEEE Workshop on Signal Processing Systems: Design and Implementation, SIPS 2003 (pp. 126-132). Article 1235656 (IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation; Vol. 2003-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SIPS.2003.1235656

Shing, Tenqchen ; Shu, Ying Haw ; Sun, Ming Chang et al. / Calculation the infinite norm ball of constant modulus receivers by D-K iterations. 2003 IEEE Workshop on Signal Processing Systems: Design and Implementation, SIPS 2003. editor / Wonyong Sung ; Myung Hoon Sunwoo. Institute of Electrical and Electronics Engineers Inc., 2003. pp. 126-132 (IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation).

@inproceedings{ae980c7c36c4427ba8cf8c4c432104b4,

title = "Calculation the infinite norm ball of constant modulus receivers by D-K iterations",

abstract = "We propose a method to calculate the infinite norm ball for the geometrical characterization of the constant modulus algorithm (CMA) and O. Shalvi and E. Weinstein's blind estimation of linear receivers (IEEE Trans. Inform. Theory, vol.36, no.2, p.312-20, 1990). The constant modulus algorithm uses the second and fourth order moments of a pre-whitened chip-rate received signal. The approach provides a framework within which various blind and non-blind Wiener receivers can find an ellipsoid by infinite norm balls of different types. A necessary and sufficient condition for equivalence among constant modulus, Shalvi-Weinstein, zero-forcing, and Wiener receivers is obtained. Their locations and their relationship with Wiener receivers are provided for the special orthogonal channel and general two-dimensional (2D) channel-receiver impulse response. It is also shown from the calculation of the infinite norm ball via D-K iterations in 2D, that each CM or SW receiver can be obtained associated with one and only one Wiener receiver for a QAM system. Some design examples are simulated to verify our results.",

keywords = "Blind equalizers, Cost function, Ellipsoids, Quadrature amplitude modulation, Random variables, Stochastic processes, Sufficient conditions, Sun, Two dimensional displays, Vectors",

author = "Tenqchen Shing and Shu, \{Ying Haw\} and Sun, \{Ming Chang\} and Feng, \{Wu Shiung\}",

note = "Publisher Copyright: {\textcopyright} 2003 IEEE.; 2003 IEEE Workshop on Signal Processing Systems, SIPS 2003 ; Conference date: 27-08-2003 Through 29-08-2003",

year = "2003",

doi = "10.1109/SIPS.2003.1235656",

language = "英语",

series = "IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "126--132",

editor = "Wonyong Sung and Sunwoo, \{Myung Hoon\}",

booktitle = "2003 IEEE Workshop on Signal Processing Systems",

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}

Shing, T, Shu, YH, Sun, MC & Feng, WS 2003, Calculation the infinite norm ball of constant modulus receivers by D-K iterations. in W Sung & MH Sunwoo (eds), 2003 IEEE Workshop on Signal Processing Systems: Design and Implementation, SIPS 2003., 1235656, IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation, vol. 2003-January, Institute of Electrical and Electronics Engineers Inc., pp. 126-132, 2003 IEEE Workshop on Signal Processing Systems, SIPS 2003, Seoul, Korea, Republic of, 27/08/03. https://doi.org/10.1109/SIPS.2003.1235656

Calculation the infinite norm ball of constant modulus receivers by D-K iterations. / Shing, Tenqchen; Shu, Ying Haw; Sun, Ming Chang et al.
2003 IEEE Workshop on Signal Processing Systems: Design and Implementation, SIPS 2003. ed. / Wonyong Sung; Myung Hoon Sunwoo. Institute of Electrical and Electronics Engineers Inc., 2003. p. 126-132 1235656 (IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation; Vol. 2003-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Sun, Ming Chang

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N2 - We propose a method to calculate the infinite norm ball for the geometrical characterization of the constant modulus algorithm (CMA) and O. Shalvi and E. Weinstein's blind estimation of linear receivers (IEEE Trans. Inform. Theory, vol.36, no.2, p.312-20, 1990). The constant modulus algorithm uses the second and fourth order moments of a pre-whitened chip-rate received signal. The approach provides a framework within which various blind and non-blind Wiener receivers can find an ellipsoid by infinite norm balls of different types. A necessary and sufficient condition for equivalence among constant modulus, Shalvi-Weinstein, zero-forcing, and Wiener receivers is obtained. Their locations and their relationship with Wiener receivers are provided for the special orthogonal channel and general two-dimensional (2D) channel-receiver impulse response. It is also shown from the calculation of the infinite norm ball via D-K iterations in 2D, that each CM or SW receiver can be obtained associated with one and only one Wiener receiver for a QAM system. Some design examples are simulated to verify our results.

AB - We propose a method to calculate the infinite norm ball for the geometrical characterization of the constant modulus algorithm (CMA) and O. Shalvi and E. Weinstein's blind estimation of linear receivers (IEEE Trans. Inform. Theory, vol.36, no.2, p.312-20, 1990). The constant modulus algorithm uses the second and fourth order moments of a pre-whitened chip-rate received signal. The approach provides a framework within which various blind and non-blind Wiener receivers can find an ellipsoid by infinite norm balls of different types. A necessary and sufficient condition for equivalence among constant modulus, Shalvi-Weinstein, zero-forcing, and Wiener receivers is obtained. Their locations and their relationship with Wiener receivers are provided for the special orthogonal channel and general two-dimensional (2D) channel-receiver impulse response. It is also shown from the calculation of the infinite norm ball via D-K iterations in 2D, that each CM or SW receiver can be obtained associated with one and only one Wiener receiver for a QAM system. Some design examples are simulated to verify our results.

KW - Blind equalizers

KW - Cost function

KW - Ellipsoids

KW - Quadrature amplitude modulation

KW - Random variables

KW - Stochastic processes

KW - Sufficient conditions

KW - Sun

KW - Two dimensional displays

KW - Vectors

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M3 - 会议稿件

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SP - 126

EP - 132

BT - 2003 IEEE Workshop on Signal Processing Systems

A2 - Sung, Wonyong

A2 - Sunwoo, Myung Hoon

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2003 IEEE Workshop on Signal Processing Systems, SIPS 2003

Y2 - 27 August 2003 through 29 August 2003

ER -

Shing T, Shu YH, Sun MC, Feng WS. Calculation the infinite norm ball of constant modulus receivers by D-K iterations. In Sung W, Sunwoo MH, editors, 2003 IEEE Workshop on Signal Processing Systems: Design and Implementation, SIPS 2003. Institute of Electrical and Electronics Engineers Inc. 2003. p. 126-132. 1235656. (IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation). doi: 10.1109/SIPS.2003.1235656

Calculation the infinite norm ball of constant modulus receivers by D-K iterations

Abstract

Publication series

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Bibliographical note

Keywords

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