A likelihood ratio analysis of digital phase modulation

 

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dc.contributor.author Schoonees, Johann August en_ZA
dc.date.accessioned 2016-05-09T08:55:59Z
dc.date.available 2016-05-09T08:55:59Z
dc.date.issued 1998 en_ZA
dc.identifier.citation Schoonees, J. 1998. A likelihood ratio analysis of digital phase modulation. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/19508
dc.description Bibliography: p. 180-188. en_ZA
dc.description.abstract Although the likelihood ratio forms the theoretical basis for maximum likelihood (ML) detection in coherent digital communication systems, it has not been applied directly to the problem of designing good trellis-coded modulation (TOM) schemes. The remarkably simple optimal receiver of minimum shift keying (MSK) has been shown to result from the mathematical simplification of its likelihood ratio into a single term. The log-likelihood ratio then becomes a linear sum of metrics which can be implemented as a so-called simplified receiver, comprising only a few adders and delay elements. This thesis project investigated the possible existence of coded modulation schemes with similarly simplifying likelihood ratios, which would have almost trivially simple receivers compared to the Viterbi decoders which are typically required for maximum likelihood sequence estimation (MLSE). A useful notation, called the likelihood transform, was presented to aid the analysis of likelihood ratios. The work concentrated initially on computer-aided searches, first for trellis codes which may give rise to simplifying likelihood ratios for continuous phase modulation (CPM), and then for mathematical identities which may aid in the simplification of generic likelihood ratios for equal-energy modulation. The first search yielded no simplified receivers, and all the identities produced by the second search had structures similar to the likelihood ratio of MSK. These observations prompted a formal proof of the non-existence of simplified receivers which use information from more than two symbols in their observation period. This result strictly bounds the error performance that is possible with a simplified receiver. It was also proved that simplified receivers are only optimal for modulation schemes which use no more than two pairs of antipodal signals, and that only binary modulation schemes can have simplified receivers which use information from all the symbols in their observation period. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Electrical Engineering en_ZA
dc.title A likelihood ratio analysis of digital phase modulation en_ZA
dc.type Doctoral Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Engineering and the Built Environment
dc.publisher.department Department of Electrical Engineering en_ZA
dc.type.qualificationlevel Doctoral
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Schoonees, J. A. (1998). <i>A likelihood ratio analysis of digital phase modulation</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering. Retrieved from http://hdl.handle.net/11427/19508 en_ZA
dc.identifier.chicagocitation Schoonees, Johann August. <i>"A likelihood ratio analysis of digital phase modulation."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering, 1998. http://hdl.handle.net/11427/19508 en_ZA
dc.identifier.vancouvercitation Schoonees JA. A likelihood ratio analysis of digital phase modulation. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering, 1998 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/19508 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Schoonees, Johann August AB - Although the likelihood ratio forms the theoretical basis for maximum likelihood (ML) detection in coherent digital communication systems, it has not been applied directly to the problem of designing good trellis-coded modulation (TOM) schemes. The remarkably simple optimal receiver of minimum shift keying (MSK) has been shown to result from the mathematical simplification of its likelihood ratio into a single term. The log-likelihood ratio then becomes a linear sum of metrics which can be implemented as a so-called simplified receiver, comprising only a few adders and delay elements. This thesis project investigated the possible existence of coded modulation schemes with similarly simplifying likelihood ratios, which would have almost trivially simple receivers compared to the Viterbi decoders which are typically required for maximum likelihood sequence estimation (MLSE). A useful notation, called the likelihood transform, was presented to aid the analysis of likelihood ratios. The work concentrated initially on computer-aided searches, first for trellis codes which may give rise to simplifying likelihood ratios for continuous phase modulation (CPM), and then for mathematical identities which may aid in the simplification of generic likelihood ratios for equal-energy modulation. The first search yielded no simplified receivers, and all the identities produced by the second search had structures similar to the likelihood ratio of MSK. These observations prompted a formal proof of the non-existence of simplified receivers which use information from more than two symbols in their observation period. This result strictly bounds the error performance that is possible with a simplified receiver. It was also proved that simplified receivers are only optimal for modulation schemes which use no more than two pairs of antipodal signals, and that only binary modulation schemes can have simplified receivers which use information from all the symbols in their observation period. DA - 1998 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1998 T1 - A likelihood ratio analysis of digital phase modulation TI - A likelihood ratio analysis of digital phase modulation UR - http://hdl.handle.net/11427/19508 ER - en_ZA


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