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DTSTAMP:20261004T101021Z
DESCRIPTION: \n\nAbstract\n\nMost modern communication systems employ sever
 al 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 st
 ructure which can be well represented using tensors. A tensor is a multi-w
 ay array which can be seen as a higher order generalization of vectors or 
 matrices. A unified mathematical framework capable of intuitively modellin
 g multi-domain communication systems can be developed with the help of ten
 sors. The use of tensors to characterize\, analyze\, and build multi-domai
 n communication systems is proposed in this thesis. A generic system model
  is defined in this work for multi-domain communication systems with N inp
 ut domains and M output domains. The multi-linear channel between such hig
 her order input and output signals is defined as an order M+N tensor\, whi
 ch couples the input and output through the Einstein product. The suggeste
 d framework is generic\, where the physical interpretations of the domains
  can vary depending on the specific system being modelled.\n\nAn informati
 on theoretic analysis of multi-domain communication systems is considered 
 by deriving the Shannon capacity and input power allocation for a fixed hi
 gher order tensor channel under a family of power constraints. Owing to th
 e multi-domain nature of the input signals\, the power constraints in mult
 i-domain communication systems can span one or more domains. This thesis d
 emonstrates the tensor framework's ability to mathematically represent a v
 ariety of such power constraints. Shannon capacity of tensor channels unde
 r such family of power constraints is derived. Water-filling is extended f
 rom a matrix setting to higher domains in such a tensor-based formulation\
 , encapsulating the impact of various domains and allowing collaborative m
 ulti-domain precoding and power allocation. It is also shown that as the n
 umber of domains increases\, the multiplexing gain for a tensor channel ca
 n increase exponentially\, indicating the ability of the tensor-based comm
 unication systems to offer the enormous information transmission rates req
 uired for beyond 5G systems. In addition\, this thesis illustrates how the
  tensor framework can be used to characterize the capacity and rate region
 s of multi-user MIMO channels. The tensor-based technique leads to a coord
 inated users transmission scheme. The tensor framework treats the multi-do
 main interference terms as information bearing entities\, and thus ensures
  higher achievable sum rates as compared to the independent users transmis
 sions.\n\nFurther\, the Einstein Product of tensors is used to develop a f
 ramework for minimum mean square error (MMSE) estimation for multi-domain 
 signals and data. Both proper and improper complex tensors are addressed b
 y the framework. The traditional linear and widely linear MMSE estimators 
 are extended to the tensor setting\, resulting in multi-linear and widely 
 multi-linear MMSE estimation. Further\, a relation between the MMSE error 
 covariance tensor and the gradient of the mutual information is extended f
 rom a vector setting to tensors\, known as the tensor I-MMSE relation. Fur
 thermore\, the tensor I-MMSE relation is used to find the capacity of tens
 or channels when the input is drawn from arbitrary distributions. In the p
 resence of circularly symmetric Gaussian noise and under no constraint on 
 the input constellation\, an input drawn from a circularly symmetric Gauss
 ian distribution achieves the channel capacity. However\, under practical 
 scenarios\, the input is often drawn from discrete signalling constellatio
 ns which are far from Gaussian distributed. By making use of the tensor I-
 MMSE relation\, an iterative precoder is developed in this thesis which ac
 hieves capacity of the tensor channels when the input is limited by the ch
 oice of signalling constellations.\n
DTSTART:20221003T180000Z
DTEND:20221003T200000Z
LOCATION:\, Room 603\, McConnell Engineering Building\, CA\, QC\, Montreal\
 , H3A 0E9\, 3480 rue University
SUMMARY:PhD defence of Divyanshu Pandey - Information theoretic aspects of 
 tensor based multi-domain communication systems
URL:https://www.mcgill.ca/ece/channels/event/phd-defence-divyanshu-pandey-i
 nformation-theoretic-aspects-tensor-based-multi-domain-communication-34249
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