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Information Theoretic Aspects of Tensor Based Multi-Domain Communication Systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Information Theoretic Aspects of Tensor Based Multi-Domain Communication Systems./
作者:	Pandey, Divyanshu.
面頁冊數:	1 online resource (286 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
Contained By:	Dissertations Abstracts International85-01B.
標題:	Families & family life. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30548684click for full text (PQDT)
ISBN:	9798379872281

Information Theoretic Aspects of Tensor Based Multi-Domain Communication Systems.
Pandey, Divyanshu.

Information Theoretic Aspects of Tensor Based Multi-Domain Communication Systems. - 1 online resource (286 pages)

Source: Dissertations Abstracts International, Volume: 85-01, Section: B.

Thesis (Ph.D.)--McGill University (Canada), 2022.

Includes bibliographical references

Most modern communication systems employ several domains for transmission and reception such as space, time, frequency, users, code sequences, and transmission media. Thus, the signals and systems involved in information transfer have an inherent multi-domain structure which can be well represented using tensors. A tensor is a multi-way array which can be seen as a higher order generalization of vectors or matrices. A unified mathematical framework capable of intuitively modelling multi-domain communication systems can be developed with the help of tensors. The use of tensors to characterize, analyze, and build multi-domain communication systems is proposed in this thesis. A generic system model is defined in this work for multi-domain communication systems with N input domains and M output domains. The multi-linear channel between such higher order input and output signals is defined as an order M +Ntensor, which couples the input and output through the Einstein product. The suggested framework is generic, where the physical interpretations of the domains can vary depending on the specific system being modelled.An information theoretic analysis of multi-domain communication systems is considered by deriving the Shannon capacity and input power allocation for a fixed higher order tensor channel under a family of power constraints. Owing to the multi-domain nature of the input signals, the power constraints in multi-domain communication systems can span one or more domains. This thesis demonstrates the tensor framework's ability to mathematically represent a variety of such power constraints. Shannon capacity of tensor channels under such family of power constraints is derived. Water-filling is extended from a matrix setting to higher domains in such a tensor-based formulation, encapsulating the impact of various domains and allowing collaborative multi-domain precoding and power allocation. It is also shown that as the number of domains increases, the multiplexing gain for a tensor channel can increase exponentially, indicating the ability of the tensor-based communication systems to offer the enormous information transmission rates required for beyond 5G systems. In addition, this thesis illustrates how the tensor framework can be used to characterize the capacity and rate regions of multi-user MIMO channels. The tensor-based technique leads to a coordinated users transmission scheme. The tensor framework treats the multi-domain interference terms as information bearing entities, and thus ensures higher achievable sum rates as compared to the independent users transmissions.Further, the Einstein Product of tensors is used to develop a framework for minimum mean square error (MMSE) estimation for multi-domain signals and data. Both proper and improper complex tensors are addressed by the framework. The traditional linear and widely linear MMSE estimators are extended to the tensor setting, resulting in multilinear and widely multi-linear MMSE estimation. Further, a relation between the MMSE error covariance tensor and the gradient of the mutual information is extended from a vector setting to tensors, known as the tensor I-MMSE relation. Furthermore, the tensor IMMSE relation is used to find the capacity of tensor channels when the input is drawn from arbitrary distributions. In the presence of circularly symmetric Gaussian noise and under no constraint on the input constellation, an input drawn from a circularly symmetric Gaussian distribution achieves the channel capacity. However, under practical scenarios, the input is often drawn from discrete signalling constellations which are far from Gaussian distributed. By making use of the tensor I-MMSE relation, an iterative precoder is developed in this thesis which achieves capacity of the tensor channels when the input is limited by the choice of signalling constellations.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379872281Subjects--Topical Terms:

