Finite sample identifiability of multiple constant modulus sources

Amir Leshem; Nicolas Petrochilos; Alle Jan Van Der Veen

doi:10.1109/sam.2002.1191071

Finite sample identifiability of multiple constant modulus sources

Amir Leshem
, Nicolas Petrochilos
, Alle Jan Van Der Veen

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

3 Scopus citations

Abstract

We prove that mixtures of continuous constant modulus sources can be identified with probability 1 with a finite number of samples (under noise-free conditions). This strengthens earlier results which only considered an infinite number of samples. The proof is based on the linearization technique of the Analytical Constant Modulus Algorithm, together with a simple inductive argument. We then study the finite alphabet case. In this case we provide an upper bound on the probability of non-identifiability for finite sample of sources. We show that under practical assumptions, this upper bound is tighter than the currently known bound.

Original language	English
Title of host publication	2002 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAME 2002
Publisher	IEEE Computer Society
Pages	408-412
Number of pages	5
ISBN (Electronic)	0780375513
DOIs	https://doi.org/10.1109/sam.2002.1191071
State	Published - 2002
Externally published	Yes
Event	IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2002 - Rosslyn, United States Duration: 4 Aug 2002 → 6 Aug 2002

Publication series

Name	Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
Volume	2002-January
ISSN (Electronic)	2151-870X

Conference

Conference	IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2002
Country/Territory	United States
City	Rosslyn
Period	4/08/02 → 6/08/02

Bibliographical note

Publisher Copyright:
© 2002 IEEE.

Keywords

Blind source separation
Chernoff bound
Constant modulus signals
Finite sample analysis
Identifiability
Large deviations
PSK

Access to Document

10.1109/sam.2002.1191071

Cite this

Leshem, A., Petrochilos, N., & Van Der Veen, A. J. (2002). Finite sample identifiability of multiple constant modulus sources. In 2002 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAME 2002 (pp. 408-412). Article 1191071 (Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop; Vol. 2002-January). IEEE Computer Society. https://doi.org/10.1109/sam.2002.1191071

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abstract = "We prove that mixtures of continuous constant modulus sources can be identified with probability 1 with a finite number of samples (under noise-free conditions). This strengthens earlier results which only considered an infinite number of samples. The proof is based on the linearization technique of the Analytical Constant Modulus Algorithm, together with a simple inductive argument. We then study the finite alphabet case. In this case we provide an upper bound on the probability of non-identifiability for finite sample of sources. We show that under practical assumptions, this upper bound is tighter than the currently known bound.",

keywords = "Blind source separation, Chernoff bound, Constant modulus signals, Finite sample analysis, Identifiability, Large deviations, PSK",

author = "Amir Leshem and Nicolas Petrochilos and \{Van Der Veen\}, \{Alle Jan\}",

note = "Publisher Copyright: {\textcopyright} 2002 IEEE.; IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2002 ; Conference date: 04-08-2002 Through 06-08-2002",

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doi = "10.1109/sam.2002.1191071",

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Leshem, A, Petrochilos, N & Van Der Veen, AJ 2002, Finite sample identifiability of multiple constant modulus sources. in 2002 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAME 2002., 1191071, Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop, vol. 2002-January, IEEE Computer Society, pp. 408-412, IEEE Sensor Array and Multichannel Signal Processing Workshop, SAME 2002, Rosslyn, United States, 4/08/02. https://doi.org/10.1109/sam.2002.1191071

Finite sample identifiability of multiple constant modulus sources. / Leshem, Amir; Petrochilos, Nicolas; Van Der Veen, Alle Jan.
2002 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAME 2002. IEEE Computer Society, 2002. p. 408-412 1191071 (Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop; Vol. 2002-January).

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

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AB - We prove that mixtures of continuous constant modulus sources can be identified with probability 1 with a finite number of samples (under noise-free conditions). This strengthens earlier results which only considered an infinite number of samples. The proof is based on the linearization technique of the Analytical Constant Modulus Algorithm, together with a simple inductive argument. We then study the finite alphabet case. In this case we provide an upper bound on the probability of non-identifiability for finite sample of sources. We show that under practical assumptions, this upper bound is tighter than the currently known bound.

KW - Blind source separation

KW - Chernoff bound

KW - Constant modulus signals

KW - Finite sample analysis

KW - Identifiability

KW - Large deviations

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Finite sample identifiability of multiple constant modulus sources

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