Sphere-packing bounds in the Grassmann and Stiefel manifolds

Henkel, O.

doi:10.1109/tit.2005.855594

Cited by 76 publications

(87 citation statements)

References 16 publications

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“… Stiefel manifold: According to [8], [13], Stiefel manifold provides better optimization with quick convergence. Emplying this Stiefel manifold technique, matrice obtained from Stiefel manifold enhances the receiver optimization of the basic and massive MIMO system.…”

Section: B Types Of Manifolds With Feedbackmentioning

confidence: 99%

“…In Stiefel manifold, Q is full column rank matrix which has unique solution. According to [13], Stiefel manifold can be employed in the feedback channel of the basic and massive MIMO system where dimensions of matrices could be controlled through this manifold. The space of orthonormal matrices, which is rectangular with k < n have associated in definition 1.…”

Section: B Impact Of Mse In Ee Gainmentioning

confidence: 99%

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Relevance of Energy Efficiency Gain in Massive MIMO Wireless Network

Alzahrani¹,

Thayananthan²,

Qureshi³

2017

ijacsa

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Abstract-The massive MIMO and energy efficiency (EE) analysis for the next generation technology are the hottest topics in wireless network research. This paper explains about massive MIMO wireless networks and EE for manifold channel which is an evolution massive MIMO. This research will help to design and implement a practical system of next generation network based on massive MIMO where efficient processing provides EE gain. In order to approach this research, different types of manifolds are considered with efficient techniques that depend on the rank of the channel matrix. Employing the specific manifold that helps to analyze the rate of the feedback increases not only the overall performance of the MIMO system but also the EE. We studied the convergence techniques used for optimizing quantization errors which have influences with manifold feedback. Here, we have focused on relevant areas which are very important to analyze EE gain in the future massive network. According to the selected results obtained in this research, many challenges will be possible to make useful proposals.

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Section: B Types Of Manifolds With Feedbackmentioning

confidence: 99%

Section: B Impact Of Mse In Ee Gainmentioning

confidence: 99%

Relevance of Energy Efficiency Gain in Massive MIMO Wireless Network

Alzahrani¹,

Thayananthan²,

Qureshi³

2017

ijacsa

View full text Add to dashboard Cite

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“…The Grassmann manifold G Nr,N j (C) is set of all N j -dimensional subspaces in C Nr [33]- [35]. Since each jammer and Bob have N j and N r antennas, respectively, the channel matrix from each jammer to Bob constructs an N j -dimensional subspace in C Nr .…”

Section: A Geometric Interpretations Of Jamming Channelsmentioning

confidence: 99%

“…The packing radius of Q denoted by δ p (Q) is the maximum radius of each metric ball which is non-overlapped such that [33]- [35] …”

Section: B Alignment Measure Among K Jamming Subspacesmentioning

confidence: 99%

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection: Secure DoF and Jammer Scaling Law

Lee

Choi

2014

IEEE Trans. Signal Process.

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In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of S jammers among which Bob selects K jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than KN j receive antennas, where N j is the number of jammer's transmit antenna each, and hence KN j can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals. Index TermsPhysical layer security, secure DoF, multiuser diversity, opportunistic jammer selection A part of this paper has been presented in

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“…[30], [15], whereas [30] also contains explicit constructions for packings in the (real) Grassmann manifold. In [32] a differential geometric connection (based on [16]) has been developed to construct space time (and space frequency) codes for for the coherent and non-coherent channel case. Further research [17] led to space time codes with reduced design complexity by utilizing III.5.…”

Section: Proofmentioning

confidence: 99%

Geometrical Relations Between Space–Time Block Code Designs and Complexity Reduction

Henkel¹

2006

IEEE Trans. Inform. Theory

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Abstract-In this work, the geometric relation between space time block code design for the coherent channel and its noncoherent counterpart is exploited to get an analogue of the information theoretic inequality I(X; S) ≤ I((X, H); S) in terms of diversity. It provides a lower bound on the performance of non-coherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced sub tasks. Moreover a geometrical criterion for high performance space time code design is derived.

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Sphere-packing bounds in the Grassmann and Stiefel manifolds

Cited by 76 publications

References 16 publications

Relevance of Energy Efficiency Gain in Massive MIMO Wireless Network

Relevance of Energy Efficiency Gain in Massive MIMO Wireless Network

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection: Secure DoF and Jammer Scaling Law

Geometrical Relations Between Space–Time Block Code Designs and Complexity Reduction

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