3422406
Families & family life.
Index Terms--Genre/Form:

542853
Electronic books.

Information Theoretic Aspects of Tensor Based Multi-Domain Communication Systems.
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500 $a Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
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502 $a Thesis (Ph.D.)--McGill University (Canada), 2022.
504 $a Includes bibliographical references
520 $a Most modern communication systems employ several domains for transmission and reception such as space, time, frequency, users, code sequences, and transmission media. Thus, the signals and systems involved in information transfer have an inherent multi-domain structure which can be well represented using tensors. A tensor is a multi-way array which can be seen as a higher order generalization of vectors or matrices. A unified mathematical framework capable of intuitively modelling multi-domain communication systems can be developed with the help of tensors. The use of tensors to characterize, analyze, and build multi-domain communication systems is proposed in this thesis. A generic system model is defined in this work for multi-domain communication systems with N input domains and M output domains. The multi-linear channel between such higher order input and output signals is defined as an order M +Ntensor, which couples the input and output through the Einstein product. The suggested framework is generic, where the physical interpretations of the domains can vary depending on the specific system being modelled.An information theoretic analysis of multi-domain communication systems is considered by deriving the Shannon capacity and input power allocation for a fixed higher order tensor channel under a family of power constraints. Owing to the multi-domain nature of the input signals, the power constraints in multi-domain communication systems can span one or more domains. This thesis demonstrates the tensor framework's ability to mathematically represent a variety of such power constraints. Shannon capacity of tensor channels under such family of power constraints is derived. Water-filling is extended from a matrix setting to higher domains in such a tensor-based formulation, encapsulating the impact of various domains and allowing collaborative multi-domain precoding and power allocation. It is also shown that as the number of domains increases, the multiplexing gain for a tensor channel can increase exponentially, indicating the ability of the tensor-based communication systems to offer the enormous information transmission rates required for beyond 5G systems. In addition, this thesis illustrates how the tensor framework can be used to characterize the capacity and rate regions of multi-user MIMO channels. The tensor-based technique leads to a coordinated users transmission scheme. The tensor framework treats the multi-domain interference terms as information bearing entities, and thus ensures higher achievable sum rates as compared to the independent users transmissions.Further, the Einstein Product of tensors is used to develop a framework for minimum mean square error (MMSE) estimation for multi-domain signals and data. Both proper and improper complex tensors are addressed by the framework. The traditional linear and widely linear MMSE estimators are extended to the tensor setting, resulting in multilinear and widely multi-linear MMSE estimation. Further, a relation between the MMSE error covariance tensor and the gradient of the mutual information is extended from a vector setting to tensors, known as the tensor I-MMSE relation. Furthermore, the tensor IMMSE relation is used to find the capacity of tensor channels when the input is drawn from arbitrary distributions. In the presence of circularly symmetric Gaussian noise and under no constraint on the input constellation, an input drawn from a circularly symmetric Gaussian distribution achieves the channel capacity. However, under practical scenarios, the input is often drawn from discrete signalling constellations which are far from Gaussian distributed. By making use of the tensor I-MMSE relation, an iterative precoder is developed in this thesis which achieves capacity of the tensor channels when the input is limited by the choice of signalling constellations.
520 $a La plupart des systemes de communication modernes recourent a une variete de domaines pour la transmission et la reception d'information, tels l'espace, le temps, la frequence, les utilisateurs, et les supports de transmission. Par consequent, les signaux et les systemes impliques dans le transfert d'information possedent une structure a plusieurs domaines, qui peut etre representee par des tenseurs. Les tenseurs sont au coeur du developpement d'un cadre mathematique unifie et intuitif pour la modelisation des systemes de communications a plusieurs domaines. Le deploiement de tenseurs pour caracteriser, analyser et concevoir ces systemes est propose dans cette these. Un modele y est defini pour les systemes de communications comportant N domaines d'entree et M domaines de sortie. Le canal multilineaire entre ces signaux d'entree et de sorties est defini par un tenseur d'ordre M+N, reliant les entrees aux sorties par le truchement du produit d'Einstein. Le cadre expose est general, les interpretations physiques des domaines pouvant varier selon le systeme specifique modelise.Une analyse fondee sur la theorie de l'information est conduite en etablissant la capacite de Shannon et la repartition de la puissance d'entree pour un canal tensoriel d'ordre fixe soumis a une famille de contraintes relatives a la puissance. Le caractere a plusieurs domaines des signaux d'entrees fait en sorte que ces contraintes s'appliquent a un ou plusieurs domaines. Cette these demontre que le cadre tensoriel peut representer mathematiquement une variete de contraintes relatives a la puissance. L'algorithme du water-filling est generalise a une formulation tensorielle, combinant l'incidence de chaque domaine, le precodage et la repartition de la puissance entre les domaines de maniere collaborative. De plus, on montre que le gain de multiplexage pour un canal tensoriel croit exponentiellement a mesure que le nombre de domaines augmente, indiquant la capacite des systemes de communications deployant les tenseurs a fournir les hauts debits d'information requis par les technologies au-dela du 5G. Cette these illustre egalement comment le cadre tensoriel permet de caracteriser la capacite et les regions de capacite de systemes MIMO a plusieurs utilisateurs. La technique s'appuyant sur les tenseurs mene a un schema de transmission d'utilisateurs coordonnes. Le cadre tensoriel traite les termes d'interference multi-domaines en tant qu'entites porteuses d'information, assurant ainsi des sum ratesrealisables superieurs comparativement aux transmissions d'utilisateurs independants.En outre, le produit d'Einstein des tenseurs est employe dans le developpement d'un cadre d'estimation de l'erreur quadratique moyenne minimale (MMSE) pour les signaux et les donnees multi-domaines. Les tenseurs complexes propres et impropres sont pris en compte dans ce cadre. Les estimateurs MMSE traditionnels lineaires et largement lineaires sont etendus au cadre tensoriel, donnant lieu a une estimation MMSE multi-lineaire et largement multi-lineaire. Une relation entre le tenseur de covariance de l'erreur MMSE et le gradient de l'information mutuelle est etendue d'un cadre vectoriel aux tenseurs, sous le nom de relation I-MMSE du tenseur. De meme, la relation I-MMSE tensorielle est utilisee pour trouver la capacite des canaux tensoriels lorsque l'entree est tiree de distributions arbitraires. En presence d'un bruit gaussien a symetrie circulaire et sans contrainte sur la constellation de signalisation d'entree, une entree tiree d'une distribution gaussienne a symetrie circulaire atteint la capacite du canal. Toutefois, l'entree en pratique est souvent tiree de constellations discretes qui sont loin d'etre distribuees normalement. En mettant a profit la relation I-MMSE tensorielle, un precodeur iteratif est developpe dans cette these et atteint la capacite des canaux tensoriels lorsque l'entree est limitee par le choix des constellations de signalisation.
